Abstract

Many knowledge-based systems of semantic interpretation characterize properties of a structural level and account for a rely explicitly or implicitly on an assumption of structural correspondence between those properties and properties of isomorphy between syntaotic and semantic objects, handling another level, i.e. the level to which the constraint is attached. exceptions by ad hoc measures. In this paper I argue that The correspondence may be between two different levels of constraint equations of the kind used in the LFG- (or syntactic structure, as in LFG, or between a syntactic structure PATR-)formalisms provide a more general, and yet restricted and a semantic structure or conceivably between any two formalism :in which not only isomorphic correspondences are structural aspects that constrain each other. So far it seems that expressible, but also many cases of non-isomorphic correconstraints have primarily been stated in the direction from form spondences. I illustrate with treatments of idioms, speech act to meaning, where meaning has been regarded as inherent in interpretation and discourse pragmatics. linguistic expressions and thus derivable from an expression, given a grammar and a lexicon. 1. Background and purpose In a working system, however, we are not merely interested in a decontextualised meaning of an expression, but in the content communicated in an utterance of an expression, which, as we In knowledge-based natural language understanding systems know, depend on world knowledge and context in more or less the role of syntax is by no means self-evident. In the Yalean subtle ways. A rather trivial fact is that we need to have an tradition /,~tchank & Riesbeck, 1981/ syntax has only played a understanding of the context in order to find a referent for a minor role and whatever little syntactic information there is has referring expression. A more interesting fact is that we often been expressed in simple terms. Consequently, there is no need an understanding of context in order to get at the grammar as such and syntactic conditions are freely intermixed information which is relevant for determining the referent with semantic conditions in the requests that drive the system /Moore, 1981; Ahrenberg a1987a,b; Pulman, 1987/. forward/13irnbaum & Selfridge, 1981/. Similarly, in frame-based systems such as /Hayes, 1984/ the syntactic information is In a knowledge-based system, the knowledge-base provides an stated in ~:onjunction with all other information relevant for encoding of general world knowledge as well as a basis for instances ot a frame. A justification for this approach, apart from keeping track of focal information in discourse. It seems a transparency, is that it makes sense to say that part of our natural move to combine a knowledge-based semantics with the knowledge of a concept is knowledge about how it is communidescriptive elegance and power of constraints, but as far as I cated. know, not much work has been done in this area. /Tomita & Carbonell, 1986/presents a knowledge-based machine-translation A major disadvantage of this approach is of course its lack of system based on functional grammar and entity-oriented parsing. generality. To overcome this problem we may extract general syntactic knowledge' and make use of it in a syntactic parser In this paper I discuss the role of syntax in three general and which works alongside with the semantic analyser. Examples of related aspects of utterance interpretation: referent such systems are PSI-KLONE /Bobrow & Webber, 1980; determination, classification, and role identification. A Sondheimer et ah, 1984/ and MOPTRANS /Lytinen, 1986; joint solution to these problems will fall out if we assume, as is 1987/. The promise of these systems is that you get both often done, a simple, one-to-one structural (or categorial) modularity and integration, although there are many open correspondence between syntactic and semantic objects. This is questions about how the integration can best be achieved. done explicitly e.g. by /Danleli et ah, 1987/ and /Hirst, 1987/ and, so far as I can judge, implicitly in many other systems. Moreover, one would I!ke to put the integration of syntax and However, the assumption is much too simplified and must be semantics, not just syntax and semantics per se, on a principled amended. I will illustrate some cases where the correspondences basis, i.e. we need a theory of how syntactic and semantic are more involved and argue that local constraints of the kind objects correspond. Linguistics and philosophy offer some used in the LFG-formaiism /Kaplan & Bresnan, 1982/ are able guidelines here, such as compoeitionaiity, and a number of to handle them in a fairly straight-forward way. Thus, instead of different theories, but a problem is that the semantic objects ad hoc-solutions the isomorphic cases will in this framework fall considered are usually not knowledge structures. /Hirst, 1987/, out as particularly simple instances of the general principles. though, is an attempt at a principled, modular and integrated knowledge-based system where compositionality and a principle of strong typing provide the theoretical underpinnings. These principles teem to provide a tighter straight-jacket han one would really want, however, as indicated by the many structures 2. A framework and a system that Hirst shows are problematic for his system. Another~ more recent approach is to capture correspondences I regard the process of interpretation as a process in which a between syntactic and semantic objects through constraints given object, the utterance, is assigned a description, the /Halvorsen~ 1983; 1987; Fenstad etal., 1985; Kaplan, 1987/. An analyMs. The description has different aspects, primary among them being essential feature of constraints is that they simultaneously

