Syntax and semantics of complex and ambiguous wh -questions Markus Egg & Anke Feldhaus IBM Deutschland GmbH, Institut fur Logik und Linguistik, Heidelberg e-mail:
[email protected] Universitat Tubingen, Sfb 340 e-mail:
[email protected]
Abstract
In this paper, we present a new approach to the syntax and semantics of wh questions. On the basis of an appropriate type hierarchy whose members model contributions of lexical items to sentence mood, we introduce a head-interrogative schema that licences wh -sentences syntactically and contributes the semantic interrogative operator. This syntactic basis allows the compositional construction of the semantics of multiple wh -questions and the representation of the interaction of universal quanti ers with wh -elements. In addition, an underspeci ed representation of the latter case, where systematic scope ambiguities between universal quanti ers and wh -elements are observed, is proposed. As a semantic representation language for this task we use UMRS (Underspeci ed Minimal Recursion Semantics), a computable meta-language that represents structural ambiguities in terms of underspeci cation.
Keywords: wh -questions, computational semantics, underspeci ed semantic representations, semantic metalanguage
The research presented in this paper was partially supported by the German Ministry for Education and Research (BMBF) under grant no. 01IV101V. The sole responsibility for the content of this report remains with the author.
1 Introduction In this paper, we present a new approach to the syntax and semantics of wh -questions. This approach allows a straightforward analysis of multiple wh -questions and of the interaction of universal quanti ers with wh -elements. Before outlining this approach in detail, we will sketch the standard approach to wh -questions and its problems, which motivated the new analysis. Wh -questions are usually interpreted as the set of all asked propositions. Wh phrases themselves are rendered in terms of existential quanti cation (like inde nite DPs). If propositions are interpreted as properties (i.e., sets of states of a airs), the semantics of a question like (1) is (2), the set of propositions of the type \set of all s such that x gets y at s", if x and y are persons and marks, respectively, in the given individual domain:1 (1) Who got which mark? (2) P 9x1 (person (x1 ) ^ 9x2 (mark (x2 ) ^ P = s get (x1 ; x2 )(s))) This set of propositions contains a proposition for every person in the domain. i.e., there is an implicit universal quanti cation in the semantic representation of wh -questions. Matters are made dicult by universal quanti ers in the wh -sentence. E.g., (3) has not only the reading that asks for the marks such that everyone got them: In the other, the \wh -reading", one wants to know for each person the mark he got, i.e., pairs of persons x1 and marks x2 such that x1 got x2 . This reading is equivalent to the meaning of (1). (3) Which mark did everyone get? However, this reading of (3) cannot be described by a straightforward extension of the standard approach. The only way of expressing in this approach that, in this reading, not every person must have the same mark would be to scope everyone over the wh -element: (4) P 8x1 (person (x1 ) ! 9x2 (mark (x2 ) ^ P = s get (x1 ; x2 )(s))) But (4) denotes the empty set and not the set of propositions P of type s get (a; b)(s) if there is more than one person in the individual domain A (a and b are proper names for persons and marks): While x1 varies over the whole A, a has the xed denotation F (a). Hence, the involved equation between propositions (P = s get (x1; x2 )(s)) is false for every such P as for at least one person en 2 A, en 6= F (a) [Karttunen & Peters 80]. [Karttunen & Peters 80] assume here a syntactic wh -question node Q (with nominal daughter QNP and sentence daughter S ) whose semantics depends on QNP : For wh -QNP, it combines the QNP and S meanings by functional application, for universally quanti ed QNP, it also maps the meaning of QNP onto the corresponding existential quanti cation. But analyses of wh -readings should use a semantically invariant question operator. [Engdahl 86] proposes analysis (5) (simpli ed) for the wh -reading of (3). She represents these readings in terms of functions f in A,2 which are the denotations of wh -expressions. 0
0
0
0
0
0
0
0
(5) P 9f 8x(mark (f (x))) ^ P = s8x(person (x) ! get (x; f (x))) 0
0
0
This technique scopes the universal quanti er above the wh -expression and below the equation between propositions. (5) denotes the set of propositions that every person gets some mark, viz., the mark assigned to him by a suitable function f . This approach captures both the wh- and the \functional" reading of (3) in one single representation. In We assume a Davidsonian verb semantics with an additional argument position for states of a airs or \eventualities". Here and in the rest of the paper we will neglect the semantics of tense and aspect. 2 In fact, functions from sets of individuals to individuals, but here, we only discuss the simplest case. 1
2
