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<Paper uid="P83-1010">
  <Title>A FOUNDATION FOR SEMANTIC INTERPRETATION</Title>
  <Section position="2" start_page="0" end_page="65" type="metho">
    <SectionTitle>
2. Montague semantics
</SectionTitle>
    <Paragraph position="0"> In his well-known &amp;quot;PTQ&amp;quot; paper (Montague 1973), Richard Montague presented the complete syntax and semantics for a small fragment of English. Although it was limited in vocabulary and syntactic complexity, Montague's fragment dealt with such impor- null tant semantic problems as opaque contexts, different types of predication with the word be, and the &amp;quot;the temperature is 90&amp;quot; problem; 3 for details of these, see Dowty, Wall and Peters (1981).</Paragraph>
    <Paragraph position="1"> Montague's semantic rules correspond to what we have been calling semantic interpretation. That is, in conjunction with a syntactic process, they produce a semantic representation, or translation, of a sentence. There are four important properties of Montague semantics that we will examine here. Below, we will carry three of these properties over into our own semantics.</Paragraph>
    <Paragraph position="2"> The first property, the one that we will later drop, is that for Montague, semantic objects, the results of the semantic translation, were such things as individual concepts (which are functions to individuals from the cartesian product of points in time and possible worlds), properties of individual concepts, and functions of functions of functions of functions. At the top level, the meaning, of a sentence was a truth condition relative to a possible world and point in time. These semantic objects were represented by expressions of intensional logic; that is, instead of translating English directly into these objects, a sentence was first translated to an expression of intensional logic, for which, in turn, there existed an interpretation in terms of these semantic objects.</Paragraph>
    <Paragraph position="3"> Second, Montague had a strong theory of types for his semantic objects: a set of types that corresponded to types of syntactic constituents. Thus, given a particular syntactic category, such as proper noun or adverb, Montague was able to say that the meaning of a constituent of that category was a semantic object of such and such a type. 4 Montague's system of types was recursively defined, with entities, truth values and intensions as primitives, and other types defined as functions from one type to another in such a manner that if syntactic category X was formed by adding category Y to category Z, then the type corresponding to g would be functions from senses of the type of  properties of individual concepts; that of an adverb is function between set~ v\[ individual concepts (Dowry C/~ al Ig81: 183, 187). Y to the type of X. 5 Third, in Montague's system the syntactic rules and semantic rules are in one-to-one correspondence.</Paragraph>
    <Paragraph position="4"> Each time a particular syntactic rule applies, so does the corresponding semantic rule; while the one operates on some syntactic elements to create a new element, the other operates on the corresponding semantic objects to create a new object that will correspond to the new syntactic element. Thus the two sets of rules operate in tandem.</Paragraph>
    <Paragraph position="5"> Fourth, Montague's semantics is compositional, which is to say that the meaning of the whole is a systematic function of the meaning of the parts. At first glance this sounds trivial; if the noun phrase my pet penguin denotes by itself some particular entity, namely the one sitting on my lap as I write this paper, then we do not expect it to refer to a different entity when it is embedded in the sentence \[ love my pet penguin, and a semantic system that did not reflect this would be a loser indeed. Yet there are alternatives to compositional semantics.</Paragraph>
    <Paragraph position="6"> The first alternative is that the meaning of the whole is a function of not just the parts but also the situation in which the sentence is uttered. For example, the possessive in English is highly dependent upon pragmatics; the phrase Nadia's penguin could refer, in different circumstances, to the penguin that Nadia owns, to the one that she is carrying but doesn't actually own, or to the one that she just bet on at the penguin races. Our definition above of semantic interpretation excluded this sort of consideration, but this should not be regarded as uncontroversial.</Paragraph>
    <Paragraph position="7"> The second alternative to compositional semantics is that the meaning of the whole is not a systematic function of the parts in any reasonable sense of the word. This is exemplified by the interpretation of the word depart in Woods's original system, which varied greatly depending on the preposition it dominated (Woods 1967:A-43-A-46). For example, the interpretation of the sentence: AA-57 departs from Boston.</Paragraph>
    <Paragraph position="8"> is, not unreasonably: 5For example, the semantic type of prepositions is functions mapping senses of the type of noun phrases to the semantic type of prepositional phrases.</Paragraph>
    <Paragraph position="9">  depar~ (as-57, boston).</Paragraph>