a constituent structure, (c-structure) . a functional structure, (f-structure), a semantic structure, (d-structure) and • a content structure.

I refer to these structural levels as aspects in order to emphasize the idea that they are all part of one and the same interpretation of the utterance. The c-structure and the f-structure are roughly as in LFG /Kaplan & Bresnan, 1982/, but with some important deviations. The functional structure is strictly syntactic. There are no semantic forms and hence no grammatical notions of coherence and completeness. Instead of the PRED-attribute, there is an attribute LEX whose value is a "lexeme", an abstract grammatical unit which in turn is associated with semantic objects: object types, semantic attributes, and so on.

The semantic structure is a descriptor structure ('dag') just as the functional structure, but with descriptors pertaining to the discourse referents accessed or made available by the utterance. Thus, a constituent of the semantic structure consists of a description that potentially applies to an object in the universe of discourse. The content structure differs from the semantic structure mainly in that referents for descriptions have been identified (where possible).

If a c-structure, an f-structure and a d-structure apply to an expression under a given interpretation they are said to correspond. If, similarly, a sub-expression of the input is associated with constituents at all three levels, these constituents are said to correspond.

Correspondences between c-structure and f-structure are

defined by an LFG-style grammar and a dictionary of stems and ~. affixes. Correspondences between f-structure and d-structure are

defined by the lexeme dictionary and information in the

knowledge-base. Primary among the knowledge structures are

types, attributes, and instances. Every type is associated with a

prototype, a frame-like structure whlch'defines what attributes

apply values. to instances of that type, as well as restrictions on their

Prototypes are also associated with functional constraints, thus defining possible correspondences between d-structures and f-structures. For example, the attribute AGENT, beside other restrictions on its occurrence and values, may be assigned the canonical constraint (~ SUB J) = ~. The arrows in this schema have the same interpretation as in the grammar ules: i" points to the f-structure node corresponding to the description of which the attribute is part, ~ points to the f-structure node corresponding to its value.

Semantic attributes may also be associated with contextual constraints. The context is represented by a special object, the discourse state (DS), the description of which encodes the contextual information that the system currently has available. In particular, this will include information about who is speaker and who is addressee. A simple contextual constraint can be stated as =(DS SPEAKER), which when associated with an attribute asserts, the identity between its value and the current speaker.

The relations between different structural aspects and the knowledge sources that define and constrain them are illustrated in figure 1.

In the process of interpretation the analysis is ideally constructed incrementally. When information is added to one structural aspect and there is a constraint associated with this information, we are justified in adding the information stated in the constraint o the structural aspect to which it relates. If this is not possible, e.g. due to the presence of contradicting information, the initial information can be rejected.