functional readings (for (3), such a reading is forced if (3) is answered by The mark he dreaded to get), the asked set of entities is a set of functions that maps the individuals in the universal quanti er's restriction onto individuals that belong to the wh -expression's restriction. Mathematically, this analysis subsumes the wh -reading, as functions can be interpreted as sets of pairs of individuals (as asked for in wh -readings). We agree with Engdahl's analysis of functional readings, but see problems for the subsumption of wh -readings under this analysis. First, the set of propositions in (5) di ers from the set in (2): It isn't the set of propositions of the type \person x1 gets mark x2 at s" but the singleton set of propositions whose member is a conjunction of all propositions of this type. Hence, the equivalence of (1) and the wh -reading of (3) remains implicit. What is more, the generalization of wh - and functional readings glosses over linguistic intuitions: Wh -readings are acceptable straightaway but functional readings are harder to get and have a pun-like avour to them, which clearly distinguishes them from wh -readings in speakers' intuitions. Hence, an analysis of (3) that represents the equivalence between (1) and (3) directly while keeping functional and wh -readings distinct would be preferable. In sum, wh -questions still await a fully general semantic representation. The target is a compositional analysis that captures multiple wh -questions as well as the interaction of wh expressions and universal quanti ers. The ambiguites induced by universal quanti cation in wh -questions should be represented by underspeci cation. This threefold task will be taken up in the HPSG approach to sentence mood as developped in [Feldhaus 96] with the semantic metalanguage UMRS (Underspeci ed Minimal Recursion Semantics) [Egg & Lebeth 95], [Egg & Lebeth 96] as semantic component of the grammar. The paper is structured as follows: After an outline of the syntactic derivation of sentence mood in section 2 and an introduction to UMRS in section 3, section 4 is devoted to an alternative (predicate logic) analysis of the data in the domain of wh -questions. The UMRS structures that allow the compositional derivation of this analysis are given in section 5.
2 A syntactic analysis for wh-questions In the following section we present a syntactic description of German wh-questions within in the HPSG framework. As it is well-known, German belongs to the so-called verb-second (V2) languages3 and to the languages with overt syntactic wh-movement. Linguists agree upon the following characteristics of German wh-constructions: Exactly one wh-phrase occurs in the initial position of the wh-interrogative clause. In multiple wh-questions every wh-phrase in situ is licenced by the wh-phrase in initial position. A wh-word can be embedded in a bigger constituent which then is turned into a wh-phrase. Thereby, the whole XP may occur in initial position (pied-piping e ect). Less agreement prevails on the status of the wh-phrase which occurs in the left periphery of a wh-interrogative clause because of its ambivalent behaviour in matrix and in subordinate clauses: As for matrix wh-interrogative clauses, they pattern with \normal" topicalized XPs. The wh-phrase is situated to the left of the nite verb that is in second position. In subordinate sentences wh-phrases behave like complementizers in the sense that they force the nite verb to stay in nal position. But this need not mean that wh-phrases 3
That means that there is a syntactically realized constituent to the left of the nite verb.
3
and complementizers form a natural class. Both di er in their grammatical function and their semantic contribution. In addition, complementizers are always words, whereas whphrases can be rather complex phrases. Therefore, the assumption that complementizers and wh-phrases occupy the same structural position would be inconsistent with the Structure Maintenance Principle [Emonds 76]. Further evidence comes from particularly South German dialect areas [Bayer 84] where the wh-phrase and the complementizer occur even together at the syntactic surface. Every analysis of German wh-interrogative clauses must account for the above mentioned properties. Our approach is based on two main assumptions. First, a head-feature called mood is de ned in order to determine the sentence mood. (See for similar ideas [Lebeth 94] and [Kiss 95].) Second, an interrogative-head schema is introduced that licences wh-questions syntactically and contributes the interrogative operator semantically. In particular, the interrogative-head schema has to be applied to clauses with a mood-speci cation of type wh-interrog which is meant to represent wh-interrogative clauses. In the following we will discuss both assumptions in detail and will give an example for the syntactic analysis of a German wh-question. The value of mood is of the type mood. With [Altmann 93] we assume that the fundamental sentence mood comprises declarative, interrogative and imperative mood and that the sentence mood can be determined in several manners, e.g. by lexical categories and word order. The following (partial) type hierarchy is used for the derivation of syntactic sentence mood. mood v1/v2-ord-mooder v1-mooder
mooder
lex-mooder v2-mooder wh/ob-interrog wh-interrog imperative yes/no-interrog v2-decl v2-wh-interrog vf-wh-interrog ob-interrog
non-mooder vf
dass-decl
...
