Reversible Resolution with an Application to Paraphrasing - CiteSeerX

Reversible Resolution with an Application to Paraphrasing

Matthew Hurst

Submitted in partial ful llment of the requirements for the degree of Master of Philosophy, Computer Speech and Language Processing

The University of Cambridge

i

Preface I would like to thank the following people for their support and encouragement throughout the duration of this project. My supervisor, Dick Crouch for all his time and eort; colleagues at the Computer Lab including Barney Pell for his insight and numerous discussions, Mike Collins and Siani Baker; also Peter Douglas, Mun Yi Chew and Cynthia Chou. This thesis complies with the regulations for the one year M.Phil. course at the University of Cambridge. It represents my own work and is not substantially the same as any that I have submitted for a degree or diploma or other quali cation at any other University. The thesis is below the speci ed word limit.

Matthew Francis Hurst, August 1993

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Abstract This thesis describes a reversible resolution method based on a proof procedure. It then describes paraphrasing as an application of this mechanism and demonstrates how the proofs can be used as a quantitative measure of association in the interpretation and generation of phrases identifying objects. A suitable metric is given that implements some notion of ambiguity which is used in both interpretive and generative modes. All the elements discussed are implemented.

Contents 1

2

Introduction

1

1.1 Aims of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1.2 Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1.2.1 Reversible Resolution . . . . . . . . . . . . . . . . . . . . . .

2

1.2.2 Ideal System . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

1.3 Natural Language Processing Environment . . . . . . . . . . . . . .

2

1.4 The Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

1.5 Overview of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

1.6 Annotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

Resolution and Monotonic Interpretation

5

2.1 Monotonic Interpretation and QLF . . . . . . . . . . . . . . . . . .

5

2.1.1

2.1.2

QLF

Syntax . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

2.1.1.1

Abstract QLF . . . . . . . . . . . . . . . . . . . . .

6

2.1.1.2

Concrete QLF . . . . . . . . . . . . . . . . . . . . .

7

2.1.1.3

Subset QLF . . . . . . . . . . . . . . . . . . . . . .

8

Semantics . . . . . . . . . . . . . . . . . . . . . . . . . .

9

QLF

2.1.3 De ning CAT . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

2.2 Logic of Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

2.2.1 Contextual Entailment of Resolution . . . . . . . . . . . . . .

11

iii

iv

CONTENTS

2.2.2 Inference for Resolution . . . . . . . . . . . . . . . . . . . . .

13

. . . . . . . . . . . . . . . . . . . .

13

2.3.1 Singular De nite Terms . . . . . . . . . . . . . . . . . . . . .

13

2.3.2 Prepositional Forms . . . . . . . . . . . . . . . . . . . . . . . 2.3.3 Necessary Conditions . . . . . . . . . . . . . . . . . . . . . .

14 14

2.3 Declarative Rules De ning CAT

2.3.3.1

Salient Entity . . . . . . . . . . . . . . . . . . . . .

14

2.3.3.2

Event . . . . . . . . . . . . . . . . . . . . . . . . . .

15

2.3.3.3 2.3.3.4

Prepositional Sense . . . . . . . . . . . . . . . . . . Genitive Sense . . . . . . . . . . . . . . . . . . . . .

16 16

2.4 Resolution and Paraphrasing in clare . . . . . . . . . . . . . . . . .

16

2.4.1 clare Resolution . . . . . . . . . . . . . . . . . . . . . . . .

17

2.4.2 clare Paraphrasing . . . . . . . . . . . . . . . . . . . . . . . 2.4.3 The Advantages of a Declarative and Reversible System . . .

17 17

2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

A Algorithms

19

A.1 Top Proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19

A.2 Proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19

A.3 Skolemization

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20

A.4 Conjunctive Normal Form . . . . . . . . . . . . . . . . . . . . . . . . A.5 Compilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21 21

A.6 Paraphrasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22

Chapter 1

Introduction 1.1 Aims of Thesis This thesis describes a reversible resolution method based on a proof procedure. It then describes paraphrasing as an application of this mechanism and demonstrates how the proofs can be used as a quantitative measure of association in the interpretation and generation of phrases identifying objects. A suitable metric is given that implements some notion of ambiguity which is used in both interpretive and generative modes. All the elements discussed are implemented. The word ambiguity as used above has a simple meaning in this work: referential ambiguity (as discussed in Chapter ??). Word sense ambiguity and structural ambiguity (including scoping) are not incorporated in the general discussion of the paraphrasing application, although they can be accounted for in other components of the implementation.

