Documentation: A CCG Implementation for the LKB John Beavers Center for the Study of Language and Information Stanford University
[email protected] DRAFT - April 8, 2003
The bulk of this work was done at the University of Edinburgh, with the support of The StanfordEdinburgh Link Grant #2KBA905 and the Linguistic Grammars Online (LinGO) project at the Center for the Study of Language and Information (CSLI) at Stanford University. I'd like to thank Jason Baldridge, Tim Baldwin, Colin Bannard, Chris Callison-Burch, Ann Copestake, Dan Flickinger, Julia Hockenmaier, Geert-Jan Kruij , Ivan Sag, Mark Steedman, Maarika Traat, Aline Villavicencio, and Michael White for all of their comments, suggestions, and help in developing this system. I'd like to especially acknowledge Ann Copestake and Aline Villavicencio's earlier CCG LKB implementation as an immediate ancestor and in uence on this one even if the two diverge signi cantly. Of course, any mistakes or omissions are purely my own.
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Contents
1 Introduction 2 Background
2.1 Combinatory Categorial Grammar . . . . . . . . . . . . . . . . . . . . . . . 2.2 Typed Feature Structures and the LKB . . . . . . . . . . . . . . . . . . . .
3 Architecture of the Grammar
3.1 Representation . . . . . . . . . . . . . . . . . . 3.1.1 Category Representation in the Lexicon 3.1.2 Feature Representation . . . . . . . . . 3.1.3 Semantic Representation . . . . . . . . . 3.2 The Lexicon . . . . . . . . . . . . . . . . . . . . 3.3 Lexical Rules . . . . . . . . . . . . . . . . . . . 3.3.1 Organization of Lexical Rules . . . . . . 3.3.2 In ectional Rules . . . . . . . . . . . . . 3.3.3 Lexical Mapping Rules . . . . . . . . . . 3.3.4 Curry . . . . . . . . . . . . . . . . . . . 3.4 Syntax . . . . . . . . . . . . . . . . . . . . . . . 3.5 Summary . . . . . . . . . . . . . . . . . . . . .
4 Various Syntactic Analyses
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4.1 Coordination . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 General Coordination . . . . . . . . . . . . . . . 4.1.2 S and Nominal (Non-Type-Raised) Coordination 4.1.3 Type-Raised Coordination . . . . . . . . . . . . . 4.2 Control . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Control Hierarchy . . . . . . . . . . . . . . . . . 4.2.2 Auxiliaries . . . . . . . . . . . . . . . . . . . . . 4.2.3 Equi and Raising . . . . . . . . . . . . . . . . . . 4.3 Unbounded Dependencies . . . . . . . . . . . . . . . . . 4.3.1 Topicalization . . . . . . . . . . . . . . . . . . . . 4.3.2 Right Node Raising . . . . . . . . . . . . . . . . 4.3.3 Relative Clauses . . . . . . . . . . . . . . . . . . 4.3.4 Extraction Asymmetries . . . . . . . . . . . . . . 4.3.5 Parasitic Gaps . . . . . . . . . . . . . . . . . . . 4.3.6 Tough -Movement . . . . . . . . . . . . . . . . . . 4.4 More Analyses . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 Passive . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 Imperatives . . . . . . . . . . . . . . . . . . . . . 4.4.3 Bare Plurals/Mass Nouns . . . . . . . . . . . . . 4.4.4 Dative Shift . . . . . . . . . . . . . . . . . . . . . 4.4.5 Extraposition . . . . . . . . . . . . . . . . . . . . 4.4.6 Auxiliaries and the NICE Properties . . . . . . . 4.4.7 Predicatives . . . . . . . . . . . . . . . . . . . . . 2
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57 57 57 58 60 64 64 64 66 69 69 71 73 76 78 81 82 82 85 86 87 88 89 94
4.4.8 Expletive Subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.9 There -Insertion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 Eciency A Summary of Coverage B Miscellanea
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99 103 105
B.1 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 B.2 Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 B.3 Parse Node Labels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
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1 Introduction This paper serves as documentation to a uni cation-based implementation of a Combinatory Categorial Grammar (CCG) of the fragment of English described in Sag and Wasow (1999). The implementation of this grammar was done in the Type Description Language (TDL) using the Linguistic Knowledge Building (LKB) grammar development system, both of which were developed by Ann Copestake, John Carroll, Rob Malouf, Stephan Oepen, and others (Copestake, 2002). The LKB was designed as a tool for the development of any typed, feature-based, uni cation grammar, regardless of the underlying theory, However, much work in the LKB has been in Head-driven Phrase Structure Grammars (HPSG), as outlined in Pollard and Sag (1994), including the English Resource Grammar (ERG), a wide coverage TDL grammar of English (see (Copestake and Flickinger, 2000)). One of the purposes of the CCG implementation described here is to develop a testbed for developing CCG grammars in the same framework.1 The Sag and Wasow grammar was based heavily on recent work in HPSG, covering a wide variety of syntactic phenomenon in an introductory way. In tandem with the writing of the book, an LKB implementation of this HPSG grammar was developed by Scott Gu rey and Chris Callison-Burch at Stanford University. A second purpose of this CCG implementation is to compare HPSG and CCG grammars with overlapping coverage. Although the HPSG implementation was a more straightforward encoding of the Sag and Wasow grammar, the CCG implementation has naturally taken on quite a di erent form from the grammar outlined in the book, but the primary goal was to maintain as much similarity as possible, while still maintaining as clean a CCG approach as possible. For the CCG analyses and representation, my primary sources were Steedman (1996, 2000b), although various analyses and general design ideas were borrowed from Baldridge (2002), Carpenter (1992), Hockenmaier et al. (2001), Villavicencio (2001). Although I will motivate the assumptions about the organization of this grammar, in general this paper is only documentation for this implementation and is intended to be treated as reference. For a shorter, more theoretically-oriented discussion of some of the asumptions underlying this implementation, see Beavers (in progress).
2 Background Before outlining the details of this implementation, I'll brie y review some basic background information for both CCG and typed-feature structure grammars.
2.1 Combinatory Categorial Grammar
In this section I will outline the necessary background information for the type of CCG implemented here, largely culled from Steedman (1996, 2000b), although some ideas concerning the usefulness of modalities in CCG were taken from Baldridge (2002, p.c.) and
1 At least one previous CCG implementation has been done in the LKB, rst by Ann Copestake and then by Aline Villavicencio (cf. Villavicencio (2001)), which served as a basis for the implementation presented here, although the particular type of categorial grammar and the particular representation chosen in each of these grammars are substantially di erent enough to warrant building this implementation from the ground up.
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Kruij (2001). It is not my intention to give an introduction or history to CCG. For good short introductions to CCG, see Steedman (1998, 2000a). The basic tenant of categorial grammar is that the combinatoric properties of expressions are captured in terms of the categories assigned to them rather than phrase structure rules Ajdukiewicz (1935), Bar-Hillel (1953). For instance, a transitive verb such as eat may be assigned the category in (1a), and NPs Kim and pizza as in (1b,c). (1)
(a) eats := (SnNP)/NP : xy[eats0 (x; y)] (b) Kim := NP : kim0 (c) pizza := NP : apples0
This notation is usually referred to as a \result-left" notation, and de nes eats as a curried function that takes an NP argument to its right (indicated by / de ning a rightward argument and NP de ning the category of the argument), producing the result (SnNP) (written to the left of the /). This result is itself a function (a verb phrase) taking a single NP argument to its left (indicated by the n de ning a leftward argument), producing the result S (a sentence).2 Kim and pizza are simply assigned non-function categories NP. I will sometimes refer to function categories as \complex" categories and non-function categories as \atomic" categories. The \:" operator separates the syntactic information on the left and the semantic information on the right of a category. The semantics is represented via a -calculus expression for expository purposes, although I will ultimately adopt a di erent semantic representation.3 The most basic form of combination is that of functional application, of which there are two types, forward and backward application, de ned in (2a) and (2b) respectively4 : (2) Functional Application (a) X/Y : x:f (x) Y : y ) X : f (y) (b) Y : y XnY : x:f (x) ) X : f (y) The rule in (2a) says something of category X/Y may apply to an argument of category Y to its right to yield a result of category X, and (2b) that something of category XnY may apply to an argument of category Y to its left to yield a category of type X. Taken together these two rules de ne a very general context-free grammar. The verb eats above, with two NPs Kim and pizza, may produce a derivation as in (3).5 2 Note that slashes are left-associative, i.e. everything to the left of a slash is the result, indicated explicitly in (1) by parenthesis, which I may sometimes drop except for clarity's sake. 3 The -calculus notation is itself just a shorthand for a more basic uni cation based semantic representation, the details of which are irrelevant here (see (Steedman, 1996)). 4 For ease of reading I will always write the semantic results of combinatory operations with the appropriate -reductions. 5 I will write all derivations in terms of trees, breaking tradition with almost all work in CCG that instead writes derivations bottom-down using annotated underlines to indicate the arguments, type, and directionality of combination. My reason for this is simply that the LKB only to produces trees so for consistency I will use this representation everywhere, annotating the type and direction of combination next to the category. Except for (3), I will not write the semantics in derivations both for ease of reading and because the semantic representation of this implementation di ers considerably.
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S : eats0(pizza0; Kim0) ()
NP : Kim' Kim
(SnNP)/NP : xy[eats0 (x; y)]
NP : pizza'
eats
pizza
This tree is the result of one forward application and one backward application. Sometimes it is useful to assume that these categories also contain morphological features such as verb form and agreement, as well as syntactic features such as predicativity. These can be written as subscripts on categories, for instance that Kim is third person singular can be encoded by assigning it category NP3sg , and that eats is a nite verb wanting a third person singular argument as (Sfin nNP3sg )/NP. Following Baldridge (2002), I will assume that the farthest left-most category has special status as the \root" of the category, the ultimate result of all applications, and that complex categories have the morphological and syntactic features of their roots, an assumption that will prove useful later in the implementation. Turning next to coordination, following Steedman (1996), I assume coordination is a meta-rule over categories, where X represents a variable over any category: (4) Coordination (n ) X : g CONJ : b X : f
)n
X : :::b(f:::)(g:::)
The superscript n indicates that this meta-rule is also schematized over the many possible valences of X with appropriate realizations of the -abstraction in the semantics.6 This coordination schema allows for coordination as in the following: (5)
S ()
NP Kim
SnNP/NP (2 )
NP
SnNP/NP
CONJ
SnNP/NP
cooked
and
ate
pizza
To expand the expressive power of the grammar it is necessary to introduce a small number of combinators that may also combine categories. Steedman de nes two types of composition rules, forward and backward composition: (6) Composition (B) (a) X/Y : f Y/Z : g ) X/Z : x:f (g(x)) (b) YnZ : g XnY : f ) XnZ : x:f (g(x)) 6 An alternative approach to coordination, following Baldridge (2002), is to assign an appropriate category
to coordinators (such as XnX/X) and eliminating the rule schemas in favor of multiple coordinators.
6
The utility of composition can be seen in coordination of transitive verbs when one has an adverbial modi er. (7)
S ()
NP SnNP/NP (2 )
Kim
SnNP/NP
CONJ
cooked
and
NP SnNP/NP (>B)
pizza
(SnNP)/(SnNP)
(SnNP)/NP
suddenly
ate
Without composition this derivation could not proceed since there would be no elements to coordinate. This composition rule also requires some schematization for functions of di erent valences, at least for forward composition: (8) Generalized forward composition (Bn >) X/Y : f Y/Z/$1 : :::z:g(z:::) ) X/Z$1 : :::z:f (g(z:::)) This rule involves use of the \$-convention", another form of schematization, where /$ is a variable over rightward arguments (and n$ over leftward arguments if necessary), and $ a variable over arguments of arbitrary directionality.7 A second useful operation is that of type-raising, which plays a signi cant role in the CCG account of unbound dependencies. Type-raising takes the following form: (9) Type raising (T) (a) X : a ) T/(TnX) : f:f (a) (b) X : a ) Tn(T/X) : f:f (a) Here X is a variable over categories restricted to argument types (which can be virtually anything including NP, PP, VP) and T is a variable over categories. With type-raising we can account for such unbound dependencies as right node raising: 7 The j symbol also represents arbitrary valence, for instance some VP adverbs may occur post and pre-VP
and have category (SnNP)j(SnNP)).
7
(10)
S (>) NP
S/NP (1 ) S/NP (>B)
S/NP (>B)
CONJ
S/(SnNP) (
LAST 3
Here the list C starts where the list A starts, ends where B ends, and the end of A is now coidenti ed with the beginning of B , so C is e ectively the append of A and B . This is a cute method of doing arbitrary length list-appends via simple uni cation, but di erence lists are peculiar creatures and do not have good functionality or reliability (for instance, no random access, you can't access the last element on a list without some trickery, you can't shrink di -lists easily, etc.) In this grammar I have striven to avoid using di -lists as much as possible, and when used they are used only for monotonically growing appended lists. I should point out one very major complication with di -lists that does appear in this grammar in multiple places and sometimes forces particular design decisions. With di -lists it is impossible to state a default constraint that a certain di -list is non-empty and then later override and say it's empty. For instance, if you state the constraint in (24a), override it as in (24b), the result you get is the utterly unintended one in (24c) rather than a simply empty list: (a) 2type1 (24)
:= 3 #3 " 2 FIRST pred1 6 LIST 77 6RESTR /l 6 REST 1 57 4 5 4
(c)
(b) "type2 RESTR
"
:=
LIST LAST 1 1
type1
##
&
LAST 1
2 2 h i33 1 FIRST pred1 LIST 55 4RESTR 4
LAST 1
The reason for this is simply that the default uni cation attempts to rectify the original constraint with the overriding constraint, with the result that it ditches the uni cation in (18a), replaces it with the uni cation in (18b), but keeps the list, resulting in (24c). This nuisance is unavoidable and has forced certain design decisions in this grammar, and the reader should be aware of it. One nal note about feature structure types: the LKB makes a distinction between types and instances of types. In particular, items designated as lexical items, lexical rules, in ectional rules, and grammatical rules are all considered instances of items in the type hierarchy, even though they may introduce constraints in the same way. All mother types of these instances are, however, types. The only practical di erences are that the LKB will not display instances of types in type hierarchies when viewed, and that (for some obscure eciency reason) instances may not have multiple mothers. Therefore if a rule could be encoded as a uni cation of the constraints of two types, a third type that inherits from these two must be created rst and then the rule is an instance of this, and this approach will be seen occasionally in this grammar. Otherwise, the distinction isn't very relevant except 13
notationally, and in this document I will often distinguish between the two by encoding types as entities with inheritence and instances simply as feature structures of a certain type. Sometimes it will be useful to treat an instance as a type for expository purposes, and I'll note when I'm doing this explicitly.
3 Architecture of the Grammar In this section I will outline the architecture of the grammar, including the representation employed at the syntactic, semantic, and lexical levels and the feature geometry used to encode them. As stated before, the implementation was designed to be as pure a CCG grammar as possible but incorporating the representational schema of Sag and Wasow (1999). In particular, much of the structure of the lexicon for this grammar was based almost entirely on the lexicon in Sag and Wasow, taking advantage of the inheritence hierarchy of typed-feature structures, something rarely assumed in the CCG literature. x3.1 covers the overall representation schema I employ, and in x3.1.1, x3.1.2, and x3.1.3 I'll discusses how categories, morphosyntactic features, and semantics are encoded. In x3.2 I'll discuss the organization of the lexicon, and in x3.3 I'll discuss lexical rules, both mapping and in ectional. In x3.4 I'll discuss how the basic syntactic operators are encoded.
3.1 Representation
The top level feature structure type relevant to the syntax and lexicon is that of sign, following the nal chapter of Sag and Wasow (1999) and much literature on HPSG (cf. Pollard and Sag (1994), Ginzburg and Sag (2000)). Theoretically, a sign represents a matching of form and syntatic/semantic information, and all lexemes, words, and phrases are signs. The type sign is (for the moment) de ned to consist of three features: (25) 2sign := feat-struct &
3
ORTH *di -list-of-strings* 4SS synsem 5 DTRS list-of-signs
The feature ORTH corresponds to the orthography of a given linguistic unit and is of type *di -list-of-strings*. The feature SS represents the syntatic and semantic information associated with the sign. The nal feature, DTRS, is a list of the sign s that are the daughters of the application of a syntatic or lexical rule. The relevant type hierarchy for sign s is: (26)
feat-struct sign lex-item
lexeme
expression word
...
...
phrase
Type lex-item is a type for signs that are lexical, i.e. participate in lexical rules and the lexical hierarchy, namely word and lexeme. The type expression is the supertype of all 14
signs that may participate in the sytnax, i.e., be the daughters or mother of a syntactic rule. In this case, only word s and phrase s are syntactic. The most important feature of sign s is SS, of the type synsem. Things of type synsem represents the category and semantic information of a linguistic unit. A synsem is a feature structure with the following features: (27) 2synsem := feat-struct & 3 ROOT root-struct 4CAT category 5 SEM sem-struct
The feature SEM corresponds to the semantic information, the feature ROOT represents the root category as well as the morphological/syntactic features assigned to that category, and the feature CAT corresponds to the category information. I'll discuss the related type hierarchies and features structures for these features in the following sections before outlining the lexical hierarchy.
3.1.1 Category Representation in the Lexicon The type category has two subtypes, complex-category and basic-category : (28)
feat-struct category basic-category s
complex-category
nominal n
...
conj arg-category
pp
np
CCG literature generally assumes that basic categories are atomic types such as S, NP, N, CONJ, etc., represented here as subyptes of basic-category. However, certain relationships hold between some of these basic categories, for instance that PPs and NPs may type-raise but not Ns, and the type hierarchy here re ects groups of basic categories that some operations make reference to. Complex categories represent functions, and feature structures of type complex-category have two features, RESULT and ACTIVE, corresponding to the result of a functional application by that category (something to the left of a slash) and the arguments that that function takes: (29) complex-category := category & RESULT category ACTIVE list-of-arguments
It is necessary to have some representation of arguments, encoding both syntactic and semantic information as well as slash information. I therefore de ne a type argument consisting of two features: 15
(30) argument := feat-struct & ARG synsem SLASH slash-struct
The feature ARG represents the argument's category, and is typed as a synsem, thus giving access to the syntactic, semantic, and feature information of the argument to the complex category.12 The second feature is the SLASH feature, typed as a slash-struct :
(31) slash-struct := feat-struct & DIR direction
MODALITY modality
DIR captures slash directionality and MODALITY captures headedness directionality, with subtypes forw(ard) and back(ward) for direction and head-l(eft) and head-r(right) for modality. For convenience, I'll assume a hierarchy of slash structures to capture all four possibilities: (32)
slash-struct mod-slash
hd-slash forw-hd-slash
back-hd-slash forw-mod-slash back-mod-slash
The following constraints are appropriate for these types: (33) (a) forw-hd-slash (/ ) := slash-struct & DIR forw
MODALITY head-l (b) back-hd-slash (n ) := slash-struct & DIR back MODALITY head-r (c) forw-mod-slash (/ ) := slash-struct & DIR forw MODALITY head-r (d) back-mod-slash (n ) := slash-struct & DIR back MODALITY head-l
These four types exhaust the possibilities of slash and head directionality, and hd-slash and mod-slash allow underspeci cation of the directionalities while capturing whether there is a mismatch between the slash and head directionality. Putting all of this information together, a single argument of an intransitive verb of category Sn NP can be represented as: (34) 2argument
4ARG j CAT np SLASH back-hd-slash
3 5
12 Note that ARG is not typed as a sign, however, following standard HPSG practice, as it is assumed that
argument selection is local and thus not based on constituent structure of the argument (i.e. the DTRS list) and is not based on orthography (i.e. the ORTH feature).