GRAMMAR MORPH DICTIONARY

LEXEME DICTIONARY g PROTOTYPES ) \] DISCOURSE STATE i string c structure f structure d-structure content structure Figure 1: Structural aspects and their correspondencaL The ideas presented here have been partially implemented in LEXICAL-FUNCTIONAL a system called FALIN, which is developed as a precursor to an understanding component of a dialog system (Ahrenberg, 1987a). 1 The world of FALIN is a drawing-pad and its knowledge cover simple geometrical objects that the user can draw and manipulate using natural language. FALIN's parser (a chart parser) is constructing ac-~tructure and an f-structure in tandem, hut hands f-structures over to another module which attempts to construct corresponding d-structures and content structures. The content structure is then evaluated against the knowledge-base. 3. Structural Isomorphy

The semantic aspects that this paper considers are three very basic ones: (i) referent determination; to determine the set of discourse objects (referents) that a given utterance relates to; (ii) classification; for each of these referents to determine their type, and (iii) role identification; to determine the relations they contract with the other referents. From the first task I then exclude the problem of actual identification of referents, restricting myself to the task of deciding that there is a separate entity that some part of the utterance applies to.

Now, we can formulate a general and practical principle, which is commonly used in semantic interpreters and which offers a solution to all three problems at once, namely a principle of structural isomorphy between syntactic and semantic structure. The basic tenet of this principle is that there exists a level of syntactic representation (which I will call fnnctional structure here, but which may be represented in various ways, e.g. as a dependency structure) such that (a) every referent is expressed by some major constituent of the functional structure; (b) the type of a referent is given, directly or implicitly, by (one sense of) the head of that constituent; and (c) two referents contract a role relationship iff their respective constituents contract a grammatical relation in the functional structure. These one-to-one correspondences between syntactic and semantic objects yield isomorphic syntactic and semantic structures as long as we only consider the three mentioned aspects of semantic interpretation, and hence the name "structural momorphmm. See figure 2 for a graphical illustration. 1 FALIN can be read .~'st Attempt at LINkfping Natural Language ~nterface.

Thus, no claims are made for other aspects of semantic interpretation, such as quantification or modification. l - o.Tto-o,;~ -\] SyN~fAX ~EIV~AN'IICS Categore~natic Word1 ~ ................ ~ Referent Type1 ,.) Corl~,tituent 1\] ~ ...... ._> Referentl % : ........ Jza~ Constituent2 \] . . . . . . . Categorematic Word2 Referent Type2 Figure 2: Correspondences of syntactic and semantic objects yielding structural isomorphism.

It should t,e observed that the isomorphy principle allows for both lexical and structural ambiguity, i.e. it does not require ~hat a given word, or grammatical relation can be interpreted in only one way. What it requires is a one-to-one correspondence of syntactic and semantic objects of the same interpretation. Moreover, structural isomorphy is riot the same as composition~,lity. In one sense compositionality is more restrictive since it applies to all ~mpects of semantic interpretation. On the other hand compositionality is less restrictive since it requites derivation trees to be i~omorphic, not constituent structmea. Howe¢er, compositional systems too, e.g. /Hirst 198'1/, oi°~en ~ssume structural isomorphism for the aspects of

q col|tern here. ~

As an ilh~a~tration, consider (1). Here the speaker can be said to refer to hmr entities, a sale, a car and two male humans. The last three rdate to the first as, say, Goods, Provider and Receiver, re~pectively. Each of the referents corresponds to a major constituent, the whole sentence for the case of the sale and subject, direct object and indirect object for the others. Also, the head words as//, Jim, car and Englishman provide the type inibrmation ~ stipulated. (t) Jim sold the car to an Englishman.

in the fi'aaaework used here we could have the following grammar ule, defining constraints on the functional structure: RI: S .... NP: (t SUBJ) = $ VP: T=$ R2: VP -~ FV: ~'::~ NP:(~ OBJ) =: ~ PP*: (t POBJ)9 R3: Pl? ,-~ P: ~':::$ NP: i'==~ /I,4: NP -+ { (DET: ~:::~) N: ~::~ / PN: ~=:J. } 3 h:~ tlirst's ~lm~em prepositions and "pseudo.prepositions" (named o°()t~3 , OBJ, INDOB3) are the rdevaat syntactic objects hlstead of i~r~mla~ical ~u actions.