1.2 Resolution Resolution is the process by which the surface analysis of a sentence in a language may be completed to become associated with a context or discourse environment. In the case of noun phrases, this involves an association with some representation of a preceding phrase, or with a representation of an identity referent. For a verb based structure, in the context of this thesis, it involves a logical realisation of some expression describing the analysis. The referent of a term will in general be referred 1

2

CHAPTER 1.

INTRODUCTION

to as a token. The precise interpretation of this notation will be introduced later.

1.2.1 Reversible Resolution A mechanism capable of reversible resolution takes an analysis and associates it with a context, and also takes some part of the context (for example an object under discussion) and produces an analysis. This analysis can then be used to generate text. Such capability would be extremely useful in most Natural Language Processing systems due to the ambiguity inherent in discourse. For example, when a machine is faced with interpreting an ambiguous phrase it would be convenient if a query could be constructed by the system asking the user to specify exactly which object was being referred to. If these queries could be generated with unambiguous text then the usefulness and eciency of the system would be increased.

1.2.2 Ideal System The following example of an imaginary system demonstrates the functionality of this technology. user: The queen's croquet ball is red. Alice's ball is green. Alice hits the ball. system: The ball:

1. The queen's ball 2. Alice's ball At which point the user would make a decision as to the correct resolution. A further requirement of an ideal system would be that the phrases given for choice are in some way ecient. That is to say they don't contain more information than is required to uniquely identify them.

1.3 Natural Language Processing Environment There are two facets to the work presented in this thesis. One is the design of methods upon which a reversible resolution system can be based, and the other is the implementation of such a system.

1.4.

THE FIELD

3

's cle [2] is the processing environment in which forms a basis for both facets. The implementation is situated within the cle framework. Later sections will mention components necessary to a complete system that are not described by this thesis. These components are all implemented by calls to the cle. The following is a selection of the function of predicates employed.

SRI



Parser. Provide an analysis of the sentence. As will be shown in Chapter 2 this is not a parse but a quasi logical form representation.



Generator. A module capable of generating text from an analysis. This process is conceptually inverse to that of the parser.

 

Quanti er Scoping. A process capable of scoping an analysis. Other implementation speci c black boxes such as index grounding, logical translation etc.

The extension of the cle, clare [4][3][5], which provides a model of reasoning in a domain, is used as a comparison for the work presented in the later chapters.

1.4 The Field There has been a substantial amount of work carried out in the eld of reference resolution. Most of this research is concerned with getting the right answer, that is nding the correct co-referent for some expression. Much of the work is in the eld of Discourse Processing [9] [10] [8] [11], as well as work speci c to the cle [1]. In contrast, the work presented here deals with designing a general method of resolution rather than designing an algorithm for disambiguation. The solution produced to the problem of reversible resolution in itself oers a means of disambiguation through quantitative measurements of individual solutions (Chapter ??). Work in this area is not so abundant. Similarly, text generation from a context or domain has received much attention [13] [12] including speci c research into the generation of referring expressions [6]. However, the two elds have not been viewed as aspects of same problem and reversible resolution (with an application to paraphrasing) has not received any signi cant attention. This thesis is a rst step in combining the problems and presenting a general strategy as a solution.

4

CHAPTER 1.

INTRODUCTION

1.5 Overview of Thesis The chapters of the thesis are set out in the following manner. 1. Introduction. 2. Resolution and Monotonic Interpretation. This chapter describes and builds on the semantics of the QLF, the representational language of the cle providing a base for the work presented in this thesis. 3. Theorem Proving. The inference techniques used in resolution are described. 4. A Reversible Resolution System. The implementation is described. 5. Paraphrasing. The method is applied to the problem of paraphrasing in ambiguous contexts. 6. A Game of Croquet & The Cheshire Cat. A number of complete examples are presented and discussed. 7. Conclusion.