16
From here on out, I will employ abbrieviations where appropriate for representing arguments on an ACTIVE list, by using the standard notation of a slash, modality, and category label (e.g. n NP or / (Sn NP)). In every case these abbrieviations should be assumed to be shorthand for feature structures, for instance that the label n NP is a shorthand for the structure in (34). Complex categories themselves take on two forms in this implementation, depending on whether the representation is lexical or syntactic, in order to facilitate the encoding of lexical generalizations and syntactic rules.13 In the lexicon (i.e. the lexical hierarchy and output of lexical rules), complex categories are represented as at structures, where the result is a basic category and the arguments are stored in a single ACTIVE list, as in the encoding for a ditransitive verb category as in (35): (35) (a) ((SnNP)/NP)/NP 2 (b) complex-category 6 6RESULT Ds 4
ACTIVE nNP, /NP, /NP
3 7 E7 5
Here, ACTIVE is essentially equivalent to ARG-ST in the Sag and Wasow grammar. This representation is useful for de ning lexical generalizations (such as assignment of nominative case by nite in ection, commonalities in valence between related category types, relationships between linking properties, etc.).14 However, a second representation of complex categories is employed in the syntax, where the curried, left-associative nature of categories is represented via embedding, as for the ditransitive verb category in (36): (36) (a) ((SnNP)/NP)/NP 2 (b) complex-category 2
3 3 2 37 6 6 RESULT sD E 7 6 7 6 57 6 7 RESULT 4 6 7 6 7 ACTIVE n NP 7 RESULT 6 6 6 77 6 D E 4 57 6 7 6 7 ACTIVE /NP 6 7 D E 4 5
ACTIVE /NP
This feature structure is useful for de ning syntactic rules as in x2.1, where active arguments are the least embedded ones and results (to the left of the slashes) are the corresponding RESULT values. To convert between representations such as (35) and (36) it is necessary to de ne a special lexical rule, which I will describe in x3.3.4. The reason for this split is that embedded representations in the LKB do not lend themselves to capturing certain types of linguistic generalizations, primarily because it is impossible to state 13 This approach was suggested to me by Ann Copestake. 14 Note, however, that the order of arguments of the result-left notation is preserved in the feature structure
representation, meaning that the list of elemetns on ACTIVE is di erent than the list of elements on ARGST, since the arguments here occur right to left in the order they combine with the head (for instance, the second argument on ACTIVE in (35) is the second object of the ditransitive verb, whereas the second argument on ARG-ST is the rst object of the ditransitive).
17
constraints on arbitrarily embedded feature structures in the LKB, something that is at least somewhat statable in terms of lists. However, embedded structures do allow for a very clean and intuitive statement of CCG combinators, something that lists are not as useful for since the list manipulation tools in the LKB are rather limited.15 For the remainder of the discussion of the lexicon, I will assume the complex category representation as in (35).
3.1.2 Feature Representation
In this section I'll outline the feature types corresponding to root morphological and syntactic features. These are encoded in the ROOT feature of synsem s, which has the following features: (37) root-struct := feat-struct & RCAT basic-category FEATS features
The feature RCAT corresponds to the root of the category described by CAT, always a basic-category, and the FEATS feature corresponds to relevant features for that category. Corresponding to the basic category type hierarchy is a related hierarchy of features, as mentioned above for the ROOT feature. The feature hierarchy preserves the essence of the basic category hierarchy but is independent of it:16 (38) feat-struct features s-features comp-features
...
nominal-features pp-features
noun-features
The following features are appropriate for each of these types: (39) (a) features := feat-struct & FORM form-cat PRED boolean (b) s-features := features & FORM vform AUX boolean (c) nominal-features := features & 2CASE case 3 6 6ANA boolean7 7 4AGR agr-cat 5 LEX boolean
15 These are primarily issues with the LKB. Theoretically, it would not be dicult to have a type description
language that did allow constraints on arbitrarily embedded feature structures or a rich list manipulation toolkit. 16 An alternative proposal would be to assign these features to the atomic categories given above, very similar to the HEAD feature in HPSG. However, the approach employed here, where atomic categories and features are represented by di erent feature structures, certain problems in dealing with coordination arise, namely that often two coordinated elements must share the same category but not the same features. This is a currently a problem for HPSG (and the treatment of coordination in Sag and Wasow (1999)). In the approach assumed here, category equivalence can be expressed independent of feature equivalence. This issue will be addressed later in a separate discussion of coordination.
18
h
i
(d) pp-features := nominal-features & FORM pform h i (e) noun-features := nominal-features & FORM nform All feature structures have FORM and PRED(ICATIVE) values. The FORM value will be further speci ed depending on the category, and the PRED value corresponds to whether a certain category is predicative or not (following Sag and Wasow (1999)). The type s-features further speci es FORM to be of type vform, subtypes of which include n(ite), p(a)s(t-)p(articiple) , inf(initive), etc., and also declares appropriate a boolean value AUX (true for auxiliary verbs and false for non-auxiliary verbs). Features appropriate for type nominal-features include CASE for case, AGR for person, number, and gender agreement features, ANA for indicating whether a nominal element is anaphoric or not17 , and a feature LEX that corresponds to whether a certain category has been lexically instantiated or not, which is necessary for the treatment of certain subject/object extraction asymetries as discussed by Steedman (1996)18 . The subtypes of nominal-features, pp-features and nounfeatures each have further speci ed FORM values corresponding to their categories, namely pform and nform respectively. Type pform is used for distinguishing di erent prepositions types (such as f to, f on, f with, etc.), and nform distinguishes nouns from prepositions. The last subtype of features, comp-features, inherits from both s-features and nominalfeatures and represents the feature information for complementizers and CPs, which are encoded here as NPs but with verbal features. One notational note regarding features: I will sometimes omit full feature paths when clear from context (e.g. NP[CASE nom] for an NP with feature [ ARG j ROOT j FEATS j CASE nom]).
3.1.3 Semantic Representation In this section I'll discuss the semantic representation implemented here, encoded in the SEM feature of synsem s. Rather than the typical -calculus semantics, I will instead adopt a form of at semantics known as Minimal Recursion Semantics (MRS), as outlined in Copestake et al. (1999). In MRS there are no embeddings and no level of predicate argument structure. Rather, all predicates are stores in a list, and relationships between scopal objects and their restrictions and bodies are represented via handles. MRS provides several advantages to this implementation over a more standard predicate logic approach. First and foremost, MRS was developed with typed-feature structures in mind and therefore is compatible with the limitations of the LKB (in particular, the lack of feature structure embedding of a more straightforward predicate logic approach is a bonus since it is dicult in the LKB to state constraints on arbitrarily embedded feature structures, and also certain predicate-logic operations such as -extractions are dicult or impossible to encode straightforwardly in the LKB). Second, the LKB has speci c tools available for viewing and testing MRS structures, making development signi cantly easier. Third, the LKB also has an MRS-based generator built into it, so that any grammar that builds some form of MRS structure can potentially generate. Finally, the HPSG grammar of Sag and Wasow assumes a form of MRS semantics, as does the current LKB implementation of that grammar, and 17 This feature currently is not used in this implementation. 18 This feature is also sometimes denoted as ANT for \antecedent-governed" followed the Government and
Binding approach to certain extraction phenomenon.
19
one goal of this project has been to maintain as much semantic similarity as possible with the HPSG grammar in the hopes of maintaining compatibility. The speci c MRS semantics I will adopt here closely parallels their approach, particularly in that it does not deal with scopal relations in that I will use a at representation for predicates but I will not have a representation for handles and handle constraints. Following Sag and Wasow, I will posit the structure a sem-struct in each synsem repeated here as (40): 3 (40) sem-struct := feat-struct & 2MODE mode-cat 6 7 6KEY pred 7 4INDEX index 5 RESTR *di -list-of-preds*
The MODE feature represents the semantic type of the element, and has values ref(erential) for referential nominal objects, prop(ositional) for propositional objects (such as XPs projected by nite verbs), dir(ective) for imperatives, and ques(tion) for questions. INDEX is the index of any given lexical item or phrase. I will assume that all lexical items introduce indices, referential indices (type ref-index ) for referential elements and situation (event) indices (type sit-index ) for verbal elements.19 One notational note about indices: I will often use subscripts to represent the INDEX values of arguments on an ACTIVE list (e.g. NPi for an NP argument with feature [ ARG j SEM j INDEX i ]). The feature KEY is, informally, the \main" predicate associated with a lexical item (e.g. r dog for dog ), and is useful primarily for bookkeeping purposes. Finally, RESTR is the at list of predicates associated with any element. A predicate will be represented by a feature structure as de ned in (41): (41) pred := feat-struct & RELN reln SIT sit-index
All predicates will have a predicate name denoted in the feature RELN of type reln (subtypes of which will include speci c predicate names like r walk, r dog, r quickly, etc.), and a situation variable feature SIT. Various subtypes of pred instantiate various argument roles. For purposes of this grammar I will assume a very bleached argument naming sysem, with subtypes of pred adding additional features such as ARG1, ARG2, ARG3, etc. for referential arguments, and ARG-S for situational arguments. The predicate associated with a transitive verb like eat will be as in (42a), and the predicate for an adverb like probably as in (42b): (42) (a) 2RELN r eat 3 (b)
7 6 6SIT sit-index 7 4ARG1 ref-index5 ARG2 ref-index 3 2 RELN r probably 4SIT sit-index 5 ARG-S sit-index
19 Following Sag and Wasow, I will also assume that expletives have a unique index value, and assign them
indices of type dummy-index.
20
Although this di ers somewhat from the Sag and Wasow textbook, who posit very explicit role names for each predicate's argument (such as LOVED for the second argument of love ) it does, however, mirror the approach in the HPSG implementation, although they use slightly less bleached role names (such as ACT(OR), UND(ERGOER), etc.). In general the structure of these predicates is very straightforward and I will not discuss them much here unless necessary for certain expository purposes. How the di erent pieces of the sem-struct are tied together is dependent on the architecture of the lexical and syntactic components of the grammar, which I will turn to next.
3.2 The Lexicon
In this section I will discuss the structure of the lexicon in this implementation and the speci cs of the lexical representation. All lexeme types will have CAT values that are complex categories consisting of a basic-category RESULT value (the root of the category) and a (possibly empty) list of arguments on ACTIVE, re ected in appropriate constraints on the type lexeme : #33 " 2 FEATS j PRED /l false 6 ROOT 77 6 RCAT 1 SS 6 57 4 7 6 6 CAT j RESULT 1 basic-category 7 5 4 NEEDS-AFFIX boolean
(43) lexeme := lex-item & 2
The [ PRED false ] constraint defaults all lexemes to be non-predicative.20 The feature NEEDS-AFFIX is appropriate for lexemes as part of how the LKB handles morphology, as discussed in x2.2. Lexemes come in two varieties, const-lxm for lexemes that do not have any in ection and in -lxm for those that do: (44)
lexeme const-lxm
in -lxm noun-lxm
verb-lxm
...
...
...
Subtypes of in -lxm include nom-lxm and verb-lxm, the maximal types of the nominal and verbal lexical hierarchies. Looking rst at the verbal hierarchy, the type verb-lxm has subtypes tv-lxm for transitive verbs and iv-lxm for intransitive verbs, each of which heads hierarchies for various subtypes of transitive and intransitive verbs:21 : 20 The
analysis for predicatives assumed here ultimately derives all predicates from non-predicates via lexical rules. 21 This is not the complete verbal hierarchy, as it will ultimately be expanded in the treatment of raising and control verbs adopted here, but this will be discussed in x4.2.
21
(45)
verb-lxm ...
tv-lxm stv-lxm
ptv-lxm
iv-lxm
dtv-lxm cptv-lxm siv-lxm
piv-lxm
v-lxm
cpiv-lxm cppiv-lxm
The type verb-lxm introduces one argument as well as general properties of all verbs: 2 33 " # s-features 6 6 7 7 ROOT j FEATS 6 6 7 7 AUX /l false 6 6 7 2 377 6 6 7 6 7 7 RESULT s SS 6 6 6 7 # +777 *" 6 6 6 777 6 6CAT 6 7 4ACTIVE n CAT np 4 4 , ... 555 PRED false
(46) verb-lxm := in -lxm & 2
These constraints say that all verbs are rooted in s, are by default non-auxiliary (something that will be overridden for auxiliaries) and have at least one non-predicative argument that must precede it (i.e. the subject) it (and thus are category SnNP$). The subtypes iv-lxm and tv-lxm introduce the following constraints:22 33 2 D E CAT j ACTIVE [] , ... 7 6 6 37 2 7 7 6 6 7 7 6 6 INDEX s 7 7 6 6 7 6 SS 6 7 7 6 KEY 1 7 6 7 6 6 SEM 777 6 7 6 6 h i 4 4 4 RESTR ! 1 SIT s ! 555
(47) (a) iv-lxm := verb-lxm & 2
2 D E 33 CAT j ACTIVE [] , /[] , ... 6 6 7 37 2 6 6 7 7 6 6 7 7 INDEX s 6 6 7 7 7 6 SS 6 6 7 7 1 KEY 7 6 6 6 7 h 777 6 6SEM 6 7 i 4 4 4 RESTR ! 1 SIT s ! 555
(b) tv-lxm := verb-lxm & 2
These two types simply x some valence information, namely that all intransitive verbs have at least one argument and transitive verbs at least two, linking the INDEX to the SIT variable of the KEY predicate, which goes on the RESTR list.23 Finally, the subtypes of these veb types form leaf nodes in the type hierarchy. Looking rst at subtypes of iv-lxm, siv-lxm corresponds to strictly intransitive verbs (e.g. dine ), piv-lxm to intransitive verbs 22 From here on out I will omit some features that are not directly relevant for expository purposes for the sake of abbreviation. In particular, all direct arguments of all verbs except the copula will have the feature [ PRED false ] which I will generally omit unless necessary. 23 The linking information, that the indices are coidenti ed with the situation arguments of the predicates, appears to be redundant and could be expressed on the type verb-lxm instead, but the ultimate treatment of auxiliaries with null semantics requires that no semantic restrictions be placed on the RESTR values of the type verb-lxm. Furthermore, I'll in general not note the KEY predicate constraint when stated since it will be similar for all contentful lexemes.
22
taking PP complements (e.g. speak as in Kim spoke to Sandy ), v-lxm to intransitives taking CP complements (e.g. think ), cpiv-lxm to intransitives taking CP subjects (e.g. suck as in That Cleveland lost the series sucks ), and cppiv-lxm to intransitives with CP subjects and PP complements (e.g. occur as in That Cleveland lost the series occured to Kim ). The following constraints are appropriate for these types: 33 2 D E CAT j ACTIVE [] i 77 6 6 " 7 6 6 h i #7 77 6SS 6 4 4SEM RESTR ! ARG1 i ! 55
(48) (a) siv-lxm := iv-lxm & 2
2 D E 33 CAT j ACTIVE [] , /PP i j 6 6 77 2 6 6 7 * " # +37 6 6 7 7 ARG1 i 6SS 6 7 4 5 4 4SEM RESTR ! 5 ! 57 ARG2 j 2 " #+33 * v-lxm := iv-lxm & 2 FORM n 7 6 7 6 CAT j ACTIVE []i , /NPt 7 6 7 6 SEM j MODE prop 7 6 7 6 7 6 7 3 2 SS 6 7 6 # + * " 7 6 6 77 ARG1 i 6 6 57 5 4 4SEM 4RESTR ! ARG-S t ! 5 2 * " #+33 cpiv-lxm := iv-lxm & 2 FORM n 6 6 77 CAT j ACTIVE NPt 6 6 SEM j MODE prop 7777 6 6 6 7 SS 6 7 " 6 h 77 i # 6 6 57 4 4SEM RESTR ! ARG-S t ! 5
(b) piv-lxm := iv-lxm & 2
(c)
(d)
(e) cppiv-lxm := iv-lxm &
2 2 * " # +33 FORM n 7 6 6 CAT j ACTIVE NPt , /PPi 7 7 6 6 7 SEM j MODE prop 7 6 6 7 7 6 7 3 2 SS 6 7 6 # + * " 6 7 6 77 ARG1 i 6 6 57 5 4 4SEM 4RESTR ! ARG-S t ! 5
Turning next to subtypes of tv-lxm, the subtypes include stv-lxm for strictly transitive verbs (e.g. write ), dtv-lxm for ditransitives (e.g. give ), ptv-lxm for transitives with additional PP complements (e.g. put ), and cptv-lxm for transitive verbs with CP subjects (e.g. annoy as in That Cleveland lost the series annoyed Kim ). The following constraints are appropriate for these types: 2 h i 33 CAT j ACTIVE []i , NPj CASE acc 77 6 6 7 7 6 6 2 7 7 6 6 # +3 * " SS 6 7 7 6 ARG1 i 7 7 6 6 55 4 4SEM 4RESTR ! ! 5 ARG2 j
(49) (a) stv-lxm := tv-lxm & 2
23
2 h i 33 h i CAT j ACTIVE []i , NPk CASE acc , /NPj CASE acc 77 6 6 6 6 7 7 2 6 6 7 7 2 3 +3 6 6 7 7 * ARG1 i SS 6 6 7 7 6 7 6 6 7 7 6 7 7 6 6SEM 6 7 7 ARG2 j RESTR ! ! 4 5 4 5 4 4 55 ARG3 k
(b) dtv-lxm := tv-lxm & 2
2 h i 33 CAT j ACTIVE []i , PPk , /NPj CASE acc 77 6 6 7 7 6 6 2 7 7 6 6 3 +3 2 7 7 6 6 * ARG1 i SS 6 7 7 6 7 6 7 7 6 6 7 6 7 7 7 6 6SEM 6 4RESTR ! 4ARG2 j 5! 5 55 4 4 ARG3 k
(c) ptv-lxm := tv-lxm & 2
(d) 2cptv-lxm := tv-lxm &
2 +33 # * " h i FORM n 7 6 6 , NPi CASE acc 7 CAT j ACTIVE NPt 7 6 7 6 SEM j MODE prop 7 6 7 6 7 6 7 3 2 SS 6 7 6 # + * " 7 6 6 77 ARG1 i 6 6 5 4 57 5 4 4SEM RESTR ! ARG-S t !
There are two noteworthy points here. First, slash and category information isn't stated on the subjects of these types as this is inherited from the supertype verb-lxm. Second, in each type the linking information is explicitely stated, some of which might seem a bit redundant, but given the various di erent argument structures these types represent it is unlikely that creating new supertypes to capture linking generalizations will be worth the computational costs. With most of the information about each lexical entry inherited from the type hierarchy, the actual lexical entries are usually as simple as specifying the orthography and predicate relation name, and sometimes idiosyncratic selectional restrictions on certain arguments (for instance [ FORM f to ] for some PP taking verbs). Example entries of each of the above types are given in (50): 2 E 6 6 ORTH ! \dine" ! 6 h 6 4
(50) (a) dine v1 := siv-lxmD
3 7 7 7 i 7 5
SS j SEM j RESTR ! RELN r dine !
2 3 E 6 7 6 7 ORTH ! \speak" ! 6 7 2 3 6 7 h i 6 7 6 7 CAT j ACTIVE [], FORM f to 6 7 6 7 6 7 6 7 h 7 6SS 6 7 4 4SEM j RESTR ! RELN r speak i! 55
(b) speak v1 := piv-lxmD
24
3 7 7 7 i 7 5
2 E 6 6 ORTH ! \think" ! 6 h 6 4
(c) think v1 := v-lxm D
SS j SEM j RESTR ! RELN r think !