The morph dictionary associates functional constraints with stems and affixes as in the following illustrations. Stems are also associated with lexemes~ but affixes and function words are not. 4 LI: cat'; N, (i" LEX) = !CAR, (T NUMB) = SING 1,2: sold; FV, (j" LEX) = !SELL, (T TENSE) = PAST L3: the; DET, -~ , (1" SPEC) = DEF L4: to; P, -- , (~" PCASE) = TO

In the lexeme dictionary lexemes are associated with appropriate semantic objects. This association may be one-to-many, but only one of the alternatives can be involved in an analysis, thus making the correspondence b tween head words and types one-t(r.one. It may also involve object descriptions rather than objects. For instance, a proper name lexeme, such as !JIM, can have associations with known instances as well as with a description that can be used in the construction of a new instance. !SELL: { &Selll / &Sell2 / ... } !CAR: { &Carl / &Car2 / ... } !JIM: { Person67 /Person83 /Name18 /

(TYPE=&Person, SEX=Male, NAME=NamelS) }

Finally, the association between grammatical functions and semantic roles is captured in the definition of the latter. As attributes can be differentiated in very much the same way as object types, these correspondences can be stated at an appropriate level of generality. For instance, Provider may be analysed as a differentiation of Agent and inherit its association with the Subject function from that attribute, it is also possible to have these associations stated at the level of individual action types. If we want to express the difference between sell and buy as a difference in the role&ruction associations of Provider and Receiver~ we state the associations ii1 the definition of the two action types. In any case the prototype of &Sell\] will turn out to bear the following inibrmation: (2) _ &Selll

Type; (T LEX) = !SELL Provider; (T SUBJ) = Receiver; (t OBJ) = Goods; (T POBJ)~

(i PCASE) = TO Price; (~ POBJ)-B

($ PCASE) = FOR

Here the associations are not just simply stated as a function label associated with the role attribute, but corresponding functional descriptions are explicitly represented. This is so because more than a mere function label may be involved and, as will be shown below, the correspondences may be more complex than this.

The correspondences in a prototype should be read as a set of canonical correspondences. Alternative correspondences can be obtained from lexieal rules just as in LFG-theory /Bresnan, 1982a; cf. also Halvorsen, 1987/. Applying the Passive lexical rule to (2) we obtain an alternative set of constraints, namely (2'). 4 Lexemc labels are indicatied by an hLitial exclamation mark. Object types are indicated by an initial '&'. (2') __ &Selll

Type; Provider; " Goods; Receiver; Price; There are some reasons for stating the role-function correspondences as functional constraints induced by the semantics rather than the other way round. For one thing, definitions of types and attributes are needed for independent reasons and the introduction of the functional constraints is merely a way of encoding knowledge that pertains to them, i.e. knowledge of how they are communicated. Moreover, subcategorization properties are semantically grounded, even if not absolutely predictable. 4. Cases of non-lsomorphtsm. 4.1 Non-isomorphic constructions. There are certain linguistic construction-types that, at least on the surface~ contradict the isomorphism principle, such as Equi, Raising, Longdistance dependencies and Gapping constructions. However, in most cases it seems possible to eliminate the problems posed by these constructions already in the grammar and thus have appropriate functions assigned to constituents at functional structure. 4.2 Flexible idioms. For simplicity we may characterize a flexible idiom as a complex expression with a definte meaning whose parts may undergo variation and occur in non-adjacent positions. Fixed idioms, such as at once, back and forth, first of all do not pose the same problems as they can be taken care of already at the c-structure level. Most flexible idioms in English seem to involve a verb, such as make fun of, break someone's heart, or make up one's mind. Consider (3). (3) He broke their hearts completely.