1.6 Annotation The following annotation is used to mark term reference and referents in example text throughout the thesis. 1

objects : Objects are marked with a superscript contained in a box ( ). 1

events : Events are marked with a superscript ( ). [i. . . ]

resolution : Points of resolution are marked as numbered lists of possible resolvents (

).

introduced objects : Phrases that could introduce a new object at a point of resolution are marked 8 with a distinguishing symbol ( ). If a new object is selected, then the object [ ] 1 reference appears outside the list ( 8 ). i. . .

Some text will be completely annotated, however other examples may be partially annotated where a speci c point is being made.

Chapter 2

Resolution and Monotonic Interpretation The cle provides a representational language which is the starting point of the work presented in this thesis. The philosophy behind this language, and its semantics are described in this chapter. A declarative, monotonic and reversible treatment of resolution is presented.

2.1 Monotonic Interpretation and QLF The representational language of the cle is the Quasi Logical Form. This language embodies a powerful and desirable feature of any NLP, that of monotonic analysis. Monotonicity guarantees an incremental and nondestructive analysis of language. The advantages of such a formalism, as described in [5], are 1. Order independence of resolution operations. 2. Production of partial interpretations. 3. Reversibility for synthesis/generation. Points 1 and 2 follow the de nition of monotonic. Point 3 is desirable, and to some extent assumed by the work presented in this thesis, however it is not strictly true of the cle. 5

6

CHAPTER 2.

RESOLUTION AND MONOTONIC INTERPRETATION

This work augments these advantages by supplying a framework in which resolution is itself reversible, which further exploits the notion of monotonicity. Before describing the semantics of QLF, a brief description of the syntax is given.

2.1.1 QLF Syntax There are two major components to the language: the term and the formula. These structures will rst be expressed in their abstract form (after [5]). Following this will be a description of the concrete representation and nally the subset with which this work is concerned. 2.1.1.1

Abstract QLF

The structure of the term that shall be focussed on (term(...)) has ve major components.

 

The index. This is a unique identi er associated with a particular term. The category. The linguistic category of the expression: a list of feature value tuples. For example [num : sing; per : 3rd : : :]



The restriction. A rst order one place predicate describing the term. For example, Xboy(X) the predicate that is true for all boys.



The quanti er. A generalised quanti er, i.e. a cardinality predicate holding of two properties.



The referent. An expression of reference, either a constant or a term index.

Terms may also be variables, indices or constants. The formula is similar in structure to the term and has the following components (form(...)).

  

The index. The category. The restriction. A higher order predicate.

2.1.



MONOTONIC INTERPRETATION AND QLF

7

The resolution. A formula (the `referent' of the form expression). This is also termed the property of the formula.

2.1.1.2

Concrete QLF

The QLF representation found in the implementation diers in a number of ways.



An extra eld is added to carry the word string associated with that fragment of analysis.



The categories are represented as a prolog functor with zero or more arguments.



term referents are abbreviated to a functor notation, e.g. ent(Idx), qnt(Idx), strict(Idx), . . . .

The concrete representation is illustrated by an example of a term and an example of a form. The term resulting from the analysis of the phrase Alice, when resolved to the constant alice, has the following QLF term. term(l([alice]),idx1,proper name(tpc),X^[name of,X,'Alice'],exists,ent(alice))

The index idx1 is the unique identi er associated with this term. The category proper name(tpc) is a representation of the appropriate feature value equations. The predicate represented by the restriction is that which is true of any Alice. This is an ecient and convenient way of expressing Xname is alice(X). exists is the quanti er. The referent ent(alice) is short hand for the lambda expression Y:Y = alice. Note that this is the resolved representation of the term. The unresolved term would look like the following. term(l([alice]),idx1,proper name(tpc),X^[name of,X,'Alice'], q, r)

An example of a form, that deriving from the analysis and resolution of the phrase on the lawn, is as follows.

8

CHAPTER 2.