2 E 6 6 ORTH ! \suck" ! 6 h 6 4
(d) suck v1 := cpiv-lxmD
3 7 7 7 i 7 5
SS j SEM j RESTR ! RELN r suck !
3 2 E 7 6 7 6 ORTH ! \occur" ! 7 6 3 2 7 6 i h 7 6 6 6CAT j ACTIVE [], FORM f to 77 7 6 6 6 7 h 77 7 6SS 6 i 4 4SEM j RESTR ! RELN r occur ! 55
(e) occur v1 := cppiv-lxm D
3 7 7 7 i 7 5
2 E 6 6 ORTH ! \write" ! 6 h 6 4
(f) write v1 := stv-lxmD
SS j SEM j RESTR ! RELN r write !
2 E 6 6 ORTH ! \give" ! 6 h 6 4
(g) give v1 := dtv-lxmD
3 7 7 7 i 7 5
SS j SEM j RESTR ! RELN r give !
2 3 E 6 7 6 7 ORTH ! \hand" ! 6 7 2 3 6 7 h i 6 7 6 CAT j ACTIVE [], FORM f to , [] 77 6 6 7 6 7 6 7 h 7 6SS 6 7 4 4SEM j RESTR ! RELN r hand i! 55
(h) hand v1 := ptv-lxmD
2 E 6 6 ORTH ! \annoy" ! 6 h 6 4
(i) annoy v1 := cptv-lxmD
3 7 7 7 i 7 5
SS j SEM j RESTR ! RELN r annoy !
For illustrative purposes, the fully expanded entry for give v1, showing all inherited constraints, is given in (51).
25
3 7 6 ORTH ! \give" ! 7 6 6 37 2 7 6 2 3 7 6 RCAT 1" s 7 6 # 7 6 7 6 6 7 7 6 7 ROOT s-features 6 4 5 7 6 7 6 FEATS 7 6 7 6 PRED false 7 6 7 6 7 6 3 2 7 6 7 6 7 6 RESULT 1 7 6 6 777 6 6 7 6 h i h i CAT 4 6 7 57 6 7 6 CASE acc CASE acc , /NP ACTIVE n NP , /NP 7 6 j i k 7 6 7 6 7 6 7 6 SS 6 3 2 7 7 6 7 6 MODE prop 7 6 7 6 7 6 7 6 7 6 7 6 INDEX s 7 6 7 6 7 6 3 2 7 6 7 6 7 6 7 6 7 6 SIT s 7 6 + * 7 6 7 6 7 SEM 6 6ARG1 i 7 7 6 7 6 7 6 7 6 7 6 7 6 7 6 7! 7 6RESTR ! 6 7 6 6 ARG2 j 5 4 5 4 57 5 4 4 ARG3 k
(51) 2dtv-lxmD
E
Turning now to the nominal type hierarchy, the supertype noun-lxm inherits from in lxm and has two main subtypes, np-lxm and cnoun-lxm, corresponding to things that have category NP and things that have category N$. The full type hierarchy for nominals is given in (52). (52)
lexeme const-lxm
in -lxm
noun-lxm np-lxm pn-lxm
pron-lxm
cnoun-lxm dummy-lxm
cn-lxm
...
cn-pp-lxm
Note that np-lxm also inherits from const-lxm, the supertype of all lexemes that don't show in ection, something that will be relevant later when dealing with morphology via in ectional rules. The subtypes of np-lxm include pn-lxm for proper names, pron-lxm for pronouns, and dummy-lxm for the expletives it and there. The subtypes of cnoun-lxm, the supertype of all common noun (N$) lexemes, are cn-lxm for intransitive nouns and cn-pplxm for nouns that take prepositional complements (e.g. picture as in picture of Sandy ). The constraints appropriate for these types are given in (53).
26
2 2 2 333 noun-features 6 7 6 7 6 6 7 AGR j PER /l 3rd7 6 7 6 7 6 7 6 7 6 7 6 COUNT /l true 777 6 6 6 7 6 7 ROOT j FEATS 6 7 6 7 6 7 ANA /l false 6 7 6 7 6 7 6 7 6 7 SS 6 7 4 5 FORM /l normal 6 7 6 7 6 7 6 7 6 7 LEX true 6 7 6 7 6 7 6 77 CAT j RESULT noun 6 6 57 h i 4 4 5 SEM /l MODE ref ## " &" RESULT np
(53) (a) noun-lxm := in -lxm &
(b) np-lxm := noun-lxm
SS j CAT
(c) cnoun-lxm := noun-lxm
ACTIVE hi
33 377 7 7 7 7 7 7 7 7 77 i 7 57 RESTR ! 1 INSTANCE i ! 5 5
2 & 2CAT j RESULT n 2 6 6 6 KEY 1 6 6 6 6 6 SS 6 INDEX i 6 SEM 6 6 h 6 6 4 4 4
33 2 ROOT j AGR /l 3sg 2 377 6 6 77 6 6 INDEX i 7 6 # +77 * " 6 SS 6 7 6 6 77 name RELN r 7 7 6 6SEM 6 4KEY 1 RESTR ! 1 4 4 ! 555 INSTANCE i 2 333 & 2 2INDEX i 7 6 7 6 7 6 7 6 KEY 1 7 6 7 6 7 6 SEM SS 7 6 7 6 h i 6 4 4 557 4 1 RESTR ! INSTANCE i ! 5
(d) pn-lxm := np-lxm & 2
(e) pron-lxm := np-lxm
(f) dummy-lxm := np-lxm &
2 2 2 333 6SS 4SEM 4INDEX Ddummy-index E 557 5 4 RESTR ! !
h
i
(g) cn-lxm := cnoun-lxm & SS j CAT j ACTIVE /l hi (h) cn-pp-lxm := cnoun-lxm & 2 2CAT j ACTIVE D/PPi E
33 77 6 6 h 7 6SS 6 i 7 4 4 SEM j RESTR ! ARG i ! 55
The default constraints on the features of noun-lxm de ne nouns to be third person, nonanaphoric count nouns with referential semantics (except when explicitely overridden).24 The type np-lxm xes the valence of NPs to be empty, as well as the category type to be np. The semantic constraint on pn-lxm and pron-lxm coindexes the referential index of the nominal with the instance in the predicate, whereas for things of type dummy-lxm the index is a non-referential dummy-index and there are no semantics. For common nouns, 24 Plurals are derived via lexical rules, discussed below.
27
this semantic constraint is stated in the higher type since nothing inherits from cnoun-lxm that has empty semantics. The subtype cn-lxm has an empty active list (category N) and the subtype cn-pp-lxm has one PP on the valence list corresponding to an argument in the predicate of the noun (category N/PP). Examples of each type of lexical entry are given in (54). 2 E 6 6 ORTH ! \Kim" ! 6 h 6 4
(54) (a) kim n1 := pn-lxm D
3 7 7 7 i 7 5
SS j SEM j RESTR ! NAME \Kim" !
(b) him 1 := 2pron-lxmD
3 6 7 ORTH ! \him" ! 6 7 6 37 2 6 7 3 2 6 7 CASE"acc 6 #777 6 6 7 6 6 3sg 6 7 ROOT j FEATS 4 57 7 6 6 7 AGR 7 6 6 7 SS GEND masc 7 6 6 7 7 6 6 i h 57 4 4 5 SEM j RESTR ! RELN r male ! E
2 3 E 6 7 6 7 ORTH ! \it" ! 6 2 37 6 7 6 CASE nom 7 6 77 6SS j ROOT j FEATS 6 4AGR 3sg 57 4 5 FORM f it 2 3 dog n1 := cn-lxm D E 6 7 6 7 ORTH ! \dog" ! 6 7 h 6 7 i 4 5 SS j SEM j RESTR ! RELN r dog ! 3 2 picture n2 := cn-pp-lxm D E 7 6 7 6 ORTH ! \picture" ! 7 6 3 2 7 6 h i 7 6 7 6 CAT j ACTIVE FROM f of 7 6 7 6 7 6 6 h 77 7 6SS 6 i 4 4SEM j RESTR ! RELN r picture ! 55
(c) it 2 := dummy-lxm D
(d)
(e)
An example lexical entry with all of the inherited constraints is given in (55).
28
3 7 6 7 6 ORTH ! \picture" ! 6 37 2 7 6 3 2 7 6 RCAT 1 n 7 6 7 6 2 3 7 6 7 6 7 6 noun-features 7 6 7 6 7 6 7 6 7 6 6 7 7 6 7 6 PRED false 7 6 6 7 7 6 7 6 7 6 6 7 7 6 7 6 7 6 AGR 3sg 6 7 7 6 7 6 7 6 ROOT 6 6 7 7 6 6 7 FEATS 6COUNT true 77 77 6 7 6 6 6 7 7 6 7 6 7 6 6 7 7 6 ANA false 6 7 6 6 77 77 6 7 6 6 6 4FORM normal55 7 7 6 4 7 6 7 6 7 6 7 6 LEX true 7 6 7 6 SS 6 7 3 2 7 6 7 6 7 6 RESULT D1 7 6 7 6 E 7 6 5 4 7 6 CAT 7 6 7 6 ACTIVE /PPj 7 6 7 6 7 6 6 377 2 6 7 6 MODE ref 7 6 7 6 7 6 7 6 7 6 7 6 7 6 INDEX i 7 6 7 6 6 * " # +777 6 6 SEM 6 77 6 6 6 4RESTR ! INSTANCE i ! 57 57 5 4 4 ARG1 j
(55) 2cn-pp-lxm D
E
The next group of lexical entries are the constant lexemes that inherit only from constlxm, including prepositions, relativizers, complementizers, determiners, adjectives, conjunctions, and adverbs. The const-lxm type hierarchy is given in (56): (56)
const-lxm prep-lxm mkp-lxm
det-lxm
conj-lxm
mod-lxm
mod-prep-lxm
vac-mkp-lxmcont-mkp-lxm pdp-lxm
xp-mod-lxm
adv-pdp-lxm vp-adv-pdp-lxm np-adv-pdp-lxm
rel-lxm ...
xbar-mod-lxm adj-lxm
tv-adj-lxm
adv-lxm
iv-adj-lxm iv-adj-lxm
tough-adj-lxmptv-adj-lxm
I'll only discuss some of these types here, leaving the rest for discussion in conjunction with speci c syntactic phenomenon. First, the three simplest subtypes of const-lxm are det-lxm (category NP/N), comp-lxm (category NP/S), and conj-lxm (category CONJ), corresponding to determiners, complementizers, and conjunction respectively. The constraints appropriate for these types are:
29
comp-lxm
(57) (a) det-lxm := const-lxm &
2 2 33 ROOT j FEATS 1 noun-features 377 2 6 6 6 7 RESULT np 6 6 7 3+77 2 7 6 6 6 7 * 7 6 7 6 KEY j SIT s 6 7 7 6 7 6 6 CAT 6 6FEATS 1 7 777 6 6 ACTIVE /N i 5 577 4 6 4 6 7 7 6 6 7 2 MODE 7 6 6 7 7 6 6 7 SS 7 6 2 3 6 7 7 6 2 MODE 6 7 7 6 h i 6 7 6 7 7 6 6 7 6 7 3 SIT s 7 6 KEY 6 7 6 7 7 6 6 7 6 7 7 6 SEM 6 7 6 7 INDEX i 7 6 6 6 7 h 77 i 6 6 4 5 57 4 4 5 RESTR ! 3 BV i !
(b) 2comp-lxm := const-lxm &
# " 33 2 comp-features 7 6 ROOT j FEATS 7 6 7 6 1 n FORM 7 6 7 6 7 6 7 6 2 3 7 6 7 6 RESULT np 7 6 7 6 7 6 2 3 6 7 6 h i * +777 6 6 7 6 6 CAT 6 ROOT j FEATS FORM 1 5 77 7 6 7 6 4 7 ACTIVE /S 6 4 5 t SS 7 6 7 6 7 6 2 SEM j MODE 7 6 7 6 7 6 7 6 3 2 7 6 7 6 2 7 6 MODE 7 6 7 6 7 6 7 6 6 77 6INDEX Dt E7 SEM 6 6 57 5 4 5 4 4
RESTR ! !
(c) conj-lxm := const-lxm &
2 2 333 2 " # 1 KEY 6SS 4CAT RESULT conj SEM 4 D E557 4 RESTR ! 1 ! 5 ACTIVE hi
Items of type det-lxm take on their argument's features and index, which is bound by the quanti er relation in RESTR (via the feature B(OUND-)V(ARIABLE)). The type comp-lxm takes a nite S as its argument and adopts the mode and index values of its complement as well, producing a nite NP result. Finally, the type conj-lxm is a simple category taking no arguments and declaring few constraints (recall that the treatment of coordination implemented here is syntactic). Examples of each of these lexemes is given in (58): 3 2 E 7 6 7 6 ORTH ! \many" ! 7 6 2 7 6 " # 7 6 COUNT true 6 +7 6 7 ROOT j FEATS 6 6 7 6 AGR pl 6 6 7 h 7 6SS 6 i 4 4SEM j RESTR ! RELN r many ! 5
(58) (a) every 1 := det-lxmD
2 4
(b) that 1 := comp-lxm D
ORTH ! \that" !
3 E5
30
3 7 7 7 i 7 5
2 E 6 6 ORTH ! \and" ! 6 h 6 4
(c) and 1 := conj-lxmD
SS j SEM j RESTR ! RELN r and !
The determiner many introduces the additional constraints that it is count and plural, and by the feature sharing above the noun argument must be a plural count noun (cf. many dogs, *many dog, *many rice, etc.). The full entry is given in (59): 3 2 E 7 6 7 6 ORTH ! \many" ! 7 6 6 2 37 2 3 7 6 RCAT 1 np 7 6 3 2 7 6 6 7 6 7 7 6 6 noun-features 7 7 6 7 6 6 7 ROOT 6 7 7 6 7 6 6 4FEATS 24COUNT true 55 7 7 6 6 7 7 6 6 7 AGR pl 7 6 6 7 7 6 6 37 2 7 6 6 7 1 RESULT 7 6 6 7 7 6 * #+ " 6 7 7 6 7 6 6 77 2 FEATS CAT 6 7 6 SS 6 7 5 4 ACTIVE /N 7 6 i 6 7 3 7 6 MODE 6 7 7 6 6 7 7 6 2 3 6 7 7 6 6 7 MODE 3 7 6 6 7 7 6 6 7 6 7 INDEX i 7 6 6 7 6 7 7 6 #+ *" 7 6 7 SEM 6 7 6 6 7 6 7 many RELN r 6 4 4RESTR 557 5 4 BV i
(59) det-lxmD
The other two major subtypes of const-lxm are prep-lxm and mod-lxm. Following Sag and Wasow, I'll assume there are two major classes of prepositions, so-called \marking" prepositions (category PP/NP) that mark oblique arguments but (usually) contribute no semantics (e.g. of in Sandy is fond of Kim ) although sometimes they can (e.g. on in Sandy put the book on the table ) and predicative prepositions that contribute semantics and generally are modi ers (e.g. on in The book on the table belongs to Sandy ). The type prep-lxm is a supertype of all of these but declares no constraints. The type mkp-lxm is for marking prepositions, with subtypes vac-mkp-lxm and cont-mkp-lxm for vacuous and contentful semantics, with the following constraints:
31
33 2 3 2 pp-features 7 7 6 6 6 AGR 1 7 7 7 6 6 7 6 7 7 6 6 ROOT j FEATS 7 6 7 7 2 5 6 6 ANA 4 7 7 6 6 7 7 6 6 3 PRED 7 6 6 377 2 7 6 6 7 7 6 6 RESULT pp 7 7 6 6 7 6 2 3 3 2 7 7 6 6 7 6 SS 6 1 7 7 6 AGR 7 6 7 7 6 6 7 6 6 7 7 6 + * 7 7 6 6 2 ANA 7 6 6 7 7 6 7 7 6 6 FEATS 6 CAT 6 7 7 7 6 7 7 6 6 3 7 6 ACTIVE /NP PRED 4 5 7 6 7 7 6 6 7 6 7 6 7 6 6 777 6 5 4 CASE acc 6 6 577 4 6 77 7 6 6 6 MODE 4 55 4 4
(60) (a) mkp-lxm := prep-lxm & 2
SEM j MODE 4
(b) vac-mkp-lxm := mkp-lxm
& 2 2CAT j ACTIVE D[]i E33 7 6 6 2 37 7 7 6 6 7 7 6 6 INDEX i SS 7 6 6 D E557 5 4 4SEM 4 RESTR ! !
(c) cont-mkp-lxm := mkp-lxm &
2 2 33 D E CAT j ACTIVE []i 7 6 6 7 6 37 2 7 6 7 6 7 INDEX j 6 7 6 7 6 7 6 7 6 7 1 KEY SS 6 7 6 7 6 7 6 7 6 # + " * 7 6 7 6 SEM 7 6 7 6 7 INSTANCE j 6 6 4RESTR ! 1 ! 557 5 4 4 ARG1 i
This de nition follows the Sag and Wasow approach that marking prepositions are more or less nominal in nature, simply marking their argument but exposing most if its information to the lexical item that selects the marked NP as an argument. Some features, such as CASE, COUNT, and LEX are left underspeci ed as they are not relevant to marking prepositions. An example entry is given in (61a), with its fully speci ed entry in (61b): 2 E 6 6ORTH ! \of" ! 4
3 7 7 5 SS j ROOT j FEATS j FORM f of
(61) (a) of 1 := vac-mkp-lxm D
32
3 7 6 7 6 ORTH ! \of" ! 7 6 2 3 7 6 2 3 7 6 RCAT 12pp 7 6 3 6 7 7 6 6 7 6 7 2 7 6 ANA 6 7 6 7 7 6 6 7 7 6 6 7 7 6 AGR 3 77 ROOT 6 6 6 7 7 6 6FEATS 6 7 7 6 7 7 6 4 4PRED 4 55 6 7 7 6 6 7 7 6 FORM f of 6 7 7 6 6 7 6 2 377 6 7 6 RESULT 1 6 7 7 6 6 7 7 6 6 7 2 3 2 3 6 7 7 6 6 7 ANA 2 6 7 7 6 6 7 6 7 7 6 SS 6 6 6 7 * 6 +7 7 3 7 AGR 7 6 6 6 7 7 6 7 6 7 6 CAT 6 FEATS 6 77 777 6 6 7 6 4 PRED 6 ACTIVE NP 7 4 5 6 7 i 6 7 7 6 6 6 7 7 6 7 7 6 6 7 4 5 CASE acc 6 7 6 4 577 6 7 6 6 7 MODE 5 7 6 6 7 7 6 2 3 6 7 7 6 6 7 7 6 INDEX i 6 7 7 6 6 7 6 7 7 6 5 6MODE D E7 7 6 6 SEM 4 5 57 5 4 4
(b) 2vac-mkp-lxm D
E
RESTR ! !