Mood is partitioned by the type mooder which represents the elements and structural relations that contribute to the determination of the sentence mood and by non-mooder which describes the grammatical relationships that do not, although they interact with mood values. The type mooder has two subtypes: lex(ical)-mooder and v1/v2-order-mooder. The type lexical-mooder is the type of the mood value of all lexical elements that contribute to the determination of the sentence mood categorially. In particular, the complementizers dass \that" and ob \whether" mark a clause as declarative and interrogative, resp. A wh-word indicates the interrogative sentence mood. The type v1/v2-order-mooder with its subtypes v1-mooder and v2-mooder is part of the type hierarchy because a verb in rst position restricts the possible sentence mood to imperative or yes/no -interrogative, whereas a verb in second position can only occur in declarative or wh-interrogative clauses. On the contrary, a verb in nal clause position gives no evidence for a speci c sentence mood. Therefore its mood value v(erb)f(inal) is a subtype of non-mooder. Besides the nal verb position there are other grammatical relations that do not contribute the sentence mood. E.g.,there is no speci c echo-wh-sentence mood, but only echo characteristics which combine freely with any sentence mood [Reis 91]. This phenomenon, which can not be discussed here in detail, is modelled by mood values in the position of the dots in the type hierarchy above. As [Altmann 93] shows, the di erent mood values in a sentence interact. Thus, a clause with the nite verb in second clause position can be identi ed as wh-interrogative if a wh-word is found in the same clause. Hence, the wh -interrogatives are characterized by a mood value that is the cross-classi cation of the subtypes of v2mooder and lex-mooder. The cross-classi cation of vf and lex-mooder yields a type that
4
characterizes sentences both with respect to mood and verb position. This information can be used for the characterization of the verbs' selection properties.4 Lexical elements that contribute to the determination of the sentence mood bear a mood feature with an appropriate value. E.g., the wh-words' mood value is speci ed as wh-interrog. Lexical elements that have no bearing on the sentence mood, such as nouns and verbs, are underspeci ed with respect to their mood value, i.e., their mood feature has the value mood. The percolation of the mood value is guaranteed by the Head Feature Principle (HFP, [Pollard & Sag 94]). But as a complement or an adjunct, the wh-phrase is not the head of a verbal projection. However, we need the mood information of the wh-phrase because of the lexical property of wh-words to contribute to the determination of the clause's sentence mood. Hence, a second feature, mood-trans(fer), is de ned for the type sign which is needed to regulate the transfer of the mood value of a sister to the head within a phrase. Since the mood value of every element is speci ed within its lexical entry and also identi ed with its mood-trans value and the mood-trans value of the syntactic head is the uni cation of the mood values of head and non-head, the uni ed mood value of the head and its sister is projected by the HFP. Nevertheless, there is one exception: Verbs which select clausal wh-complements do not identify their mood value and their moodtrans value in the lexicon. Thereby it is guaranteed that an embedded wh-interrogative clause does not mark the matrix clause as interrogative. Within the proposed analysis pied-piping constructions can be described easily. The mood value of the embedded wh-word percolates to the top node of the phrase where it marks the whole XP as wh-interrog. The fact that in German the wh-word can occur everywhere in the preposed XP is correctly expressed. As said before, an interrogative-head schema is used in order to account for the structural properties of wh-interrogative clauses. The interrogative-head schema is responsible for licensing a wh-phrase in initial position. In particular, the head daughter's inherited slash value5 that represents the obligatory wh-phrase in initial position is bound o in this schema. The head daughter's mood-speci cation wh-interrog guarantees that the interrogative-head schema is distinguished from the ller-head schema [Pollard & Sag 94] and that it is not applicable to declarative sentences.
