1140 lines
38 KiB
Plaintext
1140 lines
38 KiB
Plaintext
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Research Report AI-1989-04
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Artificial Intelligence Programs
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The University of Georgia
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Athens, Georgia 30602
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Available by ftp from
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aisun1.ai.uga.edu
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(128.192.12.9)
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Series editor:
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Michael Covington
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mcovingt@aisun1.ai.uga.edu
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PROBLEMS IN APPLYING DISCOURSE REPRESENTATION THEORY
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William H. Smith
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Piedmont College
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Demorest, GA 30535
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Artificial Intelligence Programs
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The University of Georgia
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Athens, Georgia 30602
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Introduction
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Discourse Representation Theory (DRT) was developed by Hans
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Kamp 1981 in order to combine "a definition of truth with a
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systematic account of semantic representations (277)". The
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semantic representations produced are to provide a bridge between
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syntactic parses and model theoretic semantics such that the
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representations can be used to determine the truth conditions of
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a discourse. This report describes that theory, both the
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original, basic form and some extensions that have been suggested
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by Kamp and others, and applies it to a "real" discourse in order
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to indicate further extensions that will be necessary if DRT is
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to be used as a complete theory of semantic representations.
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Truth in model theoretic semantics is determined by a
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mapping from a representation of the discourse to a model, a
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mapping that preserves the properties and relationships of the
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discourse. A model consists of two sets: a set of entities (the
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universe) and a set of properties of those entities and relations
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that hold among them. The discourse representation must likewise
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consist of two sets, a set of referenced items and a set of
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propositions about those items. A discourse is held to be true
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in a model if there is a mapping such that the set of referenced
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items maps to a subset of the universe and each property or
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relation expressed by the propositions is true of the
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corresponding entities in the model.
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Kamp addressed the questions of how a discourse places items
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in the set of referenced items and of how anaphoric relations can
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be expressed in the discourse representation. In particular, he
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was concerned with situations in which an item should not be
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placed in that set yet should serve as the antecedent for an
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anaphoric relationship (the so-called "donkey sentences"). To
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that end, he developed the basic version of DRT (1981). Part 1
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2
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of this report describes that basic theory. Part 2 presents some
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extensions to the basic theory. Part 3 describes an attempt to
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represent a text in DRT and suggests further extensions that
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might be made.
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1. Discourse Representation Theory
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The central notion of DRT is the Discourse Representation
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Structure (DRS). A DRS K is a pair <U, C>, where U is a set of
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reference markers (the universe) and C is a set of conditions
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(properties, relations, or complex conditions--negation,
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disjunction, or implication). The initial DRS, K0, contains none
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of the information in the discourse. As the discourse is
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processed, the DRS construction algorithm produces a series of K'
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as it incorporates material from the discourse into K. For
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example
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(1) Pedro owns a donkey.
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K:<U:{R1, R2},
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C:{Pedro(R1),
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donkey(R2),
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own(R1, R2)}>
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Although U and C are described as sets, at least one of
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these must be ordered by time of introduction into the discourse
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if the construction algorithm is to work properly in assigning
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antecedents to anaphoric expressions (cf Goodman 1988).
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Antecedent assignment is accomplished by finding an item in U
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that agrees with the anaphoric expression (for pronouns, an
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entity that agrees in gender and number). Thus, (2) shows an
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extension of (1) (:= is an assignment operator, as in Pascal; +
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is union of sets):
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(2) He beats it.
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K: <U,
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C := C + {beat(R1, R2)}>
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(The basic theory would add R3, R4 to U, and then set them equal
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to R1, R2, respectively. A later "clean-up" operation would
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eliminate these redundant discourse markers. Here we assume that
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3
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the clean-up operation has been applied.) A discourse of any
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size, however, is likely to include several such entities; most
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often, the conflict is resolved by selecting from the candidates
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the one that was most recently encountered. In order to make
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that selection possible, the set of items must be ordered, and
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must in fact be re-ordered every time reference is made to an
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entity.
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For purposes of exposition, K0 is usually treated as
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consisting of empty sets. Such is often not the case in real
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discourse, where referring items are often exophoric, their
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referents to be found in the nonlinguistic context or in the
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shared knowledge of the participants. While DRT allows for such
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references, it is not clear how or when the antecedents are to be
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entered into K.