Before discussing predicative prepositions it will be useful to rst discuss how modi cation is implemented in this grammar. In CCG modi ers are typically treated as categories that map a category to the same category, i.e. categories of the form XjX$ (e.g. adverbs are typed as (SnNP)j(SnNP), and adjectives as N/N), although in this approach the headedness modality is always in the opposite direction of the slash directionality. With this analysis in mind, I posit two subtypes of mod-lxm in (56), xp-mod-lxm and xbar-mod-lxm, the former corresponding to XP modi ers and the latter to X modi ers, which modify elements still looking for speci ers. The constraints appropriate for these two types are given in (62): (62) (a) 2xp-mod-lxm := mod-lxm & 2
33 377 7 7 7 7 7 6 2 3 2 3 7 7 6 6 7 6 1 7 7 6 6 ROOT j FEATS 7 6 * + 7 7 6 6 6CAT 2 7 6 77 6 7 7 6 6 ARG CAT SS 7 6 4 5 6 7 7 7 6 6 ACTIVE 6 , ... 7 6 7 7 7 6 6 3 7 6 SEM j MODE 4 5 7 6 6 577 4 6 6 77 7 6 6 SLASH mod-slash 55 4 4
ROOT j FEATS 1 2 6 6 6 6 RESULT 2 6 6
SEM j MODE 3
(b) xbar-mod-lxm := mod-lxm &
33
2 2 33 ROOT j FEATS 1 2 3 6 6 7 7 6 6 7 7 RESULT 2 6 6 7 7 6 7 33 2 2 6 6 7 7 6 7 1 6 6 7 7 ROOT j FEATS 6 7 6 6 7 7 2 3 6 7 7 6 7 6 6 6 7 7 6 6 7 RESULT D2 E 7 +7 * 6 6 6 7 7 6 7 7 6 7 6 6 6 7 7 4 5 ARG 6CAT SS 6CAT 6 7 7 7 6 6 7 7 4 4 , ... 6 7 7 6 ACTIVE , ACTIVE 7 6 6 6 7 7 6 7 57 4 6 6 6 7 7 6 7 7 6 6 6 7 6 777 5 4 SEM j MODE 3 6 6 7 4 5 6 6 7 6 6 77 7 SLASH mod-slash 4 4 55
SEM j MODE 3
Essentially, both types of modi ers adopt all the feature and category information of their modi ees. In the case of X modi cation, the as yet unsaturated speci er of the modi ee is coidenti ed with the speci er of the modi er, an approach which is identical to the analysis of auxiliaries and raising assumed in the Sag and Wasow book and in this implementation. The MODE values are likewise coidenti ed, but not the INDEX values, as the indexing will be determined by individual modi ers (according to properties such as intersectivity). Note that in both cases there may be additional arguments. Looking at subtypes of these modi ers, xp-mod-lxm has subtypes adj-lxm, rel-lxm, and pdp-lxm, corresponding to adjectives, relativizers, and predicative prepositions.25 I will save the analysis of relative clauses for the discussion of unbounded dependencies, but for adjectives the type hierarchy declares one type adj-lxm for category (N/N$), with two subtypes ivadj-lxm (corresponding to adjectives of category N/N such as happy in the happy dog ) and tv-adj-lxm (category N/N/X), with two subtypes ptv-adj-lxm (corresonding to adjectives of category N/N/PP such as fond in fond of Kim ) and tough-adj-lxm (corresponding to tough -adjectives such as easy in Kim is easy to please ), which I'll likewise discuss later when discussing unbounded dependencies, but the constraints for the remainder of these types are given in (63): 33 2 ROOT j FEATS noun-features 2 377 6 6 RESULT n 77 6 6 7 6 6 # +77 *" 6 7 6 6 77 ARG j SEM j INDEX i SS 6CAT 6 7 6 4ACTIVE 577 7 6 , ... 6 77 6 6 SLASH forw-mod-slash 55 4 4 SEM j INDEX i 33 2 &2 INDEX i 77 6SS j SEM 6 4RESTR ! hARG1 ii! 55 4
(63) (a) adj-lxm := xp-mod-lxm & 2
(b) iv-adj-lxm := adj-lxm
25 Note that adjectives and relative clauses are treated as XP modi ers, since the approach here assumes that determiners select nouns as arguments (a so-called \DP" analysis) and thus what is normally an N is here treated as a fully saturated N and thus subject to XP modi cation.
34
(c) ptv-adj-lxm := tv-adj-lxm &
2 2 33 E D CAT j ACTIVE [], /PPj 6 7 6 6 7 37 2 7 6 6 7 7 6 INDEX i 6 7 7 6 6 7 7 6 7 6 KEY 1 SS 6 6 7 7 6 7 6 7 " * # + 7 6 7 6 SEM 6 7 6 77 ARG1 i 6 6 5 4 RESTR ! 1 ! 57 4 4 5 ARG2 j
The constraints on adj-lxm speci es all adjective lexemes to have a RESULT n and nominal features. The subtypes iv-adj-lxm and ptv-adj-lxm further restrict the ACTIVE list of the adjective to have no other element and one PP complement respectively. Semantically, the adjective shares an index with its modi ee as well as predicating over that index.26 Example lexical entries are given in (64): 2 E 6 6 ORTH ! \happy" ! 6 h 6 4
(64) (a) happy 1 := iv-adj-lxm D
3 7 7 7 i 7 5
SS j SEM j RESTR ! RELN r happy !
2 3 E 6 7 6 7 ORTH ! \fond" ! 6 7 2 3 6 i 7 h 6 7 6 CAT j ACTIVE [], FORM f of 77 6 6 7 6 7 6 7 h 7 6SS 6 7 4 4SEM j RESTR ! RELN r fondi! 55
(b) fond 1 := ptv-adj-lxm D
A fully speci ed entry for fond is: 26 In other words, all adjectives in this implementation are intersective adjectives. Non-intersective adjectives might be implemented by a seperate type that does not share index values but generates a new index value for the modi er phrase while the adjective predicates over the modi ee index.
35
3 2 E 7 6 7 6 ORTH ! \fond" ! 7 6 3 2 7 6 # " 7 6 1n RCAT 7 6 7 6 ROOT 7 6 7 6 2 noun-features 7 6 FEATS 7 6 6 377 2 6 7 6 7 6 RESULT 1 7 6 7 6 7 6 3 2 7 6 7 6 7 6 7 6 1 CAT 7 6 7 6 7 6 * + 7 6 7 6 7 6 7 6 h i 7 6 2 ROOT j FEATS 7 6 7 6 CAT 6 7 7 6 7 6 " # 7 6 FORM f , /PP 7 ACTIVE / of 6 j 7 6 6 6 3 7 777 6 MODE 6 6 5 4 577 4 SEM 7 6 SS 6 7 6 INDEX i 7 6 7 6 7 6 7 6 7 6 3 2 7 6 7 6 INDEX i 7 6 7 6 7 6 7 6 7 6 3 7 6 MODE 7 6 7 6 7 6 7 6 3 2 7 6 7 6 7 6 + * 7 6 SEM 6 RELN r fond 7 7 6 7 6 7 6 7 6 7 6 7 6 7 ! ARG1 i RESTR ! 6 6 5 4 5 4 57 5 4 4 ARG2 j
(65) ptv-adj-lxm D
The type xp-mod-lxm also serves as a supertype of pdp-lxm, capturing essentially the same generalization that predicative PPs are of a category NnN$: (66) pdp-lxm := prep-lxm & xp-mod-lxm &
2 2 33 ROOT j FEATS noun-features 2 377 6 6 6 7 RESULT n 6 6 7 77 7 6 6 h i 6 7 7 6 CAT 4 5 6 7 7 6 ACTIVE n [] , /NP CASE acc i j 6 7 7 6 6 7 7 6 6 7 3 2 7 SS 6 6 7 7 6 INDEX i 6 7 7 6 6 7 7 6 7 6 1 KEY 6 7 7 6 7 6 6 7 * " # + 7 6 7 6 SEM 6 7 6 77 ARG1 i 6 6 7 5 4 5 4 RESTR ! 1 ! 4 5 ARG2 j
An example entry is given in (67a), where the inheritance from xp-mod-lxm guarantees the right category, as shown in (67b): 2 E 6 6 ORTH ! \on" ! 6 6 4
3 7 7 7 i 7 5
(67) (a) on 2 := pdp-lxmD
h
SS j SEM j RESTR ! RELN r on !
36
3 2 E 7 6 7 6 ORTH ! \on" ! 7 6 3 2 7 6 # " 7 6 1n RCAT 7 6 7 6 ROOT 7 6 7 6 2 noun-features 7 6 FEATS 7 6 6 377 2 6 7 6 7 6 RESULT 1 7 6 7 6 7 6 3 2 7 6 7 6 7 6 7 6 1 CAT 7 6 7 6 7 6 + * 7 6 7 6 7 6 7 6 h i 7 6 2 ROOT j FEATS 7 6 7 6 CAT 6 7 7 6 7 6 # " 7 6 7 CASE acc , /NP ACTIVE n 6 j 7 6 6 7 6 777 6 INDEX i 6 6 5 4 577 4 SEM 7 6 SS 6 3 7 6 MODE 7 6 7 6 7 6 7 6 7 6 3 2 7 6 7 6 MODE 3 7 6 7 6 7 6 7 6 7 6 7 6 INDEX i 7 6 7 6 7 6 7 6 3 2 7 6 7 6 7 6 + * 7 6 SEM 6 RELN r on 7 7 6 7 6 7 6 7 6 7 6 7 6 7 ! ARG1 i RESTR ! 6 6 5 4 5 4 57 5 4 4 ARG2 j
(b) pdp-lxmD
The second class of modi ers consists of X -modi ers, here represented as subtypes of xbar-mod-lxm. In this implementation, the only cases of these are VP modi ers, of category (SnNP)j(SnNP)$. This general category is represented by the only direct subtype of xbarmod-lxm, adv-lxm, with constraints as in (68): (68) adv-lxm := xbar-mod-lxm &
2 2 33 ROOT j FEATS s-features 3 77 2 6 6 6 7 RESULT s 6 6 7 D E5 7 6 7 4 6 7 CAT 6 7 6 7 ACTIVE n NP, [] , ... t 6 7 6 7 6 7 6 7 3 2 6 7 6 7 SS 6 7 INDEX u 6 7 6 7 6 7 7 6 6 7 KEY 1 6 7 7 6 6 7 6 7 # + * " 7 6 7 SEM 6 6 7 7 6 6 7 SIT u 6 4 4RESTR ! 1 ! 557 4 5 ARG-S t
The type adv-lxm declares its rst argument to be of type nNP, and by inheritence of the constraint on xbar-mod-lxm we know this is coidenti ed with the speci er of its second argument:
37
(69) 2adv-lxm
3 37 2 6 ROOT j FEATS 1 s-features 6 7 3 2 6 7 7 6 6 7 2 s RESULT 7 6 6 7 7 6 7 6 2 2 3 3 6 7 7 6 7 6 6 7 1 ROOT j FEATS 7 6 7 6 6 7 377 2 7 6 7 6 6 6 6 7 7 6 7 6 2 6 6 7 7 RESULT 6 7 + * 7 6 7 6 6 6 7 7 6 7 E D 5 4 7 6 CAT 7 6 6 6 7 7 6 CAT 6 6 3 77, ... 777 ACTIVE 6 6 6 7 3 ARG n NP, j ACTIVE 7 6 7 6 6 6 7 7 6 7 7 6 7 6 " # 6 6 7 7 6 7 7 6 7 6 6 6 7 7 6 7 INDEX t SS 6 7 7 6 4 4 5 5 6 7 SEM 7 6 5 4 6 7 4 7 6 MODE 6 7 7 6 6 7 7 6 6 7 2 3 7 6 6 7 7 6 INDEX u 6 7 7 6 6 7 6 7 7 6 4 MODE 6 7 6 7 7 6 6 7 * " # +7 6 7 6 SEM 6 7 6 7 7 SIT u 6 6 4RESTR ! 57 4 4 5 ! 5 ARG-S t
Subtypes of adv-lxm include regular adverbs (e.g. quickly ) and adverbial predicative prepositions, represented by iv-adv-lxm and adv-pdp-lxm, which has subtypes np-advpdp-lxm for adverbial prepositions that take NP complements (e.g. without as in Kim left without Sandy ) and vp-adv-pdp-lxm for adverbial prepositions that take VP complements (e.g. without as in Kim left without talking to Sandy ). Speci cally, regular adverbs have category (SnNP)j(SnNP), prepositional adverbs that take NP complements have category (SnNP)j(SnNP)/NP, and those that take VP complements have category (SnNP)j(SnNP)/(S[ing]nNP). The constraints on these types are given in (adv-const ):
(70) (a) iv-adv-lxm := adv-lxm & SS j CAT j ACTIVE D[], []E
(b) adv-pdp-lxm := adv-lxm & SS j CAT j ACTIVE D[], n[], /[]E
2 h i 33 CAT j ACTIVE [], [], /NPi CASE acc 77 6 6 7 7 6 6 " 7 7 6 6 h i # 77 6SS 6 55 4 4SEM RESTR ! ARG1 i !
(c) np-adv-pdp-lxm := adv-pdp-lxm & 2
(d) 2vp-adv-pdp-lxm := adv-pdp-lxm & 2
i 33 CAT j ACTIVE [], [], / SnNP t FORM prp 77 6 6 7 7 6 6 " 7 7 6 6 h i # 77 6SS 6 55 4 4SEM RESTR ! ARG-S2 t !
h
The type iv-adv-lxm simply restricts the arguments of the adverb to two, the speci er and the VP, thus forming a category (SnNP)j(SnNP) (where the directionality is still underspeci ed). The constraints on adv-pdp-lxm are just that the modi ee VP must occur before it and that it has one argument after it, thus forming a category (SnNP)n(SnNP)/X. The subtype np-adv-pdp-lxm restricts the last argument to be an NP and vp-adv-pdp-lxm 38
restricts this argument to be a VP with a present progressive form, forming a category (SnNP)j(SnNP)/(S[ing]nNP), each type also doing explicit linking of the nal argument.27 Examples of each type are given in (71): 2 E 6 6 ORTH ! \quickly" ! 6 h 6 4
3 7 7 7 i 7 5
(71) (a) quickly 1 := iv-adv-lxm D
SS j SEM j RESTR ! RELN r quickly !
2 E 6 6 ORTH ! \on" ! 6 6 4
3 7 7 7 i 7 5
(b) on 3 := np-adv-pdp-lxm D
h
SS j SEM j RESTR ! RELN r on ! 2 E 6 6 ORTH ! \without" ! 6 h 6 4
(c) without 3 := vp-adv-pdp-lxm D
3 7 7 7 i 7 5
SS j SEM j RESTR ! RELN r without !
The full entry for without, with all inherited constraints, is given in (72):
2 3 E 6 7 6 7 ORTH ! \without" ! 6 2 37 6 7 # " 6 7 2s RCAT 6 7 6 7 6 ROOT 7 6 7 1 6 7 FEATS s-features 6 7 6 377 2 6 6 7 6 7 6 7 RESULT 2 6 7 6 7 7 6 3 3 2 2 6 7 6 7 7 6 6 7 1 6 7 ROOT j FEATS 7 6 6 7 6 7 2 3 7 6 7 7 6 6 6 7 6 7 7 6 2 7 7 6 6 RESULT 6 7 6 7 + * 7 6 7 7 6 6 D E 6 7 6 7 4 5 h i CAT 7 6 7 7 6 6 6 7 CAT 6 3 77, / SnNP v FORM prp 777 6 ACTIVE 6 6 3 nNP, n6 6 7 ARG ACTIVE 7 6 7 6 6 6 7 6 7 7 6 # 7 " 7 7 6 6 6 7 6 7 7 6 7 7 6 6 6 7 6 INDEX t 777 6 SS 6 55 4SEM 4 6 7 5 4 6 7 6 7 MODE 4 6 7 6 7 6 7 6 7 6 7 6 7 2 3 6 7 6 7 INDEX u 6 7 6 7 6 7 6 7 6 7 4 MODE 6 7 6 7 6 7 6 7 6 7 3 2 6 7 6 7 6 7 6 RELN r without +7 6 7 6 7 * 6 7 SEM 6 6 7 6 7 6 7 7 SIT u 6 7 6 7 6 7 6 7 6 7 ! RESTR ! 6 7 6 6 7 77 ARG-S t 6 6 5 4 4 5 57 4 4 5 ARG-S2 v
(72) vp-adv-adv-lxm D
Although this section has documented a large part of the lexical hierarchy of the implementation, it has not been exhaustive: several lexical types related to speci c phenomenon 27 At
the moment no constraints are in place to deal with the nature of control of the subject of the gerundive VP complement.
39
(such as raising and control types, auxiliaries (here a subtype of raising verbs), tough -adjs, etc.) have been omitted and the relevant additions to the lexical hierarchy will be discussed when these phenomenon are discussed in x4.
3.3 Lexical Rules
The lexical hierarchy given in the previous section only accounts for objects of type lexeme and the relationships between them. Many of the phenomenon treated here are treated in terms of lexical mapping rules that map one category onto another. In addition, in order for these elements to participate in the syntax they must rst undergo some lexical mapping to entities of type word. In this section I'll outline the organization of lexical rules in this implementation, and outline the system of in ectional rules that map lexeme s to word s. The mapping rules that handle many of the syntactic phenomenon covered here I'll discuss in x4.
3.3.1 Organization of Lexical Rules Lexical rules are encoded here as non-branching grammatical rules. Speci cally, all lexical rules have results of type word : 3 2 1 *" #+ 7 6 7 6 4DTRS lex-item 5
(73) word := lex-item & expression & SS /l
SS /l 1
An element of type word is the the output of a lexical rule whose input was something of type lex-item, i.e. either a word or lexeme. Thus only lexeme items are represented in the lexicon, and rules must map them to entities of type word. Lexical rules in this implementation fall into two groups: in ectional rules are those that map lexeme s to word s, and that all lexical alternations and syntactic work is handled as word to word mappings.28 The mother type of all lexical rules, whether in ectional or mapping, is the type lrule, which inherits from word, meaning that all lrule s have outputs that are words. This type inherits the constraints of word, and preserves a constraint on the type lexeme that the root category is the left-most result of a category: (74) lrule := word & "
"
ROOT j RCAT 1 SS CAT j RESULT 1
##
The relevance of this will be more obvious in the discussion of the syntax representation and also in the discussion of coordination. This type has two subtypes, in -rule for in ectional rules, which I will discuss in the next section, and lmap-rule for mapping rules which I will discuss in x3.3.3. 28 I
will refer to all types of such rules as \lexical rules", speci cally refering to \in ectional rules" as those that map lexeme s to word s with speci c morphological changes and \mapping rules" which induce valence alternations and other syntactic operations. When no ambiguity is possible, I will sometimes refer to mapping rules simply as \lexical rules".
40
3.3.2 In ectional Rules
The in ectional rule hierarchy is given in (75): (75)
in -rule morph-in -rule
const-in -rule
n-in -rule
v-in -rule
v-morph-in -rule
n-const-in -rule
n-morph-in -rule
v-const-in -rule
This hierarchy has the e ect of splitting up information along two axes. The type morphin -rule corresonds to in ectional rules that induce an overt morphological change in a lexeme and const-in -rule corresponds to in ectional rules that make no overt morphological changes. The other axis is verbal versus nominal morphology (the only two classes in English that show overt morphology), where v-in -rule corresponds to in ectional rules over verbal lexemes and n-in -rule corresponds to in ectional rules over nominal elements. The crossclassi ed types correspond to all the possible combinations. The constraints on these types are given in (76): 2 4
(76) (a) in -rule := lmap-rule & SS j ROOT j EFEATS j PRED false D DTRS lexeme
(b) morph-in -rule := in -rule &
"
h
DTRS NEEDS-AFFIX true
2 1 *" 6 6 4DTRS ORTH 1
(c) const-in -rule := in -rule & ORTH (d)
(e)
3 5
i #
3 #+7 7 5
NEEDS-AFFIX false 2 " #3 v-in -rule := in -rule & FORM /l n 6 7 SS j ROOT j FEATS 6 AUX /l false 7 6 7 D E 4 5 DTRS verb-lxm n-in -rule := in -rule & DTRS Dcnoun-lxmE
The constraint on in -rule restricts in ectional rules to only have lexeme daughters, thus making all in ectional rules lexeme to word mappings. The constraints on morphin -rule set the daughter's NEED-AFFIX feature to true. The type const-in -rule declares NEEDS-AFFIX to be false, preventing any morphological processing of the input, and sets the ORTH values of the mother and daughter to be identical. The type v-in -rule restricts its daughter to be verb-lxm items, and by default assumes that they are nite, non-auxiliary verbs.29 Finally, n-in -rule restricts its daughter to be of type cnoun-lxm. The actual in ectional rules inherit from these types: 29 These
particular defaults are only to do with this particular implementation, as most of the verbal in ectional rules happen to deal with nite, non-auxiliary matrix verbs. They might be di erent for a di erent grammar.