I
sign ssjloc
2 1
6 6 6 6 6 6 6 6 6 6 6 6 4
phrase 2 synsem 2 6 6 6 6 6 ss 6 6 6 6 6 6 4
loc
6 6 6 4
phrase h ssj...jnloc nonlocal inhjslash eset
i
H
local 2
category
verb
cat 4 head vform nite mood wh-interrog subcat elist cont j liszt 2 2 nonlocal (
6
inhjsl nloc 6 4 t-bdjsl
"
1
1
3
3
7 5 7 7 5
7 7 7 7 7 7 7 7 7 7 7 5
3
local head catjhd :vform nite mood wh-interrog
#)
3 7 7 5
3 7 7 7 7 7 7 7 7 7 7 7 7 5
The mother's [slash:eset ] restriction in the interrogative-head schema causes that So far nothing guarantees that the verb position actually corresponds to the intended verb position for the types v1/v2-mooder and vf-order. Therefore, two constraints are formulated which determine the value of the dir(ection) feature. Dir describes the direction in which the verb selects its arguments. 5 Slash values represent gaps in HPSG. 4
5
the schema can be applied only once per clause. Thereby it is possible to introduce the semantic interrogative operator by the head daughter's content value in the interrogative schema. The ssjlocjcontjliszt value 2 introduces the semantic contribution of the interrogative-head schema, viz., the interrogative operator. For the detailed discussion of the interrogative operator see section 5. With the interrogative-head schema, the formation of matrix and subordinate interrogative sentences is considered as a uniform syntactic process modulo the position of the nite verb. Verbs that are subcategorized for wh-interrogatives select complements of type vf-wh-interrog. As a result, the nal position of the nite verb in embedded whinterrogatives is guaranteed. Since every occurrence of a wh-phrase determines the mood value of the verbal projection and vf-wh-interrog and dass-decl have no common subtype, the complementizer dass \that" and a wh-phrase can not be realized at the same time.6 The restriction that every wh-phrase in situ has to be licenced by one in initial position is expressed di erently depending on the position of the nite verb: In V2-clauses with a whphrase in situ, i.e., multiple wh-questions, the application of the interrogative-head schema is forced because the ller-head schema (or any other schema that is used to describe topicalization in German) is restricted to the mood value v2-decl whereas the wh -phrase in situ forces the clause to have the mood value v2-wh-interrog. In clauses with the nite verb in nal position the simultaneous occurrence of a wh-phrase and a complementizer leads to a type mismatch for the mood value, at least in Standard German. Finally, we give an example for the description of a wh-question that shows how the interrogative-head schema interacts with the mood speci cation. Mood value percolation leads to the mood value v2-wh-interrog ( 6 ) in the structure 10 that triggers the application of the interrogative-head schema.7 (6) Wer begrusst den Gast? \Who welcomes the guest?" The co-occurrence of a wh-phrase and the complementizer dass \that" in certain German dialects can be explained by by stipulating a second dass \that"-entry with an underspeci ed mood value. 7 Rather than exploring alternative approaches here, we assume that information pertaining to empty heads are projected along Double Slash (Dsl, cf. [Borsley 89], [Kiss 95]). A dsl value of an empty head is coindexed with its local value. A dsl dependency is bound if the verbal projection is selected by a verb in second position. A lexical rule guarantees that the selector shares all relevant information with the dsl value of the selected verbal projection. 6
6
ss locj...jhdjmood nloc [inhjsl fg ]
I
ssjloc
4
2
2
H
synsem
loc cat hdjmood 6 sc hi 2 3 4 sl inh dslfg 5 nloc 4 t-bdjsl 4 mood-trans 6
6 6 6ss 10 6 6 6 4
weri
6
6 6 6 6 6 4
H
2
2
6 6 6ss 6 6 4 4
synsem "
local
begr usstj
ss
2
77 77 77 77 77 57 5
C
hdj mood 6 v2-wh-interrog cat sc 8 nloc to-bdjdsl 1 mood-trans 6 =v1/v2-ord-mooder^ 11 loc
33
#
33
2
2
hdjmood 11 6 6loc cat sc hi 6 6 8 ss 4 4 sl 4 nlocjinh dsl 1
77 77 57 5
loc 4 catjhd jmood nloc inhjsl 4
77 77 55
H
C
33
7
wh-interrog
ei
2
2
hdj mood 6ss sc 2 6 4 nlocjinhjdsl 1 mood-trans 11 = 9 ^ 7 4loc cat
11
33 57 7 5
C
ss
3
locj...jmood den Gast
H 5
mood
2
2 6ss 6 4
4loc
1
cat
hdj mood 9 sc 2 ; 3
nlocjinhjdsl 1 mood-trans 9 =mood^ ej
In this section it has been shown that the main syntactic properties of German whquestions can be adequately described by an appropriate syntactic schema together with speci c types that provide information about sentence mood and verbal position.