    <Paragraph position="10"> That is, the semantic object into which depart is translated is the procedure depart. (AA-57 is an airline Right.) However, the addition of a prepositional phrase changes this; Table 1 shows the interpretation of the same sentence after wrious prepositional phrases have been appended. For example, the addition of ~o Chicago changes the translation of depart; to connect, though the intended sense of the word is clearly unchanged, s This is necessitated by the particular set of database primitives that Woods used, selected for their being %tom/c&amp;quot; (1967:7-4-7-11) rather than for promoting compositions/Sty. Rules in the system axe able to generate non-compositional representations because they have the power to set an arbitrarily complex parse tree as their trigger, and to return an axbitrary representation that could modify or completely ignore the components of the parse trees they are supposed to be interpreting/ For example, a rule can say (1967:A44): null If you have a sentence whose subject is a flight, whose verb is leave or depart, and which has two (or more) prepositional phrases modifying the verb, one with /from and a place name, the other with a~ and a time, then the interpretation is equal (dtime (a, b), c), where a is the flight, b is the place, and c is the time.</Paragraph>
    <Paragraph position="11"> Thus while Woods's semantics could probably be made * reasonably compositional simply by appropriate adjustment of the procedure calls into which sentences are translated, it would still not be compositional by design the way Montague semantics is.</Paragraph>
    <Paragraph position="12"> 8~Ve have simplified a Little here in order to make our point. In fact, sentences like those in Table I with prepositional phrases will ~ctually cause the execution of two semantic rules: one for the complete sentence, and one for the sentence it happens to contain, A.A-57 depcrts from 8os~o~. The resulting interpretation will be the conjunction of the output from each rule (Woods 1967~9-5): AA-57 depLrts from Boston to Chicago.</Paragraph>
    <Paragraph position="13"> depar~ (aa-ST, boston) and connec~ (aa-57. boston, c~icago) Woods leaves it open (1967:9-7) a,s to how the semantic redundancy in such expressions should be handled, thou~,h one of hie suggestions is a filter that would remove conjuncts implied by others, giving, in this case, the interpretation shown in Table 1. 7Nor is there &amp;nything that prevents the construction of rules that would result in conjunctions with conflicting, rather than merely redund~tnt, terms.</Paragraph>
  </Section>
  <Section position="3" start_page="65" end_page="67" type="metho">
    <SectionTitle>
TABLE 1.
NONCOMPOSITIONALITY IN WOODS'S SYSTEM
</SectionTitle>
    <Paragraph position="0"> AA-57 departs from Boston.</Paragraph>
    <Paragraph position="1"> depart (aa-57, bos~on) A.A-57 departs from Boston to Chicago. conltecT, (aa-5T, besT, on. chicago) AA-57 departs from Boston on Monday. dday (aa-57, boston, monday) AA-57 departs from Boston at 8:00am. equal (dtlme (aa-5T. boston), 8:00am) AA-57 departs from Boston after 8:00am. greater (dtime (aa-5T, boston), 8:00am) A.A-57 departs from Boston before 8:00am. greater (8:00am, dtlme (aa-5T. boston)) Although Montague semantics has much to recommend it, it is not possible, ho~vever, to implement it directly in a practical NLU system, for two reasons. The first is that Montague semantics as currently formulated is computationally impractical. It throws around huge sets, infinite objects, functions of functions, and piles of possible worlds with great abandon. Friedman, Moran and Warren (1978a) point out that in the smallest possible Montague system, one with. two entities and two points of reference, there are, for example, 22&amp;quot;s= elements in the class of possible denotations of prepositions, each element being a set containing 2512 ordered pairs, s The second reason we can't use Montague semantics directly is that truth-conditional semantics are not useful in AI; A/uses know/edge semant.ics (Tarnawksy 1982) in which semantic objects tend to be symbols or expressions in a declarative or procedural knowledge representation system. Moreover, truth-conditional semantics really only deals with declarative sentences (Dowry eC al 1981:13) (though there has been work attempting to extend Montague's work to questions; e.g. Hamblin 1973); a practical NLU system needs to be able to deal with commands and questions as well as declarative sentences.</Paragraph>
    <Paragraph position="2">  There have, however, been attempts to take the intensional logic that Montague uses as an intermediate step in his translations, and give it a new interpretation in terms of AI-type semantic objects, thus preserving all other aspects of Montague's approach; see, for example, Hobbs and Rosenschein 1977, and Smith's (1979) objections to their approach. There has also been interest in using the intensional logic itself (or something similar) as an AI representation ~ (e.g. Moore 1981). But while it may be possible to make limited use of intensional logic expressions, Ideg there are many problems that need to be solved before intensional logic or other flavors of logical forms could support the type of inference and problem solving that AI requires of its semantic representations; see Moore 1981 for a useful discussion. Moreover, Gallin (1975) has shown Montague's intensional logic to be incomplete. (See also the discussion in Section 7 of work using logical forms.) Nevertheless, it is possible to use many aspects of