41
(77) Constant In ectional Rule: 2 (a) const-lxm in rule := const-in -rule D 4
3 E5
DTRS const-lxm
Nominal In ectional Rules: (b) sing-n in rule := n-const-in -rule
SS j ROOT j FEATS j AGR 3sg
(c) plural-n in rule := %sux (!s !ss) (!ss !ssses) (ss sses) (!ty !ties) (ch ches) (sh shes) (x xes) (z zes) n-morph-in -rule SS j ROOT j FEATS j AGR pl
Verbal In ectional Rules: (d) 3sg-verb in rule := %sux (!s !ss) (!ss !ssses) (ss sses) (!ty !ties) (ch ches) (sh shes) (x xes) (z zes) 3 2 v-morph-in -rule 37 2 6 SEM j INDEX pres-index 7 6 6 ## +77 *" " 6 6 77 CASE nom 7 6SS 6 4 4 , ... 55 CAT j ACTIVE ARG j ROOT j FEATS AGR 3sg
(e) 2non-3sg-verb in rule :=
3 v-const-in -rule 2 37 6 SEM j INDEX pres-index 6 7 6 *" " ## +77 6 6 77 6SS 6 CASE nom 7 4 4CAT j ACTIVE ARG j ROOT j FEATS , ... 55 AGR non-3sg
(f) past-verb in rule := %sux (* ed) (!ty !tied) (e ed) (!t!v!c !t!v!c!ced) 2
3 v-morph-in -rule 37 2 6 SEM j INDEX past-index 7 6 7 6SS 6 h i 7 4 4 5 CAT j ACTIVE ARG j ROOT j FEATS j CASE nom , ... 5
(g) past-participle-verb in rule := 2%sux (* ed) (!ty !tied) (e ed) 3(!t!v!c !t!v!c!ced) 4
v-morph-in -rule h i5 SS j ROOT j FEATS FORM pfp
(h) present-participle-verb in rule := %sux (!t!v!c !t!v!c!cing) (* ing) (e ing) (ee eeing) (ie ying)
42
2 v-morph-in -rule " # 6 6 FORM prp 6 SS j ROOT j FEATS 6 PRED true 6 h 6 4
DTRS SS j ROOT j FEATS j PRED false 2 4
(i) base-verb in rule := v-const-in -rule
3 7 7 7 7 7 i7 5 h
SS j ROOT j FEATS FORM base
3 i5
The const-lxm in rule in ectional rule only operates on const-lxm lexemes and simply maps them to type word without any changes. For the nominal in ections, sing-n in rule in ects common nouns for singular agreement, leaving the orthography constant and xing the AGR feature to 3sg. The three nite verbal in ectional rules, 3sg-verb in rule, non3sg-verb in rule, and past-verb in rule all assign nominative case to their input's subjects and x appropriate agreement and situational indices based on tense.30 The past-participleverb in rule and present-participle-verb in rule map verbal lexemes to their appropriate participle form, xing the FORM value, and setting PRED to true in the case of present participle. Finally, base-verb in rule simply maps the verbal lexeme to the same morphological form and xing the FORM value. None of the non- nite in ectional rules assign nominative case to their subjects.31 Recall that all lexical rules inheriting from v-in -rule inherit by default the constraint that their outputs are non-auxiliary. In ection for auxiliaries will be handled directly in the lexicon. A fully expanded entry for 3sg-verb in rule is given in (78): (78) 3sg-verb in rule := 2%sux (!s !ss) (!ss !ssses) (ss sses) (!ty !ties) (ch ches) (sh shes)3(x xes) (z zes) v-morph-in -rule 37 2 6 33 2 2 6 7 AUX false 6 7 7 6 6 7 7 7 6 6 7 6 FORM n FEATS ROOT 6 7 55 4 4 7 6 6 7 7 6 6 7 IC true 7 6 6 7 7 6 h i 6 7 7 16 6 7 SS SEM INDEX pres-index 7 6 6 7 7 6 6 7 3 2 7 6 ## + *" " 6 7 7 6 6 7 CASE nom 7 6 6 , ... 557 4CAT 4ACTIVE ARG j ROOT j FEATS 6 7 AGR 3sg 6 7 6 7 6 7 2 3 6 7 * verb-lxm + 6 7 6 7 7 6DTRS 6 7 4SS 1 5 4 5 NEEDS-AFFIX true
An example application of this lexical rule to a verb lexeme is shown in (79). The tree notation can be assumed to be shorthand for a feature structure in which the daughter is 30 The Sag and Wasow book represents tense information via predicates; I adopt this approach for simplicity. 31 The additional generalizations that nite in ection always assigns nominative case could be captured more succinctly by additional supertypes taking this into account.
43
the element on the DTRS list of the mother. The constraint on elements of type word is that the SS of the mother and daughter are uni ed, however in this example I will show the input and output values for the relevant features for illustrative purposes: 3 2 7 6 7 6 ORTH ! \sees" ! 7 6 6 2 37 33 2 2 7 6 7 6 AUX false 7 6 6 7 7 7 6 6 7 6 ROOT 4FEATS 4FORM n55 6 7 7 6 6 7 7 6 6 7 IC true 7 6 6 7 7 6 h i 7 7 6 16 SS 6 7 SEM INDEX pres-index 7 6 6 7 7 6 6 7 2 3 7 6 * " # + 6 7 7 6 6 7 CASE nom 6 4CAT 4ACTIVE NP , NP 557 5 4 AGR 3sg
(79) v-morph-in -rule D E
2 3 tv-lxmeD E 6 7 6 7 ORTH ! \see" ! 6 7 6 7 2 3 33 2 2 6 7 AUX false 6 7 6 7 6 7 6FEATS 6FORM vform77 6 7 ROOT 6 7 5 5 4 4 6 7 6 7 6 7 6 7 IC boolean 6 7 6 7 6 7 h i 6 7 1 6 7 SS 6SEM INDEX sit-index 7 6 7 6 7 6 7 6 2 * " # +37 6 7 6 7 6 6 77 CASE case 6 4 5 CAT 4ACTIVE NP , NP 5 7 6 7 AGR agr-cat 6 7 4 5 NEEDS-AFFIX true
Note that all lexemes must undergo some in ectional rule, with in -lxm s undergoing either verbal or nominal in ectional and const-lxm undergoing constant in ection in order to produce items of type word that may undergo mapping rules and appear in the syntax.
3.3.3 Lexical Mapping Rules 3.3.4 Curry
As mentioned in x3.1.1, the list based representation of arguments on the ACTIVE list is useful for making lexical generalizations, while the embedded feature structure representation is more useful for stating syntactic rules. Moving from one representation to another will require a special lexical rule called curry :
44
3 7 6 SEM 2 7 6 7 6 SS 7 6 3 ROOT 6 3 7 2 7 6 7 6 word 7 6 + * 7 6 7 6 1 ORTH 7 6 6 #7 7 " 6 6 DTRS 6 SEM 2 7 7 6 5 7 4SS 5 4
(80) curry := word & 2ORTH "
1
#
ROOT 3
The curry rule speci es that all of the root, orthographic, and semantic information of the mother and daughter are identical. Two instantiations of this rule deal with the category information: (81) (a) curry-0 := 2curry
3 6 7 SS j CAT 1 6 2 " 3+7 6 7 * ## " 6 7 1 RESULT 6 5 7 4DTRS 4SS CAT 5
ACTIVE hi
3 3 2 33 2 7 6 7 6 1 RESULT 7 6 6 D E577 4 6 7 6 RESULT 7 6 7 6 7 6 2 CAT SS ACTIVE 6 57 4 7 6 5 4 7 6 7 6 3 ne-list-of-args ACTIVE 7 6 7 6 2 2 3 3 7 6 2 3 1 7 6 * + RESULT 7 6 " # 6 6 7 7 6 7 7 6 6 6 7 7 6DTRS 4SS 4CAT 4ACTIVE FIRST 2 555 7 5 4 REST 3
(b) curry-1 := 2curry 2
The two curry rules cover two possible input cases. The rule curry-0 curries a word that has no arguments by promoting its RESULT to be the entire category of the word, so that the CAT feature is no longer complex. The rule curry-1 takes the RESULT and the rst argument on ACTIVE of a word and produces a result where that RESULT and single argument form a complex result, where the rest of the arguments of the original word form the arguments of the new category. This second rule may apply recursively until the result has a fully embedded structure. Example applications of these rules are shown in (82):
45
(82)
(a)
3 2 curry-0 D E 6 7 6 ORTH 1 ! \Kim" ! 7 7 6 3 2 7 6 2 np CAT 7 6 7 6 4 5 4SS SEM 3 5
(b)
ROOT 4
2 3 np-lxm 6 7 1 ORTH 6 2 37 6 RESULT 2 7 6 7 CAT ACTIVE 6 7 6 7 hi 6 7 6 7 6SS 6 7 7 4 4SEM 3 55
2 3 curry-1 D E 6 7 6 7 ORTH 1 ! \give" ! 6 2 37 6 7 2 3 3 2 3 2 6 7 2 6 7 s RESULT 6 7 E D 6 6 7 57777 4 6 6 RESULT 6 7 6 7 6 3 6 ACTIVE nNP 777 6 7 6 RESULT 6 6 7 6 7 6 7 5 4 D E 6 7 CAT 6 7 6 7 6 7 6 7 6 7 4 /NP ACTIVE 6 7 6 7 SS 6 7 6 7 6 7 D 4 E 5 6 7 6 7 6 7 5 ACTIVE /NP 6 7 6 7 6 77 6 6 57 4 4SEM 6 5
ROOT 7
3 2 curry-1 7 6 1 ORTH 6 2 2 3337 7 6 2 6 RESULT D2 E 77 7 6 6 7 6 6 RESULT 4ACTIVE 3 57 7 6 7 6 6 7 7 6 CAT 7 6 6 7 7 6 7 6 4 5 D E 7 6 SS 7 6 7 6 4, 5 7 6 ACTIVE 7 6 6 77 7 6 6 5 4 SEM 6 5 4
ROOT 4
ROOT 7
2 3 dtv-lxm 6 7 ORTH 1 6 2 337 2 6 7 6 7 RESULT D2 6 7 E 4 6 7 5 CAT 6 7 6 7 3 4 5 ACTIVE , , 6 7 6 7 SS 6 77 6 6 57 4 4SEM 6 5
ROOT 7
In each case, once the representation has become fully embedded the curry rules no longer apply. The nal embedded representation is the expected input to any syntactic rules. As will be shown later, the list-based representation is the expected input and output of all lexical mapping rules, so that all lexical mapping rules must apply before the curry rules, so that representation becomes curried only as the last step before a word is used by the syntactic component.
3.4 Syntax
So far I have outlined the lexical hierarchy in which most of the information about category and semantics for each lexical item is represented, the system of in ectional rules that turn lexemes into words, and representational mapping rules that prepare words for the syntax. I will defer discussion of lexical mapping rules until a more general discussion of how various phenomenon are handled in this implementation, and present in this section the syntactic component, following the series of combinators outlined in x2.1. As noted 46
in x2.2, grammatical rules are signs with non-empty daughters lists, and all of them are subtypes of the type phrase. The subtypes of phrase are organized according to their arity: (83)
sign expression
...
phrase unary
binary
ternary
...
...
...
...
These arity subtypes capture generalizations that are applicable to all phrases of particular arities regardless of the form of combination, mostly regarding orthography and semantics. In this section I'll focus only on unary and binary rules, saving ternary rules (of which the only instance of is coordination) until x4.1. The constraints on these types are:32 h
(84) (a) phrase := expression & DTRS list-of-expressions 2 (b) unary := phrase & ORTH 1 6 SS j SEM j RESTR 2 6 *" 6 6 4DTRS ORTH 1
i
SS j SEM j RESTR 2
3 7 #+7 7 7 5
(c) binary := phrase & 2ORTH A
3 3 6 7 6 7 2 3 6 7 6 7 6 7 INDEX i 6 7 6 7 6 7 6 7 6 7 6 KEY SS 6 7 6 7 6 7 6SEM 6 7 7 6 7 4 4MODE 5 55 6 7 6 7 C D RESTR 6 7 6 #" #+7 *" 6 7 6 7 ORTH B ORTH A 6 7 , DTRS 6 SS j SEM j RESTR C SS j SEM j RESTR D 7 6 7 6 7 2 3 6 7 sign 6 7 6 7 2 37 6 6 7 4 ROOT 6 7 6 7 2 377 6 6 7 6 6 7 INDEX i P-DTR 6 7 6 7 6 7 6 7 SS 6 7 6 7 6 4SEM 4KEY 6 557 6 7 4 5 6 7 6 7 MODE 5 4 5 S-DTR sign B 2 ROOT 4
The constraint on phrase only permits expression s to participate in syntax, i.e. phrases and words. All of the phrasal types have ORTH and RESTR values that are the appends 32 I'll
use the operator to indicate list appends, but the reader should be reminded that this is short hand for di erence list stitching as discussed in x2.2).
47
of their daughters' ORTH and RESTR values (the latter constraint corresponds to Sag and Wasow's Semantic Compositionality Principle, an important part of MRS).33 In addition to these commonalities each type introduces constraints particular to that arity, and I will examine these additional constraints in turn as I look at the rules that inherit from them. Looking rst at unary, the only rule that inherits from this is type-raising :34 (85) 2type-raising := unary & 2 "
33
#
RCAT s 7 6 7 6 ROOT 1 7 6 7 6 FEATS s-features 7 6 7 6 7 6 7 6 3 2 7 6 7 6 T RESULT 7 6 6 2 33 77 2 7 6 7 6 6 7 6 7 7 6 6 ROOT 1 7 6 7 7 6 6 2 3 6 7 7 6 7 6 7 7 6 6 T 6 7 7 6 RESULT 7 6 7 7 6 6 6 7 7 6 7 6 * + 7 7 6 6 6 7 6 7 7 6 7 6 h i 7 7 6 6 + * CAT 6 7 4 7 6 5 7 6 7 7 6 6 X CAT arg-cat ACTIVE ARG 6 7 7 6 7 6 CAT 7 7 6 6 6 7 7 6 7 6 SS 6 7 7 ACTIVE 6ARG 6 6 7 7 7 6 7 7 6 6 3 2 6 7 7 6 7 6 7 7 6 6 6 7 7 6 7 6 INDEX i 7 7 6 6 6 7 7 6 7 6 7 7 6 6 7 6SEM 6 7 7 6 7 6 7 7 6 6 5 KEY 5 4 4 5 5 4 7 6 6 57 4 7 6 7 6 MODE 4 6 6 77 6 6 6 6 6 6 6 6 6 6 4
7 7 7 7 7 7 7 7 77 57 7 7 7 7 5
6 2 3 6 6 INDEX i 6 7 6SEM 6 4KEY 5 5 4 h
MODE 4
DTRS SS X
i
The constraints on type-raising promote an item (with SS) X to the category Tj(TjX), where the syntactic and semantic information of T is shared between the sign and its argument and X is left unspeci ed, constrained only to be a basic argument category, currently only NP and PP, and T is constrained to be rooted in S.35 The following two instantiations of this rule have been implemented:36 3 3 37 2 6 7 6 RESULT *s 7 6 + 6 77 6 7 6 D E 7 6 SS 4CAT 4 5 6 57 ACTIVE / ARG j CAT j ACTIVE n [] 7 6 7 6 7 6 7 6 h i 5 4 DTRS NP CASE nom
(86) (a) forward-type-raising := 2type-raising 2
33 Rather than representing this in a typical list append notation (e.g. A B ) I have shown the full horror of the LKB's di -list append operation, as described above, to prepare readers for the actual LKB code. 34 For rules, I will use capital letters X, Y, Z, T, and other symbols (such as $) rather than numbers for certain reentrancies to maintain parallelism with the usual CCG notation. 35 Type-raising is also necessary for other argument types, such as in nitival VPs, adjectives, etc., but these have not been implemented here. 36 A third instantiation, intended to deal with topicalization, is described in x4.3.1.
48
3 2 3 " * 6 D E+# 7 7 6 6 SS 4CAT ACTIVE n ARG j CAT j ACTIVE /[] 57 7 6 7 6 7 6 h 7 6 i 5 4 DTRS CASE acc
(b) backward-type-raising := type-raising 2
The forward rule allows for type-raised categories of the form S/(SnNP)37 and the backward rule only allows for type-raised categories of the form Tn(T/XP). Additionally, each type of type-raising also restricts its daughter to be nominative or accusative depending to reduce computation at parse time. Note that the only constraint on the RESULT of backward type-raising rule (i.e. T) is that it be rooted in S; the actual argument structure is left underspeci ed and is lled out when uni cation occurs with other categories. A fully instantiated backward-type-raising, with all inherited constraints, is shown in (87). 2 3 6 7 ORTH 1 6 2 37 " # 6 7 6 7 RCAT s 6 7 4 ROOT 6 7 6 7 6 7 FEATS s-features 6 7 6 7 6 7 3 2 6 7 6 7 T 6 7 RESULT 6 7 6 7 6 7 6 33 7 2 2 6 7 6 7 7 6 4 6 7 ROOT 6 7 7 6 6 7 2 3 6 7 7 6 7 7 6 6 6 7 6 7 7 6 7 7 6 6 RESULT T 6 7 6 7 7 6 7 7 6 6 + * 6 7 6 7 h i 6 7 7 6 7 7 6 6 CAT 6 7 4 5 6 7 CAT 7 6 7 7 6 6 6 6 7 ACTIVE / ARG 6 7 SS 7 ACTIVE n6ARG 6 6 7 7 6 7 6 7 7 6 7 7 6 6 6 7 6 7 7 6 # " 7 7 6 6 6 7 6 7 7 6 7 7 6 6 6 7 INDEX it i 6 7 6 55 7 4SEM 4 6 7 6 7 5 4 6 7 6 7 7 MODE 6 7 6 7 6 7 6 7 2 3 6 7 6 7 6 7 6 7 2 RESTR 6 7 6 7 7 6SEM 6 7 6 4INDEX i 5 4 57 6 7 6 7 MODE 7 6 7 6 7 2 3 6 7 6 7 expression 6 7 6 7 6 7 * + 1 ORTH 6 7 6 7 3 2 6 7 6 7 6 7 CAT np DTRS 6 7 6 7 6 7 77 6SS 66 6 7 2 SEM j RESTR 5 4 4 5 4 5 ROOT j FEATS j CASE acc
(87) type-raising
An example of an application of this rule is shown in (88): 37 This is very speci c, but in English this is the only necessary instantiation of the more general T/(TnNP).