RESOLUTION AND MONOTONIC INTERPRETATION

form(idx3,prep(on),X^[X,term(...idx1 ...),term(...idx2 ...)], app(A^B^[on Locational,A,B],idx3)) idx3 is the index of the form. The category is the preposition on. The restriction is

the higher order predicate that holds for any predicate true of the two terms. The resolution (i.e. the `referent' of the form) is the application of the index (which represents the restriction) to the `lambda abstract' A^B^[on Locational,A,B] which, in this case, would produce the logical form on locational(term(...idx1 ...),term(...idx2 ...))1 . In the standard  calculus notation this is as follows. X:X(term(: : : idx1 : : :); term(: : : idx2 : : :))[AB:on Locational(A; B)] [AB:on Locational(A; B)](term(: : : idx1 : : :); term(: : : idx2 : : :)) on Locational(term(: : : idx1 : : :); term(: : : idx2 : : :)) The scoping of quanti ers over formulae is represented in the following manner.



Scope:form

Where Scope is a ordered list of term indices indicating that the quanti er associated with the term out scopes those to the right of that index. So in the scope list [+i,+j] the quanti er for the term whose index is +i out scopes that of +j. QLF allows meta-variables to replace any of fquanti er, referent, scope, resolutiong. The instantiation of these variables is the representation of monotonic incremental analysis. Resolution of a QLF is the discharge of these variables. 2.1.1.3

Subset QLF

The subset of the QLF that is used in this work is de ned by the following restrictions on the concrete representation.

   1

The quanti ers are exists and forall. Elliptical expressions are not dealt with. The referents of terms are reduced to qnt and ent whose interpretations shall be inde nite and de nite respectively.

The word sense of on (i.e. on Locational as opposed to on Temporal etc.) is selected during resolution.

2.1.

MONOTONIC INTERPRETATION AND QLF

9

2.1.2 QLF Semantics This section gives a brief description of the semantics of the QLF as presented in [5][4]. Much of the details are not explicitly discussed and the reader is referred to that report for a complete discussion. As shown above, a QLF may contain any number of meta-variables and so the semantics of the language is slightly dierent from the traditional one. Instead of a function from models to truth values, a partial function is used2 . The denotation of a formula F is a partial function [[F]] from models to truth values. This partial function is de ned by W, a relation between a formula, a model and a truth value. The quality of a monotonic semantics is apparent in the case when [[F]] with respect to some model is unde ned, i.e. W(F,m,1) and W(F,m,0). This situation occurs when meta-variables are present in the QLF and consequentially a partial interpretation is being considered. The incremental analysis provides an `extension' of [[F]] in [[F0 ]] whenever F' is a more resolved version of F. Assuming the appropriate semantic rules for logical connectives, the semantic rules that discharge meta-variables are of the general form. W(F, m, v) if W(F', m, v)

where F' is an `extension' of F.

A relation CAT of category is de ned with the following arguments.

    

category index



< referent ; quanti er > if a term, property if a form

restriction context

Rules describing the discharge of quanti er and referent meta-variables for terms are de ned as follows. 2

The reader is referred to [7] for a thorough description of declarative semantics.

10

CHAPTER 2.

RESOLUTION AND MONOTONIC INTERPRETATION

1. W(F, m, v) if W(F[ q/Q], m, v) The term term(I,C,R, q, r) is contained in the formula F 9Q: CAT (C,I,R,< r,Q>,Ctxt) 2. W(F, m, v) if W(F[ r/REF ], m, v) and W(R(REF ), m, 1) The term term(I,C,R, q, r) is contained in the formula F 9REF : CAT (C,I,R,< REF , q>,Ctxt) for some context Ctxt. What 1 says is that the truth value of F (v) is the truth value of F with, for a particular term, all instances of the quanti er q replaced by Q. 2 states that the truth value of F is the truth value of F with, for a particular term, all instances of the referent r replaced by some referent REF ; and that R, the restriction of that term, when applied to the referent term holds. In fact there is a certain amount of redundancy in this de nition as the second conjunct in 2 is extraneous by the de nition of the relation CAT . A further set of semantic rules are de ned to deal with QLF forms and quanti ction. For example, an unresolved form is evaluated by the following rule. W(F, m, v) if W(F[ r/R(P )], m, v) F is a formula form(C,R, r)

9P : CAT (C,I,R,P ,Ctxt)

The truth value (v) of a formula F is the truth value of F with the `referent' of F replaced by the application of some property P , which holds in CAT , to the restriction R. An example of the operation of these rules has already been seen in Section 2.1.1.2. The complete rule set as de ned in [5] de nes membership of the relation W. It should be noted that the de nition found there is underspeci ed in the semantics for category and the relation CAT is an expansion of the relation S (called `salient'3 in that paper) accounting for this underspeci cation. 3

[5] mentions that . . . the computational analogue of S was implemented as a collection of `resThe work of this thesis is in eect to create a compuational analogue of CAT with a more general and declarative treatment. Section 2.4 mentions the implementation of S and the drawbacks of a case by case approach. olution rules' in [1].