Montague's approach in semantics in AI. The semantic interpreter that we describe below maintains three of the four properties of Montague semantics that we described above, and we therefore refer to it as  Our semantic interpreter is a component of a system that uses a frame-like representation for both story comprehension and problem-solving. The system includes a frame language, named Frail, a problem solver, and a discourse pragmatics component; further details may be found in Charniak 1981, Wong 1981a, and Wong 1981b. The natural language front-end includes Paragram, a deterministic parser based on that of Marcus (1980). Unlike Marcus's parser, Paragram has two types of rule: base phrase structure rules and transformational rules. It is also able to parse ungrammatical sentences; it always uses the rule that matches best, even if none match exactly. Paragram is described in Charniak 1983.</Paragraph>
    <Paragraph position="3"> 91tonically, Montague regarded intensional logic merely as a convenience in specifyin K his translation, and one that was completely irrelevant to the substance of his semantic theories. lOGodden (1981) in f~ct uses them for simple translation between Thai and English.</Paragraph>
    <Paragraph position="4"> aThe queJtion-m~rk prefix indicates &amp; variable. Whenever a free v~iable in a frame is bound to a v~iable in a frame determiner, a unique new name is generated for that variable and its bindings. In this paper, we shall assume for simplicity that vaxiable names ~re maKically ~correct&amp;quot; from the start.</Paragraph>
    <Paragraph position="5"> bDo not be misled by the fact that frames and frame determiners look similar. They He actually very different: the first is a gtatic data structure; the second is a frame retrieva~l procedure. CAn instance is the result of evaluating a frame statement in Frail. It is a symbol that denotes the object referenced by the frame statement. To Absity, there is no distinction between the two; ~n instan.ce can be used wherever ~ frame Itatement c~n.</Paragraph>
    <Paragraph position="6"> The semantic interpreter is named Absity (for reasons too obscure to burden the reader with). As we mentioned above, it retains three of the four properties of Montague semantics that we discussed.</Paragraph>
    <Paragraph position="7"> The property that we have dropped is, of course, truth conditionality and Montague's associated treasury of semantic objects. We have replaced them with AIstyle semantics, and our own repertory of objects,  Frame determiner.</Paragraph>
    <Paragraph position="8"> which are components of the frame language Frail. 11 We do, however, retain a strong typing upon our semantic objects, that is, each syntactic category has an associated semantic type. Table 2 shows the types of components of Frail, how they may be combined, and examples of each; the nature of the components listed will become clearer with the examples in the next section. Table 3 gives the component of Frail that corresponds to each syntactic type. As a consequence of the kind of semantic objects we are dealing with, the system of types is not recursively defined in the Montague style, but we retain the idea that the type of a semantic object should be a function of the types of the components of that object.</Paragraph>
    <Paragraph position="9"> We have also carried over from Montague semantics the operation of syntactic and semantic rules in tandem upon corresponding objects. However, it is not possible to maintain the one-to-one correspondence of rules when we replace Montague's simple syntax with the much larger English grammar of the Paragram parser. This is because in Montague's system each syntactic rule either creates a new node from old ones-for example, forming an intransitive verb phrase from a transitive verb and a noun phrase--or places a new llAlthou~h the object that represents a Sentence is * procedure call in Frail upon a knowledge basej this is not procedur~l sem~ntics in the strict Woods sense, as the mes~aing inheres not in the procedures but in the objects they manipulate.</Paragraph>
    <Paragraph position="10"> node under an existing one--such as adding an adverb to an existing intransitive verb phrase. These are&amp;quot; actions that clearly have semantic counterparts. When we start to add movement rules such as passivizatioa and dative movement to the grammar, we find ourselves with rules that have no clear semantic counterpart; indeed with rules that, it is often claimed (e.g. Chomsky 1965:132), leave the meaning of a sentence quite unchanged.</Paragraph>
    <Paragraph position="11"> We therefore distinguish between parser rules that should have corresponding semantic rules and those that should not. As the above discussion suggests, rules that attach nodes are the ones that have semantic counterparts. In Paragram, these are the base structure rules. For this subset of the syntactic rules, semantic rules run in tandem, just as in Montague's semantics, m It is a consequence of the above properties of our semantic interpreter that we have also retained the property of compositionaiity by design. This follows from the uniform typing; the correspondence between syntactic and semantic rules that maintains this uniformity; and there being a unique semantic object corresponding to each word of English i~ (see Dowty e~ al 1981:180-181). Unlike those of Woods's (1967) airline reservation system front-end discussed in Section 2, our semantic rules are very weak: they cannot change or ignore the components upon which they operate, nor can more than one rule volunteer an interpretation for any node of the parse tree. The power of the system comes from the nature of the semantic objects and the syntax-directed application of semantic rules, rather than from the semantic rules themselves.</Paragraph>