49
(88)
2 3 arg-type-raising 6 7 ORTH 1 6 2 37 " # 6 7 6 7 RCAT s 6 7 4 ROOT 6 7 6 7 6 7 FEATS s-features 6 7 6 7 6 377 2 6 6 7 6 7 RESULT T 6 7 6 7 6 7 7 6 2 2 3 3 6 7 6 7 7 6 4 6 7 ROOT 6 7 7 6 6 7 2 3 6 7 7 6 6 6 7 7 6 7 6 7 7 6 T 6 6 7 7 RESULT 6 7 6 7 6 6 7 +777 *6 77 h 6 6 i 6 7 6 6 6 7 7 CAT 4 6 7 6 7 CAT 6 7 6 6 7 6 57 6 7 ACTIVE / ARG 6 7 SS 7 ARG ACTIVE n 6 6 6 7 7 6 7 6 7 7 6 6 6 7 7 6 7 6 7 7 6 # " 6 6 7 7 6 7 6 7 6 6 6 77 777 6 INDEX t 6 7 6 4 4 5 5 6 SEM 6 7 57 4 6 7 7 6 7 MODE 6 7 6 7 6 7 6 7 2 3 6 7 6 7 6 7 6 7 2 RESTR 6 7 6 7 6INDEX t 7 7 6 6 SEM 4 5 57 4 4 5
MODE 7
2 3 expressionD E 6 7 6 7 ORTH 1 ! \Kim" ! 6 2 37 6 7 6 7 CAT np 6 7 2 3 6 7 6 7 MODE ref 6 7 6 7 6 7 6 7 6 7 6 7 INDEX i 6 7 6 7 6 7 6 7 2 3 6 7 6 7 6 * + 6 7 RELN r name 777 SS 66SEM 6 6 7 6 6 7 7! 77 6RESTR 2 ! 6 6 7 NAME \kim" 6 4 5 4 577 6 6 6 77 6 NAMED i 4 57 4 5 ROOT j FEATS j CASE acc
Again, the RESULT of the mother will be compatible with any T rooted in S. Turning now to binary rules, three binary rules were discussed in x2.1, composition, application, and backward crossed substitution. One commonality of these rules is that they involve two daughters, one of which is the primary daughter whose left-hand result is the result of the mother (the rule with the X in it) and a subordinate daughter whose result category (i.e. Y) is \gobbled up" in the application of the rule. For the sake of generality I have added two features, P(rimary)-DTR and S(subordinate)-DTR, both of type sign, to the type binary to state generalizations regardless of order on the DTRS list. The ROOT value of the P-DTR is always the same as that of the mother and they also share INDEX and MODE values, since the mother and P-DTR share result categories. These constraints can be seen on (84b). The type hierarchy under binary is shown in (89):
50
(89)
binary comp
appl forw-appl
back-appl
forw
comp-1
back
comp-2
forw-comp-1 back-comp-1 forw-comp-2
back-cross-subst back-cross-subst-1 back-cross-subst-2
The two types forward and backward are supertypes of all rules, and simply do the linking of P-DTR and S-DTR to the appropriate elements on DTR and setting slashes where applicable, with the following constraints: 2
3
6 6 6S-DTRD2 4
7 7 7 5
(90) (a) forward := binary & P-DTR 1SS j CAT j ACTIVE D/[]E 7 6 DTRS 1 , 2
E
2
3
6 6 6S-DTRD2 4
7 7 7 5
(b) backward := binary & P-DTR 1SS j CAT j ACTIVE /l Dn[]E 6 7 DTRS 2 , 1
E
The default constraint on backward is to allow back-crossed-substitution to implement crossed rather than harmonic slashes while everything else is harmonic. The additional types composition and application are mother types of all composition and application rules. Looking rst at application, the mother type application has the following constraints: 3 2 X 7 6 S-DTR j SS Y 6 337 2 2 7 6 7 6 RESULT X 7 6 7 7 6 h i 6P-DTR j SS 6 4CAT 4ACTIVE ARG Y 557 5 4
(91) application := binary & SS j CAT
This rule simply says the primary daughter is of the form XjY, the S-DTR has the SS of Y, and the result is X. The type forward-application inherits constraints from both forward and application to de ne a rule as in (92a), as shown in (92b) with full inherited constraints: (92) (a) X/Y Y ) X (b) forward-application := forward & application &
51
2 3 A B ORTH 3 2 6 7 3 6 7 ROOT 6 7 7 6 6 7 X CAT 2 7 6 6 7 3 7 6 6 7 7 INDEX t SS 6 6 7 7 6 6 7 77 6SEM 6 4 6 7 MODE 4 5 5 4 6 7 6 7 C D RESTR 6 37 2 6 7 6 7 ORTH A 6 377 2 6 6 7 3 7 6 ROOT 6 7 7 6 6 7 3 2 7 6 7 6 6 7 X 7 6 RESULT 7 6 6 7 6 77 h 7 6 6 6 7 i 7 6 CAT 7 6 6 7 5 4 7 6 Y 7 6 ACTIVE / ARG 6 7 1 P-DTR 7 6 7 6 6 7 SS 6 7 7 6 6 7 3 2 7 6 7 6 6 7 7 6 7 6 INDEX t 6 7 7 6 7 6 6 6MODE 4 7 777 6 6 6 SEM 5 4 5 4 57 4 6 7 6 7 C RESTR 6 7 6 7 3 2 6 7 A ORTH 6 7 6 7 h i 5 S-DTR 24 Y 6 7 SS SEM j RESTR D 6 7 6 7 D E 4 5
DTRS 1 , 2
This rule looks hideous but it merely incorporates the application and directionality constraints of application and forward with the more general binary constraints on semantics and orthography to generate the rule in (92a). The instantiation of this rule in this implementation is forward-application-rule, inheriting from forward-application but adding no additional constraints. An example use of this rule is given in (93).
52
(93)
2 forward-application-rule D E 6 5 \loves", 6 \Kim" 6 ORTH 6 2 6 6 ROOT 3 6 6 6 CAT X 6 6 2 6 6 6 INDEX t 6 6 6 6 6 6 MODE 4 6 SS 6 6 6 6 6 * 2RELN r love3 6 6 SEM 6 6 6 6 7, 6RESTR 86 6 6 4ARG1 i 5 4 4 4 ARG2 j
3 7 7 37 7 7 7 7 7 7 377 7 7 7 7 7 7 7 7 7 7 2 3+777 7 7 RELN r name 77 7 7 7 6 7 7 94NAME \Kim"5 57 57 5 INSTANCE j
2 3 word D E 6 7 6 7 ORTH 5 6 37 2 # " 6 7 6 7 RCAT s 6 7 3 ROOT 7 6 6 7 7 6 FEATS s-features 6 7 7 6 6 2 377 6 6 7 6 6 7 RESULT X (SnNPi ) 7 7 6 6 6 777 h i 6 6 CAT 4ACTIVE / ARG Y 577 6 7 SS 6 7 6 6 7 7 6 6 7 3 2 7 6 6 7 7 6 6 7 INDEX t 7 6 6 7 7 6 7 6 6 7 7 6MODE D4 prop 7 6 6 SEM E5 4 57 4 4 5
3 2 word D E 7 6 7 6 ORTH 6 6 2 37 7 6 6 ROOT j FEATS j CASE acc 7 7 6 6 7 7 6 CAT 2np 6 7 6 3 77 6 7 6 7 7 6 INDEX j SS Y 6 6 7 7 6 6 7 6 7 6 MODE ref 7 77 6SEM 6 6 D E 4 5 57 4 5 4
loves
Kim
RESTR LIST 9
RESTR 8
The composition rule works similarly, with two separate composition rules have to deal with valences of one or two (as per the generalized forward composition rule in x2.1). These are represented by the types composition-1 and composition-2. The constraints on the composition types without directionality are: (94) (a) composition := binary &
2 ##+3 *" " ROOT 1 7 6 P-DTR j SS j CAT j ACTIVE ARG 7 6 2 SEM 7 6 7 6 " # 7 6 7 6 5 4S-DTR j SS ROOT 1
SEM 2
(b) composition-1 := composition &
53
2 2 3 33 2 RESULT DX E 6 7 55 SS 4CAT 4 6 7 ACTIVE Z 6 7 6 7 6 7 3 2 3 2 6 7 RESULT X 6 777 6 6 6 7 i h P-DTR j SS 4CAT 4 6 Y 557 ACTIVE ARG j CAT 6 7 6 7 6 7 2 2 33 6 7 6 7 Y RESULT D E 6 7 55 4S-DTR j SS 4CAT 4 5
ACTIVE Z
(c) 2composition-2 := composition &
3 2 2 333 2 X RESULT 7 6 D E577 6 6 RESULT 4 7 6 7 7 6 6 Z ACTIVE 7 6 7 7 6 6 SS 6CAT 6 7 6 7 7 E D 7 6 55 4 4 7 6 ACTIVE $ 7 6 7 6 7 6 2 2 3 3 7 6 RESULT X 6 777 7 6 6 6 h i P-DTR j SS 4CAT 4 6 Y 557 7 ACTIVE ARG j CAT 6 7 6 7 6 2 2 3 3 7 6 2 3 7 6 Y RESULT 7 6 D E 6 6 7 7 7 6 4 5 RESULT 6 6 7 7 6 ACTIVE Z 77 7 6 6 6 CAT S-DTR j SS 6 6 77 7 6 D E 4 4 55 7 5 4
ACTIVE $
The constraints on composition ensure that the root and semantic information of the subordinate daughter match the single argument of the primary daughter (note that it is not as simple as associating the entire synsem s as for application, since the valence of the subordinate daughter and the thing on the ACTIVE list of the primary daughter may be di erent). The type composition-1 essentially xes the valence of the subordinate daughter to 1 element, Z, and associates the argument of the primary daughter with the result of the subordinate daughter (i.e. Y; note that Y may itself be complex). The type composition-2 xes the valence of the subordinate daughter to two elements, Z and $, itself only one argument, and associates the argument of the primary daughter with the RESULT j RESULT of the subordinate daughter. In both cases the RESULT of the mother is the RESULT of the primary daughter and the remaining arguments of the subordinate daughter (Z and possibly $) are the arguments of the mother. The resultant rules, when combined with directionality, have the constraints in (95) (the CCG notation rule is shown as well for clarity): (95) (a) X/Y Y/Z ! X/Z & forward & forward-composition-1 := composition-1 D E
S-DTR j SS j CAT j ACTIVE /[]
(b) YnZ XnY ! XnZ 54
backward-composition-1
:= composition-1 & backward & D E
S-DTR j SS j CAT j ACTIVE n[]
(c) X/Y (Y/Z)/W ! X/Z/W forward-composition-2 := composition-2 &33forward & 2 2 D E
/[] 77 6S-DTR j SS j CAT 6RESULT Dj ACTIVE E 55 4 4 ACTIVE /[]
The corresponding instantiations of these types, which introduce no additional constraints, are forward-composition-rule-1, forward-composition-rule-2, and backward-compositionrule-1 (note there is no generalized backward composition rule). The fully de ned feature structure for forward-composition-rule-2 is given in (96). 3 2 B 3 7 6 3 7 6 ROOT 7 6 2 2 337 6 7 6 7 6 X RESULT 7 6 7 6 7 6 E D 7 6 4 5 7 6 RESULT 7 6 7 6 7 6 Z ACTIVE 7 6 7 6 CAT 6 7 6 7 6 77 6 E D 7 6 5 4 7 6 SS 7 6 $ 7 6 ACTIVE 7 6 7 6 7 6 2 3 7 6 7 6 7 6 4 7 6 MODE 7 6 7 6 7 7 6SEM 6 7 6 4INDEX t 5 5 4 7 6 7 6 RESTR C D 7 6 7 6 2 3 7 6 A ORTH 7 6 2 3 7 6 6 7 7 6 3 ROOT 6 7 7 6 6 7 3 2 6 7 7 6 6 7 X 6 7 RESULT 7 6 6 7 6 7 6 2 2 33+7777 6 6 6 7 6 * 6 7 6 6 7 ROOT 1 7 7 6 6 7 7 6 6 7 CAT 7 6 7 6 6 7 6 7 7 6 6 7 Y 6 ARG ACTIVE CAT 4 4 55 5777 P-DTR 56 6 4 7 6 6 7 SS 6 7 7 6 SEM 2 6 7 6 7 7 6 6 7 6 7 7 6 2 3 6 7 6 7 7 6 6 7 6 7 4 MODE 7 6 6 7 6 7 6 6 7 6 6SEM 4INDEX t 5 77 7 6 4 4 557 7 6 7 6 RESTR C 7 6 7 6 3 2 7 6 ORTH B 7 6 2 37 7 6 6 7 6 1 7 6 ROOT 7 6 7 6 2 3 3 2 6 7 7 6 7 6 6 7 7 6 Y RESULT 7 6 6 7 7 6 6 D E5777 6 4 6 RESULT 7 6 7 6 6 7 7 Z 7 6 66 6 ACTIVE S-DTR 7 7 CAT 6 6 7 7 6 7 6 SS 6 7 6 7 7 6 D E 6 4 577 6 7 6 7 6 $ ACTIVE 6 7 7 6 7 6 6 7 7 6 7 6 h i 4 5 7 6 5 4 7 6 2 D SEM RESTR 7 6 7 6 D E 5 4
A (96) ORTH 2
DTRS 5 , 6
55
If you didn't think that was grotesque enough, here is an example of this working: (97)
2 forward-composition-rule-2 E D 6 6 12 13 \quickly", \give" ! ORTH ! 6 6 2 6 3 ROOT 6 2 33 2 6 6 6 X 6 RESULT 6 6 D E57 6 6 RESULT 4 6 6 6 Z 7 ACTIVE 6 6 7 CAT 6 6 6 7 6 D E 6 4 5 6 6 6 ACTIVE $ 6 6 6 6 2 6 6 SS 6 INDEX u 6 6 6 6 6 MODE 4 6 6 6 6 6 6 6 6 6 * 2RELN r quickly3 6 6 SEM 6 6 6 6 6 7, 6 6 6 5 6 6RESTR ! 84ARG-S t 6 6 4 SIT u 4 4
3 7 7 7 37 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 37 7 7 7 7 7 7 7 7 7 7 3 777 2 7 7 7 RELN r gives +7 7 7 7 7 6 7 7 7 ARG1 i 7 6 7 7 96 ! 7 7 7 7 5 557 4ARG2 j 7 5 ARG3 k
2 3 word D E 6 7 6 7 12 ORTH ! ! 6 2 37 6 7 " # 6 7 RCAT s 6 7 3 6 7 ROOT 6 7 6 7 6 7 FEATS s-features 6 7 6 7 6 7 3 2 6 7 6 7 X (SnNPi ) RESULT 6 7 6 7 6 33+777 2 2 6 6 6 7 * 7 6 6 7 6 7 CAT Y 7 6 6 7 6 7 CAT 7 7 6 6 7 6 6 7 6 11 ACTIVE /4ARG 4SEM 55 577 SS 6 4 6 7 6 7 6 7 ROOT 3 6 7 6 7 6 7 6 7 2 3 6 7 6 7 6 7 6 7 INDEX u 6 7 6 7 6 7 6 7 6 7 4 6MODE D 7 7 6 6 SEM E5 4 57 4 4 5
2 3 word D E 6 7 6 7 13 ! ORTH ! 6 37 2 6 7 6 7 3 ROOT 6 2 3377 2 6 6 7 6 6 7 RESULT DY (SnNPEi ) 77 7 6 6 6 5777 4 6 RESULT 6 7 6 6 6 7 ACTIVE Z /NPj 77 CAT 6 7 6 6 7 7 6 7 6 6 7 E D 5 4 7 6 6 7 $ /NPk SS 6 7 ACTIVE 6 7 7 6 6 7 3 2 7 6 6 7 7 6 6 7 INDEX t 7 6 6 7 7 6 7 6 6 7 MODE D4 7 7 116 6 6 SEM E 5 4 57 4 4 5
quickly
gives
RESTR ! 9 !
RESTR ! 8 !
Some of the constraints in (96) are due to constraints on the words involved. This discussion concludes the implementation of functional application and the CCG combinators composition and substitution.
3.5 Summary
In this section I outlined the representation of categories, semantics, and signs used in this implementation, and outlined the architecture of the grammar. Speci cally, most of the grammatical information is encoded in the lexical type hierarchy, feature constraints and inheritance to capture as many grammatical generalizations as possible. All lexical 56
items are typed as some subtype of lexeme, and in ectional mapping rules turn these into word s, where they may participate in the syntax after undergoing a curry operation to make convert their lexical categorial representation into a syntactic one. The syntactic component is likewise implemented via feature structures using inheritance, and in the preceding section I outlined encodings of application, type-raising, and composition rules. In the next section I'll o er treatments of a wide variety of speci c syntactic phenomenon, mostly in terms of the lexical type hierarchy but I'll also propose to analyze some phenomena in terms of one syntactic rule (backward crossed substitution) and a series of lexical mapping rules that map categories onto categories.
4 Various Syntactic Analyses In this section I will outline the implementation of a variety of syntactic phenomenon employed in this grammar. From here on out I will focus primarily on the syntactic work that these lexical rules and hierarchies do, and not present the representations in as much detail as before. I will mostly suppress the feature structures by not always giving fully instantiated feature structures and showing derivations in terms of trees with categories labeling the nodes and the direction and type of combination shown in parentheses to save space, showing feature structures only when necessary for illustrative purposes and often abbreviating the structures and omitting irrelevant features.
4.1 Coordination
In x3.4 I discussed unary and binary syntactic rules, which serve as implementations of functional application and the combinators discussed in x2.1. In this section I will discuss coordination, as also outlined in x2.1.
4.1.1 General Coordination
Coordination is here implemented as a ternary rule. The type ternary inherits from phrase and has the following subtypes:
(98)
phrase ternary coord
...
t-coord nt-coord s-coord nom-coord
The type coord is the mother-type of all coordination rules, and the types nt-coord and t-coord correspond to coordination of non-type-raised categories and type-raised categories respectively. The separation of these two types of coordination is motivated by the more particular semantics of type-raised categories, something I'll return to when I discuss that 57
type of coordination. Finally, sit-coord and ref-coord correspond to coordination of conjuncts with situational indices and referential indices respectively. The types ternary and coord introduce the following constraints: (99) (a) 2ternary := phrase &
ORTH A B C " " ## 6 6 1 KEY 6 SS SEM 6 RESTR /l D E F 6
6 6 6 # 2ORTH B *" 6 6DTRS ORTH A 6 "KEY 1 , 6 SS j SEM j RESTR /l D 4SS 4
SEM j RESTR /l
3 7 7 7 7 7 7 7 3" #+7 7 #7 ORTH C 7 5, SS j SEM j RESTR /l F 7 5 E
(b) 2coord := ternary &
3 2 2 33 1 RCAT 7 6 " #77 6 6 7 6 7 6 2 ROOT PRED 4 5 7 6 7 6 SS FEATS 7 6 7 6 3 7 6 FORM 5 4 7 6 7 6 4 SEM j MODE 7 6 6 2 2 2 2 3 3 7 7 6 3 3 2 2 3 3 7 6 1 1 RCAT RCAT 7 6 6 6 7 7 *6 6 + " # " # 6 7 7 6 6 6 777 h 777 7 i6 6 6 7 6 2 2 PRED PRED ROOT ROOT 4 4 5 5 6 6 7 7 7 7 7 6 DTRS 6SS 6 , SS j CAT conj , 6SS 6 FEATS FEATS 6 6 77 77 7 6 3 3 FORM FORM 6 6 7 7 6 4 4 5 5 4 4 5 5 7 5 4
SEM j MODE 4
SEM j MODE 4
Like the constraints above on binary and unary, these constraints simply x the phrasal orthography and append the daughter's RESTR lists. The default constraint on the RESTR append will prove useful when analyzing coordination of type-raised categories. The constraints on coord ensure that the middle daughter is a coordinator, and that the two conjuncts are rooted in the same category, and share the same MODE, PRED, and FORM values, something common to all coordination. With these two types in place, I'll look next at the constraints on non-type-raised coordination and type-raised coordination individually.