2.2.

LOGIC OF RESOLUTION

2.1.3 De ning

11

CAT

Given that certain arguments of the CAT relation are members of in nite sets (context, restriction) and that others are dependant on these arguments (referent), all elements of CAT can never be explicitly enumerated. The description of this relation should, then, take the arguments that are nite (category, quanti er) and use some compact de nition to accomodate the in nite arguments. A de nition of CAT based on theorem proving ful lls this role.

2.2 Logic of Resolution Before continuing with a more formal de nition an example of resolution is presented. The phrase The girl runs has the following abstract form. runs(term(idx1,,X:girl(X), q, r))

Resolving this means instantiating the meta-variables q and r, and a possible resolution might be. runs(term(idx1,,X:girl(X),exists, alice)) We can see how the category limits the selection of the quanti er and the selection of the referent with respect to the restriction, that is - we require a single de nite object in context for which the restriction holds. This suggests a de nition of CAT as a series of rules de ning how the uninstantiated arguments are formed and how values can be found with respect to the context, for example3

CAT (C,I,R,,Ctxt) single object in context matching restriction(Ent,R,Ctxt) Consequently, inference can be used to, in this example, nd some value of Ent which holds for R in Ctxt.

2.2.1 Contextual Entailment of Resolution The process of resolution in the QLF formalism is simply the instantiation of meta variables with respect to the relation CAT . As described previsously, this relation

12

CHAPTER 2.

RESOLUTION AND MONOTONIC INTERPRETATION

involves the context of processing and can be expressed logically in the following manner. Ctxt

[ Assumption j= [Res F , F']

where, for forward resolution ()), F' is a more instantiated version of F; and for backward resolution (() F is an unresolved QLF of the partially instantiated F'. This distinction will be made clear in Chapter ?? when resolution in both directions is explained in detail. The addition of a set of Assumptions is included for completeness, though in this work is in fact an empty set. Assumptions can be used, for example, to promote a possible referent to be most salient when there are two equally likely possibilities. [4] describes the use of assumptions in such contexts. In brief, resolution of the example The girl runs would have the entailment Ctxt(C)

j=

[ most salient(i1,C,X:girl(X),alice)

runs(term(idx1,,X:girl(X), q, r))

,

runs(term(idx1,,X:girl(X),exists,alice))

The conditions on a QLF that lead to equivalence between a resolved and unresolved formula can be encoded as a series of declarative statements. These statements take category, index, /property, restriction and implement the interaction of context with respect to these by a number of logical primitives. That is to say, the abstract notation used to de ne CAT (3 ) is realised as a rule with either of the following structures. term(...) if C form(...) if C

where C is a set of logical primitives de ning the CAT , and the term and form contain the arguments to the relation, context being globally de ned. Before continuing it should be brie y mentioned that the de nition of equivalence suggested in context with the QLF semantics rules is not clear. There are three possibilities.

2.3.

DECLARATIVE RULES DEFINING

CAT

13

1. True in the same set of contexts and false in the same set of contexts. 2. Just true in the same set of contexts. 3. Just false in the same set of contexts.

2.2.2 Inference for Resolution If we can transform a QLF into a rst order logical representation then we can exploit existing techniques to verify the satisfaction of the restriction in context. Chapter ?? describes a method which does this in a concise and ecient manner. Using inference on the domain allows resolution to be completely declarative and, therefore, applicable in both directions. All that is required to ensure this is that we allow the inference mechanism to instantiate not only arguments of predicates, but the predicates themselves.