3 The UMRS formalism UMRS represents structural semantic ambiguities by underspeci cation (like UDRT [Reyle 93], QLF [Alshawi & Crouch 92], or USDL [Pinkal 96]). UMRS has roots in MRS (Minimal Recursion Semantics) [Copestake et al. 95]. It is employed for the semantic construction in an HPSG grammar [Pollard & Sag 94] in the German VERBMOBIL project. UMRS is a metalanguage: it consists of constants that denote expressions of an appropriate object language and (possibly underspeci ed) dependencies between the constants. For convenience, we will use predicate logic (PL) as object language in this paper. However, other languages could also serve as object languages. UMRS (and MRS) semantic representations are at lists of metalanguage constants. The constants of the metalanguage are called \relations" and are interpreted as types in a typed feature structure formalism. Dependencies between relations on such a UMRS list are speci ed in terms of a feature handel that appears in every relation. Its value serves as an address for the relation. If the handel value of one relation is coindexed with the value of a feature (except handel) 7
5
33 57 7 5
in another relation, the latter has the former as immediate argument. Consider e.g. the negation (operator) and the verb (argument) in the UMRS representation of not rain (7): 3 (7) *2not rel #+ " rain rel 6handel 4inst
hd arg
17
, handel inst
25 3
3 4
In a fully speci ed sentence, there must be a function-argument chain (called \main FA chain") from the relation with the widest scope down to the main verb of the sentence. Apart from handel, all relations have the feature inst, whose value stands for the main argument of the object language expression that the relation denotes. E.g., the inst value of verbal relations corresponds to the main eventuality argument. Other features are introduced by subtypes of relations. e.g., hd arg, by the type for operator relations. UMRS represents semantic structural ambiguities by specifying for each operator the range of its potential arguments. Relations for operators have two additional list-valued features hout and hnon. They list the handel values of relations that can be immediately subordinated to the relation in question (the value of hout) or the handel values of those that cannot (the value of hnon). The hd arg value of an operator relation must be an element of the list that is equal to the hout value minus the hnon value. If there is more than one element on this list, the scope of the operator is underspeci ed. The value of hout is determined globally: In appropriate domains (scope islands), all potential arguments (as speci ed in the lexical entries) are collected in a list. This list is coindexed with the hout value of every operator in the domain. E.g., every DP argument has the handel value of its governing verb on the hout list. hnon is a local feature that enumerates for each operator (handel values of) impossible arguments, especially its own handel value (no operator is its own argument). (8) illustrates this mechanism for Every man loves a woman (without mood and tense). The list of potential arguments' handel values 20 comprises the handel values of the determiners and the verb. The lexical items (terminal nodes) specify the potential arguments in hinhoutjhin. hinhoutjhin values of daughters are appended in the mother, the top node of the domain coindexes the value of hinhoutjhin with hinhoutjhout. hinhoutjhout values of mother and daughters are coindexed, and lexical items coindex the hinhoutjhout value with the hout value of all operator relations in their liszt value. 2 3
(8) 20 1 6 9 hin
6hinhout 20 hout 6 2 6 6 handel 6 4inst 4cont liszt
2 6hinhout 6 6 6 6 6 6 6 6 6 6cont 6 6 6 6 4
hin
handel
6inst 6 6 6 6 6 6 6liszt 6 6 4
9
20 9 3
1 2 13
,
?