4.1.2 S and Nominal (Non-Type-Raised) Coordination The constraints on type nt-coord are given in (100): (100) 2nt-coord := coord &# "
3 7 7 7 3 2 2 6 7 2 33 6 7 INDEX k 6 7 7 " " *" " ## 6 ##+ 3 2 6 7 7 6 7 6 7 6 + * 6 7 7 6 7 6 CAT 1 CAT 1 CONJ-INDEX k 777 6 6 7 6 6 , SS DTRS SS , 6SS 6SEM 6 7 7 6 6 7 7 ANDARG1 i 5! 557 RESTR ! SEM j INDEX i 6 SEM j INDEX i 7 4 6 7 4 4 5 4 4 5 ANDARG2 j
CAT 1 SS 6 SEM j INDEX k 6 6
58
The syntactic constraint is simply that the two conjuncts must have the same category. The semantic constraints here create a new index for the conjoined entity, k, and predicate the coordinator's key predicate over the indices of the conjuncts, i and j . In general, this is the semantic approach taken to coordination in this implementation, namely that coordination always creates a new index to represent an aggregate entity comprised of the conjuncts. This seems intuitively incorrect (for instance, it doesn't appear to capture distributed readings) and is in fact necessitated by LKB-internal considerations (for instance there is no predicate copying operation that would allow for predicating over multiple indices). However, following typical MRS approach, the semantic representation generated here is not intended to be fully speci ed, but rather is a compact representation from which something more interested in the ne tuned semantics may unpack various readings. In this sense the representation adopted here is meant to indicate simply that a coordination has occurred, and from this representation it may be inferred that either a collective or distributed reading may be possible, so that this representation does not actually represent a collective reading only. Turning now to S and nominal coordination, the constraints on ref-coord and sit-coord are given in (101): (101) (a) 2ref-coord := nt-coord2 &
3
AGR pl 6 6CASE 1 7 6 SS j ROOT j FEATS 5 4 6 6 2 LEX 6
6 ## *" " " 6 E " D C CASE 1 6 4DTRS SS j ROOT j FEATS , SS j SEM j RESTR ! ref-conj pred ! , SS j ROOT j FEATS 2
LEX
(b) sit-coord := nt-coord &
3 2 2 3 +3 + 2 * * sit-conj pred 6 7 7 6 7 6 6 6 6DTRS [], 4SS j SEM j RESTR ! 4CONJ-INDEX s7 5! 7 5. [] 7 5 4 SIT s
The constraints on ref-coord ensure that the indices are all referential (this is done via a predicate type ref-conj pred that types ANDARG1, ANDARG2, and CONJ-INDEX as ref-index ). Furthermore, CASE and LEX information are uni ed and agreement of the coordinated entity is set to plural. Note that this implicitly implies that all referential coordination is of nominal entities, as is indeed the case in this implementation. The constraints on situational coordination likewise set all indices to be of type sit-index, and also x the situation index of the conjunct predicate to be the same as the conjoined index; no feature uni cation is necessary beyond the FORM and PRED uni cation in coord. Note that by unifying the categories in their entirety, all linking of shared arguments is done automatically. Thus a derivation like (102a) is possible yielding the semantics in (102b):
59
L
(102) (a)
S (>) s
S (= s
and(w;x))
S /NP (>B) w
(S nNP )/NP
NP
cooks
w
i
i
(b)
k
k
S /NP (>B) pizza
CONJ
k
S /(S nNP ) ()
nNPj )
2 sem-struct 6MODE prop 6 6 KEY 1 6 6 INDEX s 6 3 2 6 6 * 6RELN r name 7 6 6 6INSTANCE i 7 6 7, 6RESTR ! 6 4NAME \Kim"5 4 SIT t
NP
S (S
j
inf
Sandy
inf
nNPj
(>)
nNPj )/(Sbse nNPj )
to
2 32 3 RELN r expect RELN r name 6INSTANCE j 7 6ARG1 i 7 7 7 16 6 6 7, 6 7, ARG-S u NAME \Sandy" 4 54 5 SIT s SIT t
S
bse
nNPj
leave
3 7 7 7 7 7 7 3 +7 2 7 RELN r leave 7 7! 7 16 5 7 4ARG1 j 7 5 SIT u
The only di erence between equi and raising is whether or not the controlling verb assigns a semantic role to the controlled argument, following typical HPSG approach (cf. Steedman (1996) who de nes a binding theory based on predicate argument structure that involves a di erent treatment of control).
4.3 Unbounded Dependencies
The treatment of unbounded dependencies (UBDs) in CCG more or less falls out of the composition and type-raising rules, dependent on speci c categories of elements that license UBDs. In this section I'll present analyses of a handful of UBD types.
4.3.1 Topicalization The only speci c form of unbound dependency the Sag and Wasow textbook deals explicitly with is topicalization, which they analyze in terms of a special grammatical rule called the Head Filler Rule and a feature GAP to pass extracted arguments from daughter to mother. The CCG approach to topicalization generally requires only additional category assignment to topicalized arguments, namely assignment of the category S/(S/X), where X is an argument type, to something in sentence initial position. In this implementation I simply treat topicalization as a special kind of type-raising: (120) X ) S/(S/X) top-type-raising := type-raising &
69
2 2 33 3 2 INDEX t 7 6 3 7 6 6 7 6 * 2RELN r topic + 7 7 6 7 6 7 6 7 6 7 SEM 6 7 6 7 6 7 6 7 6 A SIT t ! RESTR ! 7 6 5 4 7 6 5 4 7 6 7 6 7 6 7 6 ARG1 i 6 7 6 377 2 7 6 6 7 6 7 6 RESULT s 7 6 7 6 7 6 7 6 7 6 3 3 2 2 7 6 7 6 7 6 ROOT j FEATS j FORM n 7 6 7 6 7 6 7 6 7 7 7 6 6 6 7 6 SEM j MODE prop 7 6 7 7 7 6 6 6 7 6 7 6 7 7 6 6 6 7 6 33 77 777 2 2 6 7 6 6 6 6 1 CAT 7 6 7 7 7 6 6 6 7 SS 6 7 6 7 7 6 6 7 6 7 6 7 7 6 6 2 7 SEM 6 7 7 7 6 6 6 7 6 7 7 6 6 7 6 7 7 7 6 6 6 7 6 3 2 7 7 6 6 2 3 7 6 7 7 6 6 6 7 6 + * 7 7 6 6 COUNT 4 77 77 777 6 7 6 6 6 6 6 6 CAT 6 7 7 7 6 6 6 7 6 7 6 7 7 6 +7 *6 6 5 7 7 ANA ARG 6 ACTIVE / 7 7 7 7 6 6 6 6 7 6 7 7 6 6 6 7 7 6 7 7 7 7 6 6 6 6 7 6 7 7 6 6 6 7 7 6 6 7 7 7 7 6 6 6 6 6 CAT.ACTIVE /6ARG 6 PRED 7777 77 77 6 6 7 6 6 6 6 7 6 7 7 6 FEATS 6 6 7 7 6 7 6 7 7 7 6 6 6 6 7 7777 77 77 6 6 6 ROOT 6 CASE 6 6 6 7 6 7 6 7 7 6 6 6 7 7 6 7 7 7 7 6 6 6 6 7 6 7 6 6 4AGR 8 577 7 6 7 7 7 6 6 6 6 7 6 7 7 6 6 7 6 7 7 7 7 6 6 6 6 6 7 77 77 6 6 9 57 FORM 6 7 6 6 6 7 6 4 5 5 4 4 7 6 6 6 55 577 4 4 4 7 6 5 4 3 RCAT 7 6 7 6 7 6 3 2 2 7 6 3 7 6 CAT 1 " 7 6 # 7 6 7 6 6 7 7 6 7 6 6 7 INDEX t 7 6 7 6 6 7 SEM 2 7 6 7 6 6 7 A RESTR 7 6 7 6 6 7 7 6 7 6 3 2 6 7 7 6 7 6 6 7 RCAT 3 7 + *6 7 6 6 7 7 6 3 2 7 6 7 6 6 7 7 6 4 7 6 COUNT 7 6 6 7 DTRS 6SS 6 7 7 6 7 6 7 7 6 7 6 7 6 5 7 6 ANA 6 7 7 6 7 6 7 6 7 6 6 7 7 6 7 6 7 6 7 6 6 7 6 PRED ROOT 7 6 7 6 7 6 7 6 6 7 FEATS 6 7 7 6 7 6 7 6 6 7 7 7 CASE 6 7 6 7 6 6 6 7 77 6 7 6 7 6 7 6 6 7 7 6 4 5 4 8 AGR 7 6 555 4 4 5 4
FORM 9
This is a type-raising rule like any other that restricts its output to be of category S/(S/X), where X is restricted to basic argument types by a constraint on type-raising, and S must be nite and propositional (to prevent topicalization in, for instance, yes/no questions such (cf. *Kim did John see? ). The hideous part of this rule is in the features, where all of the features except LEX are explicitly co-identi ed. This is because the result of topicalization (as will be seen later when discussing extraction of subjects from CPs) needs to be underspeci ed for LEX, so the entire SS of the DTR cannot be uni ed into its place in the mother since this would also unify in an unwanted value for LEX. This is again an LKB issue, since the LKB doesn't allow for generalization, only uni cation. Note that it is also impossible to state sentence initial constraints in the LKB, so this rule acts just like any other type-raising rule in its application. An example derivation is in (121):
70
(121)
S (>) S/NP (>B)
S/(S/NP) (Top) NP
S/(SnNP) (B) SnNP/PP (>)
NP
SnNP/PP/NP
Kim
put
PP/NP NP
on
the book
The semantic constraints on type-raising, that the type-raised entities are co-identi ed with the arguments on the type-raised and thus share SEM values, combined with the uni cation of the arguments of the type-raised categories with the arguments of verbal projections ensures correct linking of the semantics. In particular, the semantics of the above derivation is shown in (122):38 3 2 7 6 INDEX s 7 6 7 6 2 3 7 6 put RELN r 7 6 3 2 6 7 6 " # " # RELN r name 6ARG1 j 7 7 6 RELN r the RELN r table 6 7, 6ARG2 k 7 7 7 6 ! INSTANCE j , , 7 6 56 4 * BV m INSTANCE m 6 7+7 6 7 6 NAME \Kim" 4ARG3 i 5 7 7 6 RESTR 7 6 SIT s 7 6 3 2 7 6 " #" # RELN r on 7 6 7 6 RELN r the RELN r book 6 7! 7 6 INSTANCE i , , 5 4 5 4 BV k INSTANCE k ARG1 m
(122) MODE prop
For the remainder of this discussion I'll only give the full MRS semantics of each derivation where relevant, otherwise I'll assume the lexical linking combined with appropriate uni cation generates the expected semantics.
4.3.2 Right Node Raising One form of unbounded dependency that was not treated in the Sag and Wasow textbook (and to my knowledge has no known satisfactory analysis in HPSG in general) is that of Right Node Raising (RNR). However, one of the major pluses of CCG is that a treatment of RNR simply falls out of the interaction between type-raising, composition, and coordination, and therefore this implementation extends the Sag and Wasow fragment considerably, producing analyses like those shown in x2.1 in (10), repeated here as (123): 38 I'm suppressing the SIT variables except where relevant, as their use is not worked out in the textbook
or either this or the HPSG implementation.
71
(123)
S (>) NP
S/NP (1 ) S/NP (>B)
S/NP (>B)
CONJ
S/(SnNP) () NP (>)
(SnNP )
i
NP /N i
the
N /N /(S i
i
inf
N (>) slept
i
i
N /N (>B) i
N
i
SnNP/NP (>B)
nNP/NPi )
easy
i
i
cat
(SnNP)/(SnNP)
(SnNP)/NP
to
please
i
The predicative uses of tough -adjectives will be discussed in x4.4.7.
4.4 More Analyses
The three main focus areas of this implementation were coordination, control, and unbounded dependencies, which were described above in x4.1-x4.3. In this section I will go over the treatment of various other syntactic phenomenon also addressed here.
4.4.1 Passive The treatment of passives adopted here involves only a lexical mapping rule, following the Sag and Wasow approach. This lexical rule simply permutes the argument structure of the lexical item and xes some morphological features of the root features. However, to get all of the possible argument structure possibilities correct (including the various argument 82
structures that may passivize and whether the output has the optional by -phrase) it is necessary to create a small type hierarchy for passive rule types: (146) lmap-rule passive passive-by
passive-no-by
passive-tv
passive-xtv
passive-tv-by
passive-xtv-no-by
passive-tv-no-by
passive-xtv-by
...
The types passive-by and passive-no-by are supertypes for passive rules that do and don't introduce by -phrases respectively, and the types passive-tv and passive-xtv are for passive rules that do and don't operate on strictly transitive verbs and transitive verbs with an extra complement (e.g. ditransitives). The constraints on these types are given in (147): (147) SnNPi&ref ?index/$1 /Xj ) SnXj /$1 (/PPby;i ) 3 2 33 2 (a) passive := lmap-rule & 2 s-features 7 6 7 6 6 7 6 7 6 FORM pas 7 7 6 7 6 7 6 ROOT j FEATS 7 6 7 6 6 4PRED true57 7 6 7 6 7 6 7 SS 6 AUX 1 7 6 7 6 7 6 2 3 7 6 7 6 7 6 RESULT s 7 6 6 D E5 7 7 6 4 5 4 CAT 7 6 ACTIVE nNP, ... 7 6 7 6 6 3 3 2 2 3 7 2 7 6 7 6 FORM pfp 7 6 7 6 6 6PRED false77 6 7 7 6 6 ROOT j FEATS 577+7 4 *6 6 7 6 7 6 7 7 6 6 2 AUX 7 6 7 SS 6 DTRS 6 7 3 7 2 6 7 7 6 6 D E 7 6 7 7 6 6 7 6 ACTIVE n NP, [] , ... 7 7 6 6 5 4 6 55 7 4 4CAT 5 4 RESULT s 2
3
6 * 6 D E+ 6 4DTRS SS j CAT j ACTIVE []i , ...
7 7 7 5
(b) passive-by := passive & SS j CAT j ACTIVE [], /PP hFORM f byi, ... i 6 7 (c) passive-no-by := passive & 2
* "
#+
3
RELN r a 6 SS j SEM j RESTR ! ! A7 6 7 BV i & ref-index 6 7 6 D E33+ 6 *2 2 6 CAT j ACTIVE [] , ... i 6DTRS 4SS 4 55 4
SEM j RESTR A
3 7 * 6 E+7 D 7 6 4DTRS SS j CAT j ACTIVE [], /NPi 5 2
(d) passive-tv := passive & SS j CAT j ACTIVE D[]i , ...E 6
83
7 7 7 7 5
2
3 7 * 6 E+7 D 6 7 4DTRS SS j CAT j ACTIVE [], [], /NPi 5
(e) passive-xtv := passive & SS j CAT j ACTIVE D[]i , ...E 6
(f) passive-tv-by := passive-tv & passive-by & SS j CAT j ACTIVE D[], []E (g) 2passive-xtv-no-by :=Dpassive-xtv & passive-no-by & 3 E SS j CAT j ACTIVE [], 1 7 6 * 6 D E+7 7 6 4DTRS SS j CAT j ACTIVE [], 1 , [] 5
(h) passive-tv-no-by := passive-tv & passive-no-by & SS j CAT j ACTIVE D[]E (i) 2passive-xtv-by := passive-xtv & passive-by & 3 E D SS j CAT j ACTIVE [], [], 1 7 6 * 6 D E+7 7 6 4DTRS SS j CAT j ACTIVE [], 1 , [] 5
The passive rule takes a past perfect, non-predicative input and produces a predicative passive output, where both the input and output must have NP subjects (recall that CPs, which may passivize as well, are treated as NPs here). The type passive-by ensures that the nal complement is a by -phrase coindexed with the subject of the input, and the type passive-no-by simply adds existential semantics to the subject of the input which is not overtly realized. The type passive-tv de nes the input as a simple transitive and the type passive-xtv de nes the input as a two complement transitive, where the direct object (the rst picked up) is always an NP. The maximal types simply x the valence of the output with or without the by -phrase, and ensuring for double complements that the non-passivized second complement appears on the ACTIVE list of the mother wholesale. The actual rules, passive-tv-by-1, passive-tv-no-by-1, passive-xtv-by-1, and passive-xtv-no-by-1 inherit from these types with no additional constraints. A sample analysis of a use of passive-xtv-by is shown in (148): (148) S ()
NP
j
j
Kim
SnNP (>)
(SnNP )n(SnNP ) j
j
j
j
i
NP
k
SnNP /NP /NP i
k
i
i
SnNP /PP /NP (passive-xtv-by ) j
PP (>)
SnNP /PP (>)
was
k
a book
j
given
84
P /NP
NP
by
Sandy
i
i
i
4.4.2 Imperatives
The treatment of imperatives is again by lexical rule, and this is another point of di erence between the HPSG grammar, which does this as a syntactic rule. The imperative lexical rule simply xes appropriate agreement and morphological features of the subject and verb and eliminates the subject of a verbal category. The constraints on this rule are given in (149): (149) 2Sbase;prop nNP2per ) Sfin;dir imper := lmap-rule & 3 2
3 2 s-features 6 7 6 6 6 7 6 AUX 1 7 7 6 6 7 6 ROOT j FEATS 7 6 6 7 6 FORM n 5 4 6 7 6 6 SS 7 6 PRED false 6 7 6 6 # " 7 6 6 6 RESULT s 7 6 5 4 SEM j MODE dir CAT 6 A ACTIVE 6 6 6 2 2 " # 6 1 6 AUX 6 6 6 ROOT j FEATS 6 6 6 FORM base 6 6 6 *6 6 6 6 SEM 2j MODE prop 6 SS 6 DTRS 6 6 6 6 6 6 RESULT s 6 6 6 6 6 6 6 CAT 6 4ACTIVE backslashNPhAGR 2peri 4 4 4
3 7 7 7 7 7 7 7 7 7 7 7 7 7 33 7 7 7 7 7 7 7 7 7 7 7 +7 7 7 7 7 7 7 37 7 7 7 7 7 7 7 7 777 7 7 5 5 5 A 5
This rule takes a base form SnNP$, sets the subject agreement to second person (which would be relevant for binding theory) and drops the subject from the active list, xing the verb's form as nite and non-predicative so it satis es the root condition. Furthermore, the semantics of the mother is [MODE dir(ective)] while the daughter's is propositional, following the approach in Sag and Wasow's grammar. An example imperative is given in (150): (150)
S (>) S
/NP (imper )
NP
S
nNP2per /NP
pizza
f in;dir
bse;prop
eat
Note that this rule is not restricted to verbs, and in fact shouldn't be. Anything of the category SnNP$ may undergo this rule, a desirable result since modi ers are functors and as such may functionally head sentences that are imperatives. An example application to a modi er is shown in (151):
85
(151)
S (>) S
f in;dir
(S
/(S
bse;prop
bse;prop
nNP)
S
(imper )
bse;prop
nNP2per )/(Sbse;prop nNP)
S
bse;prop
quickly
nNP
(>)
nNP2per /NP
eat
NP pizza
4.4.3 Bare Plurals/Mass Nouns The analysis of bare plurals and mass nouns is quite similar to the analysis of imperatives in that anything that can ultimately head a bare NP (including relative clauses, adjectives, etc.) may undergo the rule. The rules for bare plurals (bare-pl-n ) and mass nouns (baremass-n ) share a common supertype, bare-nom. The essential idea is that a category of N$1 (e.g. N, NnN, NnN/(S/NP), etc.) is mapped to a category of type NP$1 . The constraints on these are given in (152): (152) N$1 ) NP$1 (a) bare-nom := lmap-rule & 2
3 2 3 1 np ROOT j RCAT " #7 6 7 6 7 6 1 RESULT SS 4 5 7 6 CAT 7 6 ACTIVE A 7 6 6 2 2 3 7 7 6 3 6 * ROOT j RCAT n # +77 6 " 6 6 6 77 7 7 6DTRS 6 4SS 4CAT RESULT n 55 7 5 4
ACTIVE A
2 3 7 6 4DTRS hSS j ROOT j FEATS j AGR pli 5 3 2 bare-mass-n := bare-nom 7 6 4DTRS hSS j ROOT j FEATS j COUNT falsei 5
(b) bare-pl-n := bare-nom (c)
The type bare-nom captures the basic N$1 ) NP$1 insight, and the two instantiations of this type x speci c properties related to plurals and mass nouns (although I don't o er a treatment of their semantics here, presumably an important reason for separating the two rules). Two example bare plural NPs, one with a modi er and one without, are given in (153):
86
(153)
(a)
(b)
NP (>) pl
PP
NP /PP (bare-pl-n ) pl
N /PP
NP N
pictures
() it
it
SnNP /XP it
f in;s
SnNP
(extraposition )
S
f in;s
Kim left
f in;s
sucks
Recall that the dummy it has a special index it-index and as such may not have any referential role assigned to it. Thus the output of this rule may not passivize, since the 88
by -phrase for the passive has an argument structure wanting a index of type ref-index ) (cf. *That Kim left was sucked by it ). Notice, however, that the output of this rule is now eligible to undergo the extractable-subject rule, yielding derivations as in (158):
(158)
S (>) S/NP?