2.3 Declarative Rules De ning

CAT

Two cases of resolution are presented showing how the resolution rules employ conditions to de ne the category semantics for singular de nite terms, and prepositional forms.

2.3.1 Singular De nite Terms A rule de ning the semantics of this category must provide a quanti er and a referent that holds for the relation CAT . The existential quanti er is appropriate in the subset of QLF considered in this work. The referent should be some salient entity such that the category of that entity is in some sense equivalent to the category of the term being resolved (i.e. number agreement etc) and that the restriction of the term being resolved holds for that entity. So we wish to state two conditions that must hold in order for the resolution to be a correct declaration of CAT for a singular de nite term. The rule, then, is stated as term(Idx,,Rstr,exists,ent(Ent))

14

CHAPTER 2.

RESOLUTION AND MONOTONIC INTERPRETATION

( salient entity(Ent,Idx,) satisfy qlf(term(Idx,,Rstr,exists,ent(Ent)))

2.3.2 Prepositional Forms The condition that most hold of the following resolution of a prepositional form is that a prepositional sense, i.e. a word sense, of the preposition must exist. The rule is simply stated as form(Idx,prep(P),Rstr,app(X^Y^[PSense,X,Y]))

( prepositional sense(PSense,P) app { lambda application, has already been mentioned in Section 2.1.1.2.

Other rules are described in Chapter ??.

2.3.3 Necessary Conditions The above rules have introduced a number of conditions that are used as logical primitives to describe the semantics of category. The following is a description of some of these conditions. Note that the condition of satisfaction is left to Chapter ??). 2.3.3.1

Salient Entity

Salience is a well used term in the eld of computational linguistics. It has a de nite intuitive meaning, but such a de nition is of little help when we wish to implement the notion. The simple interpretation might be something like The degree of salience re ects the degree to which something is (locally) focussed in a discourse4 . 4 The de nition starts here, and can continue for several pages. However, for the purposes of this work, a straightforward de nition is used. Salience through relationship and metonymy, and other vaguer connections is not discussed.

2.3.

DECLARATIVE RULES DEFINING

CAT

15

Salience not only describes the relationship between the category of a term being resolved and the category of a possible referent term, but also the notion of degree. In implementing a system we require to implement this notion and associate some degree of focus with whatever token we wish to represent things. The approach that is taken in this implementation is to associate a number with the token. For further details refer to Chapter ?? where a model of salience is discussed. In terms of CAT , salient entity restricts the selection of possible referents by the relationship between category and referent, or more precisely, category and referent category. 2.3.3.2

Event

This primitive is used to associate some event with the property of verb formulas. A property with a verb category only holds for CAT if there is some event associated with that instance of the verb. Events in the analysis of language are very important, and are of equal viability as candidates for resolution as objects. For example: 1

Alice hit

It

Mary's ball

1

[i 1 1 ]

hurt her

1

1

The pronoun it could refer to the act of hitting( ) the ball or the ball( ) itself. Other examples include the prepositional location of an act (e.g. running on the ground) and issues to do with time reference. Assigning an event to an act is part of the resolution process and so the implementation of this condition actually involves a call to the resolution mechanism. We desire either a new event term to be constructed, or that the event be resolved to some previous act. However, the issues involved in resolving events are far beyond the scope of this project. Regardless of tense, problems still occur. Consider the following sentences. 1

1.

Alice runs

2.

The runner

on the ground

[i 1

8]2

1

.

is in a hurry.

16

CHAPTER 2.

3.

[ii 1 2

She runs

8]3

RESOLUTION AND MONOTONIC INTERPRETATION

quickly.

1

Sentence 1 introduces a new event( ), and that event is given a location. Sentence 2 involves a noun phrase centred on a verb. The event associated with this verb could 1 resolve to the event of running( ) previously described, though this is not a de nite 8 solution as running might be some general activity that Alice takes part in( ). The nal sentence again might have association with a general or local event and might 2 even be resolved to whatever event occurs in the phrase the runner( ). A compromise is made in this project. An speci c event may be referred to by a noun phrase, but in resolving an event as part of the resolution of a verb, a new event is generated. 2.3.3.3

Prepositional Sense

This primitive states that a formula with a prepositional category holds in CAT for the appropriate property (i.e. the application of a  expression to the restriction) if there is a prepositional sense. This prepositional sense then becomes the rst order predicate which is abstracted over in the app resolution. Prepositions may have multiple senses. An example of prepositional ambiguity is:



on 0! on Locational



on 0! on Temporal

2.3.3.4

Genitive Sense

The selection of a genitive sense is similar to that of the prepositional sense.