11
[
12
7 7 37 7 7 55
3
hout
2
,
2
every rel
3
9 7 handel " *6 6inst 3 7 7 man rel 6 10 7, handel 11 6restr 7 6 20 6hout inst
7 5 4hnon 9 hd arg
8
7 7 37 7 77 77 77 77 7 #+77 77 77 10 77 77 3 77 55
2
hin
1, 6
6hinhout 20 hout 6 2 6 6 handel 6 4inst 4cont liszt
1 2
3
?
12 8
[
5
7 7 37 7 7 5 5
2
6 6 6 6 6 6 6 6 6 6 6cont 6 6 6 6 4
hinhout
hin hout
2
handel
6inst 6 6 6 6 6 6 6liszt 6 6 4
3
6
20 6 4
2
indef rel
handel *6 6inst 6 8 6restr 6 6hout 4hnon
7 7 37 7 77 7 3 77 77 77 6 7 #+77 " 77 4 7 woman rel 7 77 7 7, handel 7 77 7 77 20 4 inst 77
7 5 55 6
2 6 6 6 6 6 6 6 6 6cont 6 6 4
hinhout
hin hout
2
handel
6inst 6 6 6 6 6liszt 4
3
1
arg1
7 7 37 7 7 3 7 77 7 +77 1 7 77 77 2 7 77 5 55 3
arg2
4
20 1 2
2 * love rel 6handel 5 6inst 4
hd arg
(8) represents the ambiguity of operator scope by underspeci cation. It comprises two desambiguated readings: The immediate argument of every rel is either love rel or indef rel as its hd arg value is an element of < 1 ; 6 > (its hout minus its hnon value). If the verb is chosen, indef rel must have every rel and not love rel as its immediate argument (two functions may not have the same immediate argument). If indef rel is chosen as the argument of every rel, indef rel must have love rel as its argument (if it had every rel as its argument, we would get an ill-formed cyclic function-argument chain). (TL below spells out the desambiguation process in detail.) In sum, the relative scope of the determiners is open in (8), but both have (immediate or mediated) scope over the verb, as desired. UMRS structures can be translated into an appropriate object language. When dealing with underspeci ed operators, the translation involves (nondeterministic) determination of scope. Rule TL speci es the recursive steps in the interpretation of UMRS structures: TL: Replace [ L1 [ L2] by [ L1 ] (xn [ L2] ), if L1 contains an operator relation R1 . If the scope of R1 is underspeci ed, L1 contains everything (im-)mediately subordinated to R1 (and nothing else). If the scope of R1 is xed to R2 , L1 contains everything (im-)mediately subordinated to R1 except R2 and everything (im-)mediately subordinated to R2 (and nothing else). R1 has at least one possible hd arg value and the inst value n . If R1 has no possible hd arg values, the structure is ill-formed and one or more of the nondeterministic choices must be reset. If there are no choices left, the translation fails. The handel value of R1 matches the relevant type restriction (if any). If the hd arg value of R1 carries a type restriction, this becomes the new relevant type restriction. L2 is the same as L2 , except that the handel value of R1 is added to the hnon list of all relations of L2 . If the hd arg value of R1 is already determinate, it must be added to the hnon list of all relations of L2 , too. This rule prevents ill-formed desambiguations of UMRS structures: cyclic functionargument chains as well as branching function-argument chains (in which more than one function has the same immediate argument) are ruled out. In addition, identical indices must be translated as identical variables, as coindexations in UMRS structures model important dependencies between relations that matter in the object language, too (e.g., the coindexation between the inst value of a DP and the value of the appropriate argument feature in its governing verb). 0
0
9
4 Complex wh -questions in PL In this section, we will sketch a new object language representation for wh -questions in PL that yields equivalent results to the standard approach for simple and multiple wh questions, but also captures the problems posed by universal quanti ers in wh -questions. For ease of exposition we restrict the discussion to English examples. The basic idea is to represent wh -expressions in terms of universal quanti cation, not of existential quanti cation. Wh -elements appear before, non-wh -elements after the equation of propositions, as in the semantic representation of (1). The -operator (based on [Link 91]) represents the smallest upper bound. Hence, (9) denotes like (2) the set of propositions of type \set of s such that x gets y at s", for all pairs of persons x and marks y in the given individual domain. Who is represented as P 8x (person (x) ! P (x)). (9) P 8x1 person (x1 ) ! 