S/(S/NP ) (Top )
LEX;i
i
(>B)
Kim S/(SnNP ) (>T)
SnNP /NP?
it
it
it
SnNP /NP? it
LEX;i
/(S
f in;s
SnNP /XP it
f in;s
SnNP
LEX;i
/NP ) (ext-subj ) i
(extraposition )
(>) S
f in;s
/NP
i
left
f in;s
sucks
4.4.6 Auxiliaries and the NICE Properties
Auxiliaries in English undergo four syntactic operations unique to them: negation, inversion, contraction, and ellipsis, the so-called NICE properties. In this implementation, negation, inversion, and ellipsis are implemented in terms of lexical mapping rules, whereas contraction is implemented via an in ectional rule. Looking rst at contraction, the in ectional rule contracted-verb in rule inherits from v-morph-in -rule : & (159) 2contracted-verb in rule := v-morph-in -rule 3 2 2 MODE prop 6 6 6 INDEX s 6 6 6 6 2 3 6 6 6 * 6 RELN r not + SEM 6 6 6 6 6 7! 6 6RESTR ! 6 6 4SIT s 6 5 4 6 SS 6 6 6 ARG-S t 6 6 6 6 6 6 6 6ROOT j FEATS jh AUX true i 6 4 6 CAT j ACTIVE CASE nom , ... 6 6 6 *" " ##+ 6 6 4DTRS SS j SEM INDEX t
RESTR A
33 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 A7 7 57 7 7 7 7 7 7 7 7 7 7 77 57 7 7 7 7 7 7 5
This rule operates only on [AUX true] items, and essentially just inserts negation semantics on the RESTR list of the daughter, xing the index value so that the argument of the negation is the daughter's index and the new index of the mother is the situation of the negation40 , as well as assigning nominative case to the subject and xing the morphological 40 This doesn't work, it results in the uni cation of the two indices since the LKB tries to simultaneously
inherit the daughter's semantics and replace it with a new one that just happens to unify. This is an LKB problem, in my opnion.
89
form (note that no morphological mapping rules are supplied; all contracted forms are listed as irregulars in irregs.lsp). The other three NICE rules are subtypes of a type nice-aux :41 (160)
lmap-rule nice-aux
...
inv-aux neg-aux ellipsis
The constraints on these types are given in (161): (161) (a) nice-aux := lmap-rule & 2
3 7 7 7 *" #+ 6 D E 7 6 7 4DTRS SS j CAT RESULT s, ACTIVE nNP, ... 5 "
ROOT j FEATS j AUX true SS 6 6 CAT j RESULT s 6
#
(b) "inv-aux := nice-aux & "
# h i # ROOT j FEATS j FORM n SS , DTRS SS j SEM j MODE prop SEM j MODE ques
(c) (SAUX + nNPi )/ (SnonfinnNPi ) ) (SAUX + nNPi )/ (Snonfin nNPi )/ADVnot negation := nice-aux & 2
33 2 ROOT j FEATS j FORM n 2 7 6 6 2 33 7 7 6 7 6 ROOT.FEATS.PRED false 7 6 7 6 6 7 7 6 6 7 7 6 6 7 7 6 6 7 7 6 2 2 / S n CAT S n 6 7 7 6 6 7 7 6 6 7 + * 7 6 2 3 6 7 7 6 6 7 7 6 6 7 7 6 INDEX s 6 7 7 6 6 7 7 6 SS 6CAT j ACTIVE 1 , 2 / SjX, /6ARG 6 7 2 3 7 6 6 7 7 7 6 7 * + 7 6 6 7 6 7 7 6 not RELN r 6 7 7 6 7 6 7 7 6 SEM 6 6 7 6 7 7 6 6 7 6 7 7 6 RESTR ! ARG-S t ! 6 7 4 5 6 4 555 77 6 4 4 7 6 7 6 SIT s 6 77 6 7 6 5 4 7 6 7 6 SEM j INDEX s 7 6 7 6 3 3 2 2 7 6 E + D * 7 6 7 6 1 2 77 6CAT ACTIVE , 7 6DTRS 6 SS 55 4 4 5 4 SEM j INDEX t
(d) (SAUX + nNPi )/ (SnonfinnNPi ) ) (SAUX + nNPi ) 41 The types negation and ellipsis are actually rules (instances) in this grammar, but I'll list them here as types for consistency's sake.
90
ellipsis := nice-aux & 2 2CAT j ACTIVE D 1 E 6 6
3 3 7 6 7 37 2 7 6 6 7 INDEX t 7 6 6 7 7 6 7 6 6 7 7 6 MODE 2 7 6 6 7 7 6 SS 6 7 6 6 7 7 KEY 3 7 6 6 7 7 6 SEM * " # + 6 7 7 6 6 77 6 6 7 7 6 RELN r ellipsis 6 7 5 4 4 RESTR ! 1 B 5 6 7 SIT t 6 7 6 7 6 2 2 33 7 6 7 E D 6 7 6 1 , / SjX A 77 7 CAT RESULT s , ACTIVE 6 6 6 7 6 7 7 6 *6 +7 2 3 6 6 7 7 6 7 6 6 7 7 INDEX t 6 7 6 7 7 DTRS 6 SS 6 7 6 7 6 6 7 7 2 7 MODE 6 7 6 6 6 7 7 6 SEM 6 7 6 6 77 7 6 7 3 5 KEY 4 4 4 5 5 4 5 A
RESTR B
The constraints on nice-aux restrict these operations to only apply to auxiliaries with leftward NP subjects (and thus imposing an ordering on their application, namely that inversion must occur last since it rearranges the arguments). The type inv-aux constrains its input to be nite and propositional and its output to be nite and a question, but will require further subtypes which I'll outline in a moment. The type negation constrains its input and output to be nite and stipulates that the subjects of each are coidenti ed, and inserts an adverb into the argument list in canonical form (SnXP)/(SnXP) with negation semantics, and predicates it over the input's index and associates the mother's index with the negation's situation index, otherewise preserving the argument structure.42 Note that this rule only operates on inputs that have not undergone ellipsis or inversion (i.e. are canonical auxiliaries), thus imposing an ordering on the application of this rule. Note also that the VP argument of the input must have a slash / , in other words the directionality of the slash and the headedness go the same way, to prevent application of NICE rules to pre-verbal adverbs, as discussed in x2.1. An example derivation is given in (162): (162)
S ()
NP
Kim (SnNP)/ (SnNP) (>)
(SnNP)/ (SnNP)/((SnNP)/(SnNP)) (negation ) (SnNP)/ (SnNP)
(SnNP)
(SnNP)/(SnNP) leave not
should
Note that this sentence is structurally ambiguous, as the instance of not could also be a case of non- nite negation, with the following lexical entry for: 42 This doesn't work semantically for the same reason contraction doesn't work above.
91
3 2 E 7 6 7 6 ORTH ! "not" ! 6 37 2 7 6 7 6 ROOT j FEATSDj FORM non n 7 6 E 7 6 7 6 7 6 7 6 CAT j ACTIVE [], /[] 7 6 7 6 3 2 7 6 7 6 SS 6 7 7 6 1 KEY 7 6 6 h 777 6 i 7 6 6 4 4SEM 4RESTR ! 1 RELN r not ! 555
(163) not 1 := iv-adv-lxm D
This entry for not allows for negation of any nite SnNP, and in particular the above sentence has the following derivation: (164)
S
f in
() (SnNP) (>)
nNP)/(Sbase nNP)
should (S
base
nNP)/(Sbase nNP)
not
(S
base
nNP)
leave
For more details on the di erences between the two kinds of negation (most of which is not implemented here) see Warner (2000), Sag (2000). Next, the type ellipsis essentially removes the verbal complement (always the second complement, i.e. the last to be picked up) from the ACTIVE list and instead introduces an elliptical semantics predicated of its index (also the index of the auxiliary). An example derivation is given in (165): (165)
S () i
i
Kim
i
NP
on
S ()
(predicative-mod )
i;pred
(b)
nNPi
(SnNP )/(S
nNPi
is
(S
pred+
i
)
S
pred+
pred+
nNPi )/Ni
nNPi
(>)
(predicative-np1 )
NP
? /N
i;pred
N
i
linguist
i
a
With this analysis of predicatives, the rest of the tough -adjective analysis falls into place. In x4.3.6, I had sketched an attributive lexical entry for tough -adjectives like easy. Since they have the same form as all other attributive adnominals (NjN$) then it may undergo this rule as well, yielding derivations such as: (172) S (>) SnNP (>)
NP
i
i
the cat
(SnNP )/(S i
pred+
is
nNPi )
(S
pred+
(S
pred+
nNPi )/(Sinf nNP/NPi )
N /N /(S i
i
inf
4.4.8 Expletive Subjects
(>) SnNP /NP (>B)
(predicative-mod )
nNPj /NPi )
easy
nNPi )
j
i
(SnNP )/(SnNP )
(SnNP )/NP
to
please
j
j
There is one other aspect of tough -adjectives implemented here, namely expletive subjects as in It is easy to please Kim, which also involve predicative uses of easy. This is again 96
j
i
implemented as a lexical rule, here with the input being a predicative tough -adjective (since expletive subjects do not occur attributively). The rule expl-tough-subj encodes this rule with the following constraints: (173) (Spred+nNPi )/(Sinf nNP/NPi ) ) (Spred+ nNPi t)/(Sinf nNP) := lmap-rule & 2expl-tough-adj 2
3 3 7 6 2 6 33 7 2 7 6 7 6 CAT 2 SnNP 7 6 7 6 7 6 7 6 " " ## + * 7 6 7 6 7 6 7 6 h i 7 6 7 6 FORM inf SS j CAT 6 7 6 7 6 7 7 3 FEATS ACTIVE n NP INDEX it-index , /6ARG 6 ROOT 7 6 7 7 6 7 6 7 6 PRED false 7 6 6 55 7 4 7 6 4 5 4 7 6 4 7 SEM 6 7 6 7 6 3 2 3 2 7 6 1 7 RESULT 6 7 6 6 2 2 2 333 77 6 7 6 7 6 7 6 6 2 RESULT D E 77 77 +7 *6 6 6 7 6 6 6 + * 577 77 7 6 7 6 CAT 4 6 6 h i6 7 6 7 6 ACTIVE /NP SS j CAT DTRS 7 6 6 7 6 7 7 6 7 6 7 ARG ACTIVE n NP INDEX ref-index , 6 6 7 6 7 7 6 7 6 6 6ROOT 3 6 77 77 6 7 6 7 6 4 5 5 4 5 4 6 5 7 4 5 4 SEM 4
RESULT 1 s
The subject argument of the mother is now the expletive it (so chosen by restricting the index to be it-index, which is only satis ed by the dummy it lexical entry), and the single verbal argument of the mother is simply a VP rather than a VP with a /NP second argument, although the semantics and features remain the same. This allows for derivations like the following: (174)
S (>) NP it
SnNP (>)
it
it
(SnNP )/(S it
pred+
nNPit )
(S
is
(S
pred+
pred+
(S
pred+
nNPit )/(Sinf nNPj )
i
i
inf
97
(predicative-mod )
nNPj /NPi )
easy
(>) SnNP (>)
(expl-tough-adj )
nNPi )/(Sinf nNPj /NPi )
N /N /(S
nNPit )
j
(SnNP )/(SnNP ) j
j
to
(SnNP ) (>) j
(SnNP )/NP j
please
i
NP
i
the cat
4.4.9
There
-Insertion
The nal phenomenon covered here are existential there -sentences, which are here derived from non-existential uses of be.45 The analysis essentially derives a category for be as in There are dogs in the garden from the category for be in Dogs are in the garden. The mother type of the mapping rule for doing this is given in (175): (175) (SnNPi )/(Spred+ nNP) ) (SnNPthere)/(Spred+ nNP)/NPi there-insertion := nice-aux & 2
3 33 2 2 LEX true 6 6 7 6 # h +7 * " 7 6 PRED false7 7 6 7 6 i 7 6 1 FEATS AGR 7 6 7 6 6 , 2 / PRED true , /NP6 SS j CAT j ACTIVE nNP 4CASE acc 57, ... 7 7 6 7 INDEX there-index 6 7 6 5 4 AGR 1 7 6 7 6 7 6 3 SEM 7 6 3+ 2 7 6 # + * * " 7 6 1 7 6 AGR 5 4DTRS 4SS j CAT j ACTIVE NP , 2 , ... 5
SEM 3
This type inherits from nice-aux and thus only applies to auxiliaries, and the constraints on this rule shue the arguments a bit, moving the NP subject to the direct object position (and xing accusative case), and inserting a dummy there subject that agrees with the direct object (cf. There are/*is dogs in the garden ) while leaving the predicative second argument in place. That this argument is predicative restricts the application of this rule to just be. Two instances of this rule account for cases of there -insertion with and without a previous negation operation: 3 SS CAT ACTIVE [], [], [] 7 6 7 6 7 6 *" #+ 6 D E 7 7 6 4DTRS SS j CAT ACTIVE [], [] 5
(176) (a) there-insertion-1 := there-insertion & 2
"
D
E#
(b) 2there-insertion-2 := there-insertion & " #
3 6 7 SS CAT ACTIVE [], [], [], 1 6 7 6 7 6 *" " ##+7 6 7 6 7 4DTRS SS j CAT ACTIVE [], [], 1 SnX / SnX 5
D
E
The instance there-insertion-1 simply restricts the ACTIVE list of the input to two elements (the subject and predicative) and the second rule restricts it to three elements (the subject, predicative, and an adverb). An example derivation with there-insertion-1 is shown in (177): 45 The alternative in the Sag and Wasow book is to make this a lexical entry, which would be better if it didn't involve listing all of the in ectional forms in the lexicon as well.
98
(177)
S ()
(>)
(there-insertion )
nNPi )
S NP
pred
nNPi
in the garden
i
dogs
are
This rule is likewise ordered with respect to other operations. It may occur after negation, but must occur before ellipsis (since the type there-insertion requires a predicate on its daughter's ACTIVE list) and it must occur before inversion since the rst argument must be an NP.
5 Eciency One of the biggest problems with CCG in computational terms is that the combinatoric power gives any sentence an exponential number of parses, with both canonical and noncanonical constituent structure. In particular, the combination of type-raising and composition leads to an explosion in the number of parses of a canonically non-ambiguous sentence such as Kim eats pizza, which has ve parses as shown in (178): (178) (b) S (>) (a) S ()
NP
Kim (SnNP)/NP eats S ()
Kim
NP
eats
SnNP (>)
Kim (SnNP)/NP eats
NP pizza
Type-raising and composition allow for a number of non-canonical consitituents to be created, something that is desirable for purposes of non-canonical coordination (such as right node raising and argument cluster coordination), and may well be useful for intonation and information structure, but, especially when these issues are not of concern, this power poses an uneccesary computational burden on the parser. Ideally we'd like to eliminate spurious ambiguities, pruning away the unwanted parses and keeping only parses that represent socalled canonical constituent structures, and only as many of those as will elucidate structural ambiguities. Eisner (1996) shows that for a CCG grammar with application, composition, and substitution, the parse forest associated with each tree can be partitioned into semantic equivalence classes (modulo information structure and possibly quanti er scoping) in which only one \canonical" constituent structure per class. The reason for this is simply that for any \spurious" constituent structure there is always a semantically-equivalent derivation that could have involved a canonical constituent structure. Coupled with this proof, Eisner provides a parsing strategy for a CCG grammar that has application, composition, and substitution that will eliminate all such spurious ambiguity. The implementation here adopts his parsing strategy, updating it to include also type-raising. I won't go into the speci c details of his proof or algorithm46 , but the basic idea is to de ne a CCG Normal Form that all acceptable parses must adhere to. Informally, the normal form is as de ned in (179): (179) CCG Normal Form: Don't compose, substitute, or type-raise unless you have to. Speci cally, composition must not occur when application would have worked, substitution must not occur after lots of composition (i.e. after too many llers have been picked up), and type-raising should only occur when needed for composition (this isn't in Eisner's algorithm, but seems plausible to me). To illustrate these ideas informally with a few examples, you should never compose when an application is possible, so don't do (180a) when you could do (180b): (b) A (>) (180) (a) A (>) A/C (>B) A/B
C
B (>)
A/B
B/C
B/C
C
This restriction can be encoded by simply preventing an application in a certain direction happening when a composition in that direction just happened, because two applications in the same direction would have done. Second, any time you can compose two categories and then have the result be the subordinate daughter of another composition, do this instead of letting the result be a primary daughter. So don't do (181a) when you could do (181b): (b) A/D (>B) (181) (a) A/D (>B) A/C (>B) A/B
C/D B/C
B/D (>B)
A/B B/C
46 Because I didn't understand it.
100
C/D
This can be encoded by preventing the result of a composition in a certain direction from being the primary daughter of a composition in the same direction. Third, type-raising is only necessary when that argument can't be picked up by a function because that function can't pick up an argument higher its argument structure rst. If this assumption is true, then a type-raised category should never be allowed to apply since the function it applies to could have applied to it instead. In other words, don't do (182a) when you could do (182b): (182) (a)
(b)
A (>) A/(AnB) (>T)
A (B (b) bc - output of or < or a lexical item 47 Eisner (1996) also gives a normal form restriction for substitution, but the conditions under which it is
applicable do not arise in this grammar and substitution will have no constraints here.
101
(d) (e) (f) (g) (h) (i) (j)
tr - output of >T or T or B or > or < or a lexical item bc-ot-tr - output of or T or B, > or T or