2.4 Resolution and Paraphrasing in clare A brief note is given here on the methods used by clare to resolve and paraphrase QLFs. In a later chapter, a comparison will be made between the two techniques.

2.5.

SUMMARY

17

2.4.1 clare Resolution As in this work, clare uses a set of resolution rules to specify the resolution of its QLFs. The dierences of the systems are described by the points below.



clare uses resolution rules that prescribe the use of methods, i.e. prolog predicates, to nd a resolution. This system uses resolution rules that require one general technique.



clare's resolution rules are procedural and non-reversible. This system's rules are declarative and reversible.

2.4.2 clare Paraphrasing The literature on clare [4][14] suggests a reversible system but describes a compromise. As with resolution, a less general method is used based on case methods. It should also be mentioned that clare's generation is not functionally the reverse of the analysis of text into QLFs and consequently can't generate from QLF's that it can produce by analysis.

2.4.3 The Advantages of a Declarative and Reversible System There are several advantages of implementing resolution in a declarative and reversible way. Many of these advantages are simply to do with the exibility of the resulting system. The mechanisms underlying the module are free of changes made to the declarative state of the system. Consequently, the rules are the only components that require to be modi ed.

2.5 Summary This chapter has set the scene for the remainder of this project. It has introduced the Quasi Logical Form as a representational language for linguistic analysis and demonstrated how resolution can exploit a monotonic semantics to provide a exible and reversible treatment through a declarative statement of the relation CAT . The next few chapters continue by presenting the inference mechanism, grounding the theory presented in an implementation and detailing the results of applying the method to the task of paraphrasing in ambiguous contexts.

18

CHAPTER 2.

RESOLUTION AND MONOTONIC INTERPRETATION

Appendix A

Algorithms A.1 Top Proof top proof

 

qlf restriction

0! >

format

top proof(< partial

qlf >; < ent >)

case 1. scoped expression (a) discharge < partial qlf >

top proof( < partial qlf >; > ent >) 2. proof conjunction (a) < partial qlf > = [and,< conj 1 >; < conj 2 >] (b) top proof(< conj 1 >; < ent >) (c) top proof(< conj 2 >; < ent >) (b)

3. other (a) match < rule > by subsumption (b) < rule > = < partial qlf > (c)

< antecedents >

top proof rec(< antecedents >; < ent >)

A.2 Proof proof

19

20

APPENDIX A.

 

predicate

ALGORITHMS

2 entity 0! >

format

proof(< ent >; < f act >) case

)> ) proof(< some arg >; < f act >) < antecedent list >)  DOM ) proof rec(< ent >;
 DOM

6



2. < ent >  Args 3. (< f act >

antecedent list >)

4. DOM

!

equivalent

) proof(< ent

0

>; < f act[=] >)

A.3 Skolemization Skolemize

 

logical f orm

2 P ol 0!

logial f ormskolemized

format

skolemize(< logical

f orm >; < V ars >; < P ol >; < skolemized f orm >)

case < logical f orm > 1.

forall(V,Form)^< P ol > = true skolemize(Form,V [ < V ars >; < P ol >; < skolemized forall(V,Form)

(a) 2.

(a) (b)

f orm >)

flip(< P ol >) skolemize(exists(V,Form)< V ars >; < P ol >; < skolemized

f orm >)

exists(V,Form)^< P ol > = true (a) replace(V,Vars,Form) (b) skolemize(Form,< V ars >; < P ol >; < skolemized f orm >) 4. exists(V,Form)^< P ol > = false (a) skolemize(Form,V[ < V ars >; < P ol >; < skolemized f orm >) 5. not(Form) 3.

(a) (b) 6.