  </Section>
  <Section position="4" start_page="67" end_page="70" type="metho">
    <SectionTitle>
4. Examples
</SectionTitle>
    <Paragraph position="0"> Some examples will make our semantic interpreter clearer. First, let's consider a simple noun phrase, the book. From Table 3, the semantic type for the  in the canonical way--the frame name is added as an argument to the frame determiner function--and the result, (the ?x (book ?x)), is a Frail frame statement (which evaluates to an instance) that represents the unique book referred to. 14 A descriptive adjective corresponds to a slot-filler pair; for example, red is represented by (color=red), where color is the name of a slot and red is a frame instance, the name of a frame. A slot-filler pair can be added as an argument to a frame, so the red book would have the semantic interpretation (the ?x (book ?x (color=red))).</Paragraph>
    <Paragraph position="1"> Now let's consider a complete sentence: Nadia bought the book from a store in the mall.</Paragraph>
    <Paragraph position="2"> Table 4 shows the representation for each component of the sentence; note that the basic noun phrases have already been formed in the manner described above. Note also that we have inserted the pseudoprepositional subject and object markers susJ and osJ, which are then treated as if they were real prepositions; see Hirer and Charniak 1982 or Hirst 1983 for details of this. For simplicity, we assume that each word is unambiguous (we discuss our disambiguation procedures in Section 6); we also ignore the tense cn the verb. Table 5 shows the next four stages in the interpretation. First, noun phrases and their prepositions are combined, forming slot-filler pairs. Then the prepositional phrase in the mall can be attached to a store (since a noun phrase, being a frame, can have a slot-filler pair added to it), and the prepositional phrase from a store in the marl is formed. The third stage shown in the Table is the attachment of the slot-filler pairs for the three top-level prepositional phrases to the frame representing the verb. Finally, the period, which is translated as a frame determiner function, causes instantiation of the buy frame, and the translation is complete.</Paragraph>
    <Paragraph position="3"> 5. Semantic help for the parser As we mentioned earlier, any parser will occasionally need semantic help. In Marcus-type parsers, this need occurs in rules that have the form &amp;quot;If semantics prefers 14Note ~hat it is the responsibility&amp;quot; of the frame system to determine with the help of the pragmatics module which one of the books that it m~ty know about is the correct one in context.  such questions, we have a Semantic Enquiry Desk r, hat operates upon the same semantic objects as the semantic interpreter. Because these objects are components of the Frail frame language, the Enquiry Desk can use the full retrieval and inference power of Frail in answering the enquiry.</Paragraph>
    <Paragraph position="4"> 6. Word sense disambiguation One problem that Montague semantics does not address is that of word disambiguation. Rather, there is assumed to exist a function that maps each word to a unique sense, and the semantic formalism operates on the values of this function.Is Clearly, however, a practical NLU system must take account of word sense ambiguity, and so we must add a disambiguation facility to our interpreter. Fortunately, the word translation function allows us to ~dd this facility transparently.</Paragraph>
    <Paragraph position="5"> Instead of simply mapping a word to an invariant unique sense, the function can map it to whatever sense is correct for a particular instance.</Paragraph>
    <Paragraph position="6"> Our disambiguation facility is called Polaroid Words. Is Each word in the system is represented by 15This is not quite true. Specified unique translations axe given for proper names and for a few important function words, such as the and be; see Monta~e 197312\]:261 , or Dowry ~ ~l 1981:192ff.  a separate process that, by talking to other processes and by looking at paths made by spreading activation in the knowledge base, figures out the word's meaning. Each word is like a self-developing photograph that can be manipulated by the semantic interpreter even while the picture is forming; and if some other process needs to look at the picture (e.g. if the Semantic Enquiry Desk has an &amp;quot;if semantics prefers ~ question from the parser), then a half-developed picture may provide enough information. Exactly the same process, without the spreading-activation phase, is used to disambiguate case roles as well. Polaroid Words are described more fully in Hirst and Charniak 1982 and Hirst 1983.</Paragraph>
    <Paragraph position="7"> 7. Comparison with other work Our approach to semantic interpretation may usefully be compared with other recent work with similar goals to ours.</Paragraph>