At the c-structure and f-structure levels it is analysed in the same way as any other sentence. In particular, each constituent will have its own LEX-dsecriptor: (4) -LEX

TENSE SUBJ OBJ

Object types for both ordinary breaking and heart-breaking are associated with IBREAK in the lexeme dictionary. The object type for heart-breaking also involve a reference to the lexeme tHEART, however. The object type &Breaksomeone's-heart carries the following information associated with the attributes of its prototype: (1" LEX) = tSELL (T ACT/PASS) = PASSIVE /I POBJ)~ ~

PCASE) = BY (T SUB J) = II POBJ)3 ~

PCASE) = TO (1" POBJ)~ J. (I PCASE) = FOR IBREAK PAST \[LEX ~LEX |NUMB

POSS IHE\] IHEART \]~ PL \[LEX ITHEY (5) __ &Break-someone's-heart:

Type; II LEX) ---- 'BREAK / -~\]

OBJ LEX)= 'HEART I \[ Cause; (T SUBJ)----- ~ L ~patient; (1- OBJ POSS) = £ _~

This means that while there is a simple one-to-one correspondence between Subject and the role of Cause, the other function-role correspondences involve structural distortions. They are still expressible by local constraints, however, and this holds for any flexible verbal idiom where the fixed parts have a grammatical relation to the verb, or to some complement of the verb, i.e. for the great majority of verbal idioms in the language.

In some cases a part of the idiom may play a double role. On the one hand it is part of the expression of the idiom and on the other hand it brings with it a referent of its own. Consider the following discourse: (6) A: He hasn't shown his face here for the last couple of

weeks, has he?

B: Who wants to see it anyway? To describe the fact that the phrase hie face can express a referent we may allow for this possibility in the statement of correspondences in the protytype for the action. (7) __ &Show-one's-face:

Type; Ii LEX) = ISHOW

oBJ LEX) = ~FACE

OBJ POSS LEX) = IREFL (T SUB J) = (~ OnJ) = I~ ADV)~

PCASE) = LOC Agent; Object; Location; 4.3 Constituted discourse objects. An utterance is itself a discourse object, i.e. it may be referred to in the discourse that follows. When this happens the utterance will be classified one way or the other, as in utterances of the following sort: 81 That is a difficult question to answer.

I think your statement needs clarification. Except for performative utterances there is no head word in the utterance that can be used to for its classification, however. Instead the classification will have to rely on other information, such as clause-structure and punctuation.

Speech-act interpretation is often regarded as something entirely different from semantic interpretation proper. This, I would argue, is a mistake. Illocutionary categorization is constrained by words and world knowledge in very much the same way as categorization of other referents? The essential difference between the illocutionary act as a referent and other referents is that the illocutionary act come into being with the utterance of the words, whereas the other referents exist independently. This means that we can postulate (at least) two ways in which an uttered expression relates to discourse referents, first, it relates to referents described by the utterance, and second, to referents constituted by the utterance, in particular the illocutionary act. The analysis of an utterance would be incomplete if it does not include a classification of the utterance, as well as the discourse objects that fulfils the roles of Speaker and Addressee. (10) Show me the files. 5 Similar problems arise with sentences each as The question is why he did it, The fact is that he did i~ where the subjects are not interchangeable: *The fact is why he did it.

Consider now how (I0) may be analysed. Let us classify it by meaus of the object type &Directive which we assume to be supertype for commands, orders, directions and similar ~Jpeech acts. The prototype for this type may be assigned the following set of constraints (as one alternative): (11) __ &Directive

Type; (~ MOOD) = IMPERATIVESpeaker; =(DS SPEAKER) I Addressee; =(DS ADDRESSEE) lAction; ~=~ In order to distinguish objects being described from objects being constituted w~ distinguish two modes of correspondence. The ~-arrow indic~..tes" an f-structure node corresponding in constitutive mode. 6 The schema associated with the Action attribute says that the f-structure node corresponding to the d-structure node for the directive in constitutive mode actually coincides with the f-str~mture node describing the action being directed, thus encoding the one-to-two relation between the utterance and the discourse objects it relates to. 4.4 Implied referents a~d types. As is well known, in situated discol~rse we regularly do not give explicit expression of the referents being talked about as such information can be inferred from the context. Obvious illustrations are given by short answers to questions as in (12). Similarly, we may suppress head words if t~hey are inferrable, as in (13). (12) - Who is the manager of the sales department?