2 B) 2 =^;2

(A

(a) (b) (c) 7.

flip(< P ol >) skolemize(Form< V ars >; < P ol >; < skolemized

_

skolemize(A< V ars >; < P ol >; < skolemized skolemize(B< V ars >; < P ol >; < skolemized

(A

(a)

=

! B)

flip(< P ol >)

f orm >)

f orm >) f orm >)

A.4.

21

CONJUNCTIVE NORMAL FORM

(b) (c) (d)

skolemize(A,< V ars >; < P ol >; < skolemized flip(< P ol >) skolemize(B,< V ars >; < P ol >; < skolemized

replace

 

var

0!

skolem f unction

format

replace(< V 1. 2. 3.

>; < V ars >; < F orm >)

form vars filter for var(< F orm >) variable set < V ars > [ form vars create new skolem function from variable set

4. < V >

skolem function

A.4 Conjunctive Normal Form 0! Q = :P _ Q :(:P ) = P :(P _ Q) = :P ^ :Q :(P ^ Q) = :P _ :Q P _ (Q ^ R) = (P _ Q) ^ (P _ R) (Q ^ R) _ P = (P _ Q) ^ (P _ R)

1. P 2. 3. 4. 5. 6.

A.5 Compilation 

compile

{ {

qlf

0!

aqlf

format

compile(< string >) 1. string to qlf(< string >; < qlf 2. compile out(< qlf >) 3. process leaves and abstract



compile out

>)

f orm >) f orm >)

22

APPENDIX A.

{

ALGORITHMS

format

compile out(< qlf

>)

1. traverse by de-construction. 2. ensure consistency of multiple occurrences.



traverse

{

format

traverse(< QLF

>; < Abstract QLF >; < Leaves >)

1. recurse on structure by de-construction case 1. var 2. atomic

! recurse on X, Y word sense >j< Args >]

3. and X Y 4.

[< word sense >

recurse on < Args > and return
; < string >) 1. nd all: reverse resolve(< qlf >; < token >) ! < qlf set > 2. evaluate metric(< qlf set >; < evaluatedqlf set >) 3. sort(< evaluatedqlf set >; < sortedqlf set >) 4. qlf to string(< topqlf >; < string >)

Bibliography [1] Hiyan Alshawi. Resolving quasi logical forms. Computational Linguistics, 16(3), September 1990. [2] Hiyan Alshawi, editor. The Core Language Engine. The MIT Press, 1992. [3] Hiyan Alshawi, David Carter, Richard Crouch, Steve Pulman, Manny Rayner, and Arnold Smith. CLARE-3: Software Manual, 1992. [4] Hiyan Alshawi, David Carter, Richard Crouch, Steve Pulman, Manny Rayner, and Arnold Smith. CLARE: A Contextual Reasoning and Cooperative Response Framework for the Core Language Engine. Stanford Research Institute, 1992. [5] Hiyan Alshawi and Richard Crouch. Monotonic semantic interpretation. In 30th Annual Meeting of The Association for Computational Linguistics, 1992. [6] Robert Dale. Generating Referring Expression in a Domain of Objects and Processes. PhD thesis, The University of Edinburgh, 1988. [7] Michael R. Genesereth and Nils J. Nilsson. Logical Foundations of Arti cial Intelligence. Morgan Kaufmann, 1987. [8] B. J. Grosz and C. L. Sidner. Attention, intentions, and the structure of discourse. Computational Linguistics, (12), 1986. [9] J. Hobbs. Coherence and co-references. Cognitive Science, 3(1), 1979. [10] J. Hobbs. Resolving pronoun references. In B. J. Grosz et al, editor, Readings in Natural Language. Morgan Kaufmann, 1986. [11] C. Linde. Focus of attention and the choice of pronouns in discourse. In T. Givon, editor, Syntax and Semantics, pages 337{359. Academic Press Inc., 1979. 23

24

BIBLIOGRAPHY

[12] D. D. McDonald. Mumble, a exible system for language production. In Proceedings of the Seventh International Joint Conference on Arti cial Intelligence, 1981. [13] K. R. McKeown. Generating Natural Language Text in Response to Questions About Database Structure. PhD thesis, The University of Pennsylvania, 1982. [14] S. M. Shieber, G. van Noord, F. C. N. Pereira, and R. C. Moore. Semantic head driven generation. Computational Linguistics, 16, September 1990.