8x2 mark (x2 ) ! 8P (P = sget (x1 ; x2 )(s) ! P 2 P ) (10) xP (x) = P (P (x) ^ 8y(P (y) ! x y)) This allows an adequate representation of the cases in which universal quanti ers interact with wh -expressions. E.g., (3) had two readings, depending on whether the universal quanti er outscoped who or not. The reading in which it doesn't is depicted in (11): (11) P 8x2 mark (x2 ) ! 8P P = s8x1 (person (x1 ) ! get (x1 ; x2 )(s)) ! P 2 P Now if we simply let the universal quanti er everyone have scope over the wh -element, we get (9), which also represented the semantics of (1). Hence, the proposed analysis of wh -elements describes the equivalence of the meaning of sentence (1) with one reading of sentence (3) simply and intuitively: this equivalence is put down to a mere scoping possibility of a universal quanti er whose scope is not yet xed. The crucial point in our analysis is that the scope of universal quanti ers (below or above the equation between propositions) determines whether they are used as usual or as wh -elements. Thus, the proposed PL analysis ful lls the rst part of the desiderata for an analysis of wh -questions as expounded in section 1. Next we will show a compositional and underspeci ed UMRS analysis of wh -questions that can be translated into this PL analysis. 0
0
0
0
0
0
0
0
0
0
0
0
0
5 Constructing complex wh -questions in UMRS Both yes/no-questions and wh -questions include in their semantics an interrogative operator. For wh -questions, this operator is introduced by the head-interrogative schema that licences wh -questions syntactically (see section 2). The UMRS representation of this operator is a list of two relations quest rel and interr rel that are only loosely connected (by the index 2 ). In the representations of full wh -sentences, all wh -elements must have scope over interr rel but not over quest rel. 2 3 (12) 2 interr rel 3 quest rel
*6handel 6 6inst 6 6hout 4hnon
hd arg
17
7 7 37 hi 5 27
,
6handel 4 7 6inst + 5 7 6 7 6int arg 2 7 6 7 6hout 3 7 6 7
4hnon 4 5
hd arg
The two relations quest rel and interr rel together represent the semantics of the interrogative operator: The former introduces the -operation over the set P of asked propositions P , the latter, the relation of inclusion in P and the equation between propositions ([[[quest rel ]]]= P P (P (P )); [ [interr rel ]]] = P 8P (P = P ! P 2 P )). 0
0
00
10
0
0
00
0
UMRS represents ambiguities of operator scope by listing for each operator locally its potential arguments. As the global list of potential arguments is the same in a domain, all operators in a domain have nearly the same local list of potential arguments: their hout value minus their handel value. Hence, so far, this approach overgenerates considerably, even if TL rules out some unwanted readings of UMRS structures.8 This problem a ects UMRS representations of wh -questions, too: Neglecting \proper" universal quanti ers (i.e., those that do not model wh -elements; they can appear anywhere below quest rel ), the desired readings of these UMRS structures respect this ordering in the main FA chain: quest rel > wh-representation1 > : : : > wh-representationn > interr rel > other material of the sentence (\>" abbreviates \has immediate scope over"). But if we just mark the interr rel and the relations for wh -elements as potential arguments (by putting their handel values onto the list of potential arguments), other, unwanted orderings are possible, e.g., one in which the interr rel outscopes the wh -elements. To solve this problem, we divide the main FA chain in wh -sentences. The +wh -part goes from quest rel to interr rel and includes the wh -elements. From interr rel on extends the {wh -part with e.g. the main verb of the sentence or existentially bound arguments. This division is implemented by typing handel and hd arg values: handel and hd arg values in the +wh -part have the type wh handel, in the {wh -part, the type nwh handel. These incompatible types partition the handel type. Interr rel is the divide as its handel value is typed as wh handel while its hd