    <Paragraph position="8"> One such project is that of Jones and Warren (1982), who attempt a conciliation between Montague semantics and a conceptual dependency representation (Schank 1975). Their approach is to modify Montague's translation from English to intensional logic so that the resulting expressions have a canonical interpretation in conceptual dependency. They do not address such issues as extending Montague's syntax, nor whether their approach can be extended to deal with more modern Schankian representations (e.g. Schank 1982). Nevertheless, their work, which they describe as a hesitant first step, is similar in spirit to ours, and it will be interesting to see how it develops.</Paragraph>
    <Paragraph position="9"> Important recent work that extends the syntactic complexity of Montague's work is that on generalized phrase structure grammar (GPSG) (Gazdar 1982). Such grammars combine a complex transformationfree syntax with Montague's semantics, the rules again operating in tandem. Gawron et al (1982) have implemented a database interface based on GFSG. In their system, the intensional logic of the semantic component is replaced by a simplified extensional logic, which, in turn, is translated into a query for database access. Schubert and Peiletier (1982) have also sought to simplify the semantic output of a GPSG to a more ~conventional&amp;quot; logical form; and Rosenschein and Shieber (1982) describe a similar translation process into extensional logical forms, using a context-free grammar intended to be similar to a GPSG. Iv The GPSG approaches differ from ours in that their output is a logical form rather than an immediate representation of a semantic object; that is, the output is not tied to any representation of knowledge. In Gawron et al's system, the database 17 Rosenschein and Shieber's semaxltic translation fonow~ parsing rather than running in parallel with it, but it iv strongly syntax-dLrected, and is, it seems, isomorphic to ~n in-t~ndem translation that provides no feedback to the p~rser.</Paragraph>
    <Paragraph position="10">  provides an interpretation of the logical form, but only in a weak sense, as the form must first pass through another (apparently somewhat ad hoc) translation and disambiguati0n process. Nor do these approaches provide any semantic feedback to the parset. is These differences, however, are independent of the choice of GPSG; it should be easy, at least in principle, to modify these approaches to give Frail output, or, conversely, to replace Paragram in our system with a GPSG parser. 19 The PSX-KLON~- system of Bobrow and Webber (1980a, 1980b) also has a close coupling between syntax and semantics. Rather than operating in tandem, though, the two are described as &amp;quot;cascaded', with an ATN parser handing constituents to a semantic interpreter, which is allowed to return them (causing the ATN to back up) if the purser's choice is found to be semantically untenable. Otherwise, a process of incremental description refinement is used to interpret the constituent; this relies on the fact that the syntactic constituents are represented in the same formalism, KL-OSZ (Brachman 1978), as the system's knowledge base. The semantic interpreter uses projection rules to form an interpretation in a language called JAaGON, which is then translated into KL-ONZ.</Paragraph>
    <Paragraph position="11"> Bobrow and Webber are particularly concerned with using this framework to determine the combinatoric relationship between quantifiers in a sentence.</Paragraph>
    <Paragraph position="12"> Bobrow and Webber's approach addresses several of the issues that we do, in particular the relationship between syntax and semantics. The information feed-back to the parser is similar to our Semantic Enquiry Desk, though in our system, because the parser is deterministic, semantic feedback cannot be con fluted with syntactic success or failure. Both approaches rely on the fact that the objects manipulated are objects of a knowledge representation that permits appropriate judgments to be made, though in rather a different manner.</Paragraph>
    <Paragraph position="13"> Hendler and Phillips (1981; Phillips and Hendler 1982) have implemented a control structure for NLU 18Gawron et al produce all poslible trees and their tranilations for the input sentence, s.nd then throw away any that don't make sense to the database.</Paragraph>
    <Paragraph position="14"> If'Our choice of Paragram was largely pragmatic~it w&amp;s avL/l* ble--and does not represent &amp;ny particular commitment to transformational g~ammar s.</Paragraph>
    <Paragraph position="15"> based on message passing, with the goal of running syntax and semantics in parallel and providing semantic feedback to the parser. A ~moderator&amp;quot; translates between syntactic constructs and semantic representations. However, their approach to interpretation is essentially ad hoc (James Hendler, persoaoi cummunication), and they do not attempt to put syntactic and semantic rules in strict correspondence, nor type their semantic objects.</Paragraph>
    <Paragraph position="16"> None of the work mentioned above addresses issues of lexical ambiguity as ours does, though Bobrow and Webber's incremental description refinement could possibly be extended to cover it. Also, Gawron et al have a process to disambiguate case roles in the logical form after it is complete, which operates in a manner not dissimilar to the case-slot part of Polaroid Words.</Paragraph>
  </Section>
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