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Kamp 1985 describes the DRS construction algorithm is "a set
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of rules that operate, in a roughly top-down manner, on the nodes
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of the parse tree, (2)" converting those nodes into the
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conditions of C and, when appropriate, introducing new reference
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markers into U. As was noted in the introduction to this report,
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the basic version of DRT is directed toward the role of noun-
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phrase (NP) nodes in the discourse--their relationship to U.
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It would seem, at first glance, that every NP should be
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associated with an entity in the model and should therefore have
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a corresponding marker in U. (That view is, of course, a great
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oversimplification. Most work in DRT has limited itself to
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singular concrete NPs, where the oversimplification is not so
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drastic.) When the algorithm encounters a NP, it should either
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associate it with a marker already present in U (anaphora) or
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introduce a new marker, and these were the problems that Kamp
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1981 addressed.
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The main problem for anaphora is that theories of sentential
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syntax do not provide for intersentential anaphora. DRT solves
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that problem by creating a unified representation for the
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discourse, so that all markers in the discourse are available for
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anaphoric relations (with exceptions to be treated shortly).
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Conflict resolution is not treated beyond the recency heuristic;
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this is not a weakness particular to DRT, for a full treatment of
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4
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pronominal anaphora must take into consideration grammar,
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pragmatics, and knowledge of the real world. Definite noun
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phrases perform as do personal pronouns but, since they carry
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more content, are less likely to introduce conflict. (Definite
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NPs used generically are not considered.)
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Proper nouns and indefinite NPs introduce new reference
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markers into U. Although this procedure corresponds to the
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"first glance" view of natural language, it encounters problems
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in sentences that involve negation, disjunction, or conditions:
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(3) Pedro does not own a donkey.
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(4) Pedro owns a donkey or a cow.
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(5) If Pedro owns a donkey he beats it.
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One certainly would not want to add a reference marker for
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'donkey' in (3); the semantics would require that it map to an
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entity in the model, and the sentence explicitly denies its
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existence. The same holds for the donkey in (4), since it has
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perhaps a 50-50 chance of existing (although it might be useful
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to add a marker for the thing that Pedro owns). Sentence (5) is
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the so-called "donkey sentence"; it not only introduces a donkey
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that may or may not exist, but goes on to make anaphoric
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reference to it.
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DRT handles sentences of the above types by adding to C one
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or more sub-DRSs. Each sub-DRS has its own universe, which is
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not visible to the superordinate DRS, and its own condition set,
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and the truth value of the sub-DRS is determined by the logical
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connective that controls it.
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5
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(3') K:<U:{R1}
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C:{Pedro(R1), <20>K',
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K':<U:{R2}, C:{own(R1, R2), donkey(R2)}> }>
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(4') K:<U:{R1}
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C:{Pedro(R1), K' or K'',
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K':<U:{R2}, C:{own(R1, R2), donkey(R2)}>
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K'':<U:{R3}, C:{own(R1, R3), cow(R3)}> }>
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(5') K:<U:{R1}
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C:{Pedro(R1), K' -> K'',
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K':<U:{R2}, C:{own(R1, R2), donkey(R2)}>
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K'':<C:{beat(R1, R2)}> }>
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Thus, (3) is true if there is no entity in the model that
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satisfies its universe and conditions, (4) is true if there is a
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successful mapping from one of its sub-DRSs to the model, and (5)
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is true if any mapping that satisfies the antecedent DRS also
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satisfies the consequent DRS.
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Sentences (4) and (5) introduce an additional problem; each
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could be followed by a sentence such as (6):
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(6) It is unhappy.
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The pair (5-6) is handled by including (6) in the consequent DRS
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for (5). The other pair, (4-6), seems to be overlooked by
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theorists, but it can be handled, as was suggested above, by
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adding to the main DRS a marker for the thing that Pedro owns and
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including only the properties -- donkey or cow -- in the sub-
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DRSs.
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Universal propositions have the same DRS form as
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conditionals. The scope of a universally quantified term
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relative to an existentially quantified term is indicated by the
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U in which the existentially quantified term is placed. Thus,
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the usual interpretation of (7) is represented by (7a), while the
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interpretation that places 'donkey' outside the scope of 'farmer'
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is shown in (7b):
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(7) Every farmer owns a donkey.