arg value is typed as nwh handel. This entails the types of handel and hd arg values for all relations except \proper" universal quanti ers, which must be able to appear in both parts of the main FA chain. Hence, their wh handel and hd arg values are assigned the underspeci ed handel type. This is their only di erence to wh -expressions; both are rendered by the relation every rel. In addition, quest rel is speci ed as being not a potential argument in the lexical entry of the interrogative operator (its handel value will not appear as an element of the hout list of the relevant domain), which entails wide scope of quest rel over all other operators. (13)
2
quest rel
6handel 6 6inst 6 6hout 4hnon
*
2
hd arg
every rel
6handel 6 6inst 6 6restr 6 6hout 6 4hnon
hd arg
3
2
every rel 6handel wh handel 4 7 7" 6 # 7 person rel # "mark rel wh handel 1 7 5 inst 76 7 6 2 7 6restr 7, handel 6 , handel 9 , 6 7, 6 7 3 7 6hout 3 7 inst 5 8 inst 5
7 6 hi 4 5 4hnon + wh handel hd arg wh handel 32 3 interr rel 2 3 7 6handel wh handel 7 wh handel 10 7 76 7 get rel 8 7 6inst 7 6handel 11 nwh handel 12 7 76 76 7 9 7, 6int arg 2 7, 6inst 11 7
7 6 74 5 4 , 7 , 10 , 12 7 6hout 3 3 7 arg1 5
76 7
8 11 5 4hnon 5 arg3 7 hd arg nwh handel wh handel 3
(14) P2 8x5 person (x5 ) ! 8x8 mark (x8 ) ! 8P (P = s11 get (x5 ; x8 )(s11 ) ! P 2 P2 ) The UMRS list for (1) is (13), one of the two (equivalent) PL translations of (13), (14). In prose: the set of all propositions of the type that x gets y for every pair of persons x and marks y. This is the desired representation for sentence (1). 0
0
0
0
0
0
In many cases, syntactic structure further restricts the scoping possiblities in a given domain (see e.g. [Frey 93]). For lack of space, this topic will be neglected in this paper. 8
11
Finally, we will present the UMRS structure for sentence (3), which is ambiguous between a reading in which the universal quanti er behaves like a wh -element and another in which it doesn't. (The subscripts on the every rel s are only illustrative diacritics.) 32 3 2 (15) 2 every rel1 3 interr rel quest rel
6handel wh handel 1 6 2 wh handel 11 7 inst 76 12 76 12 int arg 6 7, 6
3 7 6hout 1, 4, 7, 3 5 6
hi 4hnon 1 wh handel hd arg nwh handel 3 2 every rel2 6handel handel 7 7 7" #6 " 7 person rel # 6 8 inst mark rel 7 6 7, handel 9 , 9 restr handel 6 , 6 7 6 3 7 inst 5 6hout 8 inst
7 6 7 5 4hnon hd arg handel
7 6handel wh handel 4 7 76 7 7 6inst 7 5 76 7 7, 6restr 7, 6 7 6 7 10 7 6hout 3 7
76 7 4 5 4hnon 5+
6handel 6 6inst 6 6hout 4hnon * hd arg
hd arg wh handel
2
3 get rel 6handel nwh handel 10 7 6 7 2 6inst 7 4arg1 5 8 5 arg3
The only possible scope relations for (15) are quest rel < every rel1 < interr rel < every rel2 < get rel and quest rel < every rel2 < every rel1 < interr rel < get rel. (In the latter FA chain, the scope of every rel2 and every rel1 may be swapped, which we will neglect here and in the PL translations as it has no semantic e ect). The only PL translations for (15) are the desired (16) and (17), respectively: (16) P12 8x8 person (x8 ) ! 8x5 mark (x5 ) ! 8P (P = s2 get (x8 ; x5 )(s2 ) ! P 2 P12 ) 0
0
0
0
0
0
(17) P12 8x5 mark (x5 ) ! 8P P = s2 8x8 (person (x8 ) ! get (x8 ; x5 )(s2 )) ! P 2 P12 (16) is the same as the object language representation (14) of sentence (1) and (17), the same as (11). Hence, it is possible to derive these PL representations compositionally in terms of an underspeci ed UMRS analysis, which ful lls the second half of the list of desiderata for an analysis of wh -questions as expounded in section 1. 0
0
0
0
0
0
6 Conclusion We have presented a syntactic and semantic analysis of wh -questions in the HPSG framework. The analysis allows a compositional derivation of sentence mood and accounts for multiple wh -questions as well as for the interaction of universal quanti ers and wh expressions. Wh -elements are represented in terms of universal quanti cation. The analysis was cast in terms of UMRS, a computable semantic metalanguage that allows an underspeci ed representation of the ambiguities encountered in the interaction of universal quanti ers and wh -expressions.
References
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