- Jim l~mith. (13) I've go~ many more at home.

There are ~wo ways to react in the face of such "elliptic" utterances. One way is to say that they require special pragmatic heuristics which are independent of the principle of structural isomorphism (and vice versa) and thus simply regard them as irrelevant. However, this makes the principle limited in application. It would be better to have more general principles of utterance intelpretation that together covers both elliptical and non-elliptical utterances. Again, contextual constraints in conjunction with ordinary functional constraints can do part of the job ibr us. A phrase such as Jim Smith in itself does not give much information of course. However, when it is uttered in reply to a question, as in (12), it will have quite a well-defined meaning. In the definition of tiJe utterance type &Answer, we may thus include, beside attributes for Speaker and Addressee, also an attribute indiq',ating what question is being answered. This question can be retrieved from the discourse state, where it was put when it was raised and kept until it is answered or dropped. (14) __ _ &Answer

Type; ~peaker; Addressee; Question; _Answer; 6 This use of the symbol '1~' should \]Lot be confused with its use in Bresnau (1982a}~ where it is part of the description of long-distance dependencies.

 Restrictiona on proper correspondence

It would be premature to attempt an explicit characterization of the correspondence r lations between the structural aspects of an analysis, especially as important aspects of semantic interpretation have not even been considered. In this final section I therefore only summarize the general ideas, pointing out how they differ from structural isomorphism and state a few necessary conditions on the correspondence between f-structure and d-structure.

The referent descriptions conveyed by an utterance are constrained by linguistic form (functional structure) as well as by conceptual knowledge (prototypes) and context-of-utterance (discourse state). A referent need be given no overt expression in the utterance if it is inferable from a prototype and/or from the context.

The constraints themselves need not be one-to-one, contrary to the principle of structural isomorphy, but they are local in the sense that they can only refer to (i) structures corresponding to either (a) the object that induces them, (b) the object of which that object is an immediate part, or (c) other dependents of that dominating object, or (ii) objects of the discourse state.

To capture speech-act interpretation we recognize two modes of correspondence, one based on the relation description-described object, and the other on the relation utterance~ constituted act. (~ MOOD) = DECL = (DS SPEAKER) : (DS ADDRESSEE) e (DS QUESTIONS) ~ = 1

The f-structure is a syntactic structure, which means that it must be a minimal structure satisfying the constraints induced by the c-structure. However, it must also correspond properly with the d-structure. To account for this correspondence we must first realize that not all functional attributes need be semantically relevant e.g. those indicating grammatical gender. If ¢ is an f-structure, ¢8 will indicate an f-structure obtained m . . from ¢ by subtraction o~ semantmally irrelevant paths.

Thus, we get the following conditions on proper correspondence between d-structures and f-structures: (1) A d-structure, 6, and an f-structure, ¢, are corresponding properly in descriptive mode, only if (a) 6(Type)~ g(¢(LEX)), where g is the function defined by the lexeme dictionary; (b) There is a prototype, /'/, for 6(Type) such that (i) 6 satisfies the conditions'' of //, and (ii) Cesta is a minimalHfo structure satisfying all functional constraints reduced by r the role attributes at top level of 6. (e) For any sub-structure~ 6', of 6, there is a sub-structure, ¢', of ~, such that 6' and ¢' correspond properly in descriptive mode. (2) A d-structure, 6, and an f-structure, ¢, are corresponding properly in constitutive mode, only if (a) There is an utterance-type, D,and a prototype, IID, for/2, such that 6 satisfies the conditions of//_. IJ (b) ~b is a minimal structure satisfying all functional constr~nmts induced by //~ for the role attributes at top level of ~. (c) as l(c).

 Acknowledgements

This research has been supported by the Swedish National Board for Technical Development. I am indebted to Magnus Merkel and the other members of the Natural Language Processing Laboratory at Link6ping university, Mats Wirdn, Arne J6nsson and Nils Dahlbllck for valuable discussion of these topics.

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