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<Paper uid="C88-1003">
  <Title>Functional Constraints in Knowledge-Based Natural Language Understanding</Title>
  <Section position="2" start_page="14" end_page="15" type="metho">
    <SectionTitle>
3. Structural Isomorphy
</SectionTitle>
    <Paragraph position="0"> 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.</Paragraph>
    <Paragraph position="1"> 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 &amp;quot;structural momorphmm. See figure 2 for a graphical illustration.</Paragraph>
    <Paragraph position="2"> 1 FALIN can be read .~'st Attempt at LINkfping Natural Language ~nterface.</Paragraph>
    <Paragraph position="3"> Thus, no claims are made for other aspects of semantic interpretation, such as quantification or modification.</Paragraph>
    <Paragraph position="5"> yielding structural isomorphism.</Paragraph>
    <Paragraph position="6"> 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.</Paragraph>
    <Paragraph position="7"> 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. HoweC/er, compositional systems too, e.g. /Hirst 198'1/, oideg~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.</Paragraph>
    <Paragraph position="8">  (t) Jim sold the car to an Englishman.</Paragraph>
    <Paragraph position="9"> in the fi'aaaework used here we could have the following grammar rule, 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 &amp;quot;pseudo.prepositions&amp;quot; (named  odeg()t~3 , OBJ, INDOB3) are the rdevaat syntactic objects hlstead of i~r~mla~ical ~u actions.</Paragraph>
    <Paragraph position="10"> 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&amp;quot; LEX) = !CAR, (T NUMB) = SING 1,2: sold; FV, (j&amp;quot; LEX) = !SELL, (T TENSE) = PAST L3: the; DET, -~ , (1&amp;quot; SPEC) = DEF L4: to; P, -- , (~&amp;quot; PCASE) = TO</Paragraph>
    <Section position="1" start_page="14" end_page="15" type="sub_section">
      <SectionTitle>
In the
appropriate
</SectionTitle>
      <Paragraph position="0"> lexeme dictionary lexemes are associated with 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 between 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.</Paragraph>
      <Paragraph position="1"> !SELL: { &amp;Selll / &amp;Sell2 / ... } !CAR: { &amp;Carl / &amp;Car2 / ... } !JIM: { Person67 / Person83 / Name18 / (TYPE=&amp;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&amp;ruction associations of Provider and Receiver~ we state the associations ii1 the definition of the two action types. In any case the prototype of &amp;Sell\] will turn out to bear the following inibrmation: (2) _ &amp;Selll</Paragraph>
      <Paragraph position="3"> 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.</Paragraph>
      <Paragraph position="4"> 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 '&amp;'.</Paragraph>
      <Paragraph position="6"> 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.</Paragraph>
      <Paragraph position="7">  4. Cases of non-lsomorphtsm.</Paragraph>
      <Paragraph position="8"> 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.</Paragraph>
      <Paragraph position="9"> 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).</Paragraph>
      <Paragraph position="10"> (3) He broke their hearts completely.</Paragraph>
      <Paragraph position="11"> 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:</Paragraph>
    </Section>
  </Section>
  <Section position="3" start_page="15" end_page="16" type="metho">
    <SectionTitle>
PL \[LEX ITHEY
</SectionTitle>
    <Paragraph position="0"> 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 &amp;Breaksomeone's-heart carries the following information associated with the attributes of its prototype:</Paragraph>
    <Paragraph position="2"> 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.</Paragraph>
    <Paragraph position="3"> 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.</Paragraph>
    <Paragraph position="4"> 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.</Paragraph>
    <Paragraph position="6"/>
    <Section position="1" start_page="16" end_page="16" type="sub_section">
      <SectionTitle>
4.3 Constituted discourse objects. An utterance is itself a
</SectionTitle>
      <Paragraph position="0"> 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.</Paragraph>
      <Paragraph position="1"> I think your statement needs clarification.</Paragraph>
      <Paragraph position="2"> Except for performative utterances there is no head word in the utterance that can be used to for its classification, however.</Paragraph>
      <Paragraph position="3"> Instead the classification will have to rely on other information, such as clause-structure and punctuation.</Paragraph>
      <Paragraph position="4"> 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.</Paragraph>
      <Paragraph position="5"> (10) Show me the files.</Paragraph>
      <Paragraph position="6"> 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.</Paragraph>
      <Paragraph position="7"> Consider now how (I0) may be analysed. Let us classify it by meaus of the object type &amp;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):  In order to distinguish objects being described from objects being constituted w~ distinguish two modes of correspondence. The ~-arrow indic~..tes&amp;quot; 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.</Paragraph>
    </Section>
    <Section position="2" start_page="16" end_page="16" type="sub_section">
      <SectionTitle>
4.4 Implied referents a~d types. As is well known, in
</SectionTitle>
      <Paragraph position="0"> 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).</Paragraph>
      <Paragraph position="1">  (12) - Who is the manager of the sales department? - Jim l~mith.</Paragraph>
      <Paragraph position="2"> (13) I've go~ many more at home.</Paragraph>
      <Paragraph position="3">  There are ~wo ways to react in the face of such &amp;quot;elliptic&amp;quot; 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.</Paragraph>
      <Paragraph position="4"> 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 &amp;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.</Paragraph>
      <Paragraph position="6"> 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.</Paragraph>
      <Paragraph position="7"> 5. Restrictiona on proper correspondence It would be premature to attempt an explicit characterization of the correspondence relations 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.</Paragraph>
      <Paragraph position="8"> 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.</Paragraph>
      <Paragraph position="9"> 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.</Paragraph>
      <Paragraph position="10"> 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.</Paragraph>
      <Paragraph position="11"> 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 C/ is an f-structure, C/8 will indicate an f-structure obtained m . . from C/ by subtraction o~ semantmally irrelevant paths.</Paragraph>
      <Paragraph position="12"> Thus, we get the following conditions on proper correspondence between d-structures and f-structures: (1) A d-structure, 6, and an f-structure, C/, are corresponding properly in descriptive mode, only if (a) 6(Type)~ g(C/(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.</Paragraph>
      <Paragraph position="13"> (e) For any sub-structure~ 6', of 6, there is a sub-structure, C/', of ~, such that 6' and C/' correspond properly in descriptive mode.</Paragraph>
      <Paragraph position="14"> (2) A d-structure, 6, and an f-structure, C/, 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 ~.</Paragraph>
      <Paragraph position="15"> (c) as l(c).</Paragraph>
    </Section>
  </Section>
  <Section position="4" start_page="16" end_page="17" type="metho">
    <SectionTitle>
6. Acknowledgements
</SectionTitle>
    <Paragraph position="0"> 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.</Paragraph>
  </Section>
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