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6
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(7a) K:<C:{K' -> K'',
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K':<U:{R1}, C:{farmer(R1)}>
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K'':<U:{R2}, C:{own(R1, R2), donkey(R2)}> }>
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(7b) K:<U:{R2},
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C:{donkey(R2), K' -> K'',
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K':<U:{R1}, C:{farmer(R1)}>
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K'':<C:{own(R1, R2)}> }>
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DRT, as described so far, does a very good job of handling a
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very small subset of English sentences. Kamp and others have
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offered a number of extensions to the basic theory in order to
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expand that subset.
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2. Extensions to the Basic Theory
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The basic theory is confined to a very limited subset of
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natural language. In particular, it is limited to singular, non-
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generic NPs, to anaphoric reference (i.e. the referent is present
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in the discourse), and to sentences whose main verbs do not take
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propositions (i.e. DRSs) as arguments. Researchers have offered
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extensions to the basic theory that reduce the second and third
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of those limitations.
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Kamp 1983 and Pinkal 1986 have offered refinements to the
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reference-resolving algorithm for definite NPs that extend the
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power and accuracy of that algorithm. Kamp distinguishes four
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kinds of definite noun phrases (Pinkal: 369):
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(8a) Personal and possessive pronouns
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( b) Complex demonstratives. (Demonstrative + NP; NP may
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include a restrictive relative clause.)
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( c) Definite descriptions. ('the' + NP; NP may include a
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relative clause.)
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( d) Functional definite descriptions. ('the' + NP +
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prepositional phrase, the latter limiting the set from
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which NP selects.)
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Complex demonstratives differ from definite descriptions in that
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the latter presuppose a unique referent while the former
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presuppose a contrast between two or more possible referents.
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Resolution of referential expressions requires the following
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7
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(Pinkal: 370):
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(9a) The DRS K.
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( b) A salience ranking of the markers in UK. (Including
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recency of reference.)
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( c) A selection set of UK whose members are available as
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antecedents.
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( d) The universe of the real world needed for deictic
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reference.
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Pinkal argues that definite descriptions are not limited to the
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selection set and that there is no motivation for the distinction
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between anaphora and exophora (where the referent is not present
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in the discourse; it is either physically present--deixis--or
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present in shared knowledge).
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Guenthner et al. 1986 extend the basic theory by adding two
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new types of discourse markers: event markers and time markers.
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They include meaning rules in the DRS construction algorithm that
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assign each verb and each noun that refers to an action (e.g.
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'accident') to an event marker. Each time reference (i.e. time
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of day or extent of duration) is assigned to a time marker.
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Events are temporally ordered with respect to each other and to
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time references: an event may precede or overlap another event or
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time, it may be given a time argument expressing its duration,
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and it may be a subset of another event. The addition of event
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markers makes it possible for predicates to take DRSs as
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arguments. Guenthner et al. do not include any examples of such a
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use of event markers, but Guenthner 1987 does. In that article
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he also makes a notational distinction between events, which
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advance the time of the discourse, and situations or static
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verbs, which do not.
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Spencer-Smith 1987 does not use event markers, but adds a
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different type of discourse marker, a proposition marker. This
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extension makes it possible to include embedded predicates, such
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as infinitival complements and beliefs:
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(10) Mary wants to marry a rich man.
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8
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K:<U:{R1, P1},
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C:{Mary(R1), want(R1, P1),
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P1:<U:{R2},
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C:{rich(R2),
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man(R2),
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marry(R1, R2)}> }>
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The representation of beliefs, which is explored more fully
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in Kamp 1985, requires two further additions to DRT: internal and
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|
||
external anchors. Anchors are used to associate discourse
|
||
|
||
markers to entities in the world. External anchors are ordered
|
||
|
||
pairs, <Marker, Entity>, that associate the two as they actually
|
||
|
||
|
||
are, while internal anchors are DRS-like structures that
|
||
|
||
associate items as the speaker believes they are. The use of
|
||
|
||
anchors makes it possible to represent propositions that are in
|
||
|
||
fact contradictory but are not so in the speaker's belief system
|
||
|
||
|
||
because his internal anchors differ from the external anchors:
|
||
|
||
|
||
(11) John believes that Hesperus is pretty and Phosphorus is
|
||
|
||
not pretty.
|
||
|
||
|
||
External anchors: <R1, John>, <R2, Venus>, <R3, Venus>
|
||
|
||
Internal anchors:
|
||
|
||
K:<U:{R2, R3},
|
||
|
||
C:{evening_star(R2),
|
||
|
||
|
||
morning_star(R3)}>
|
||
|
||
K:<U:{R1, P1},
|
||
|
||
C:{John(R1),
|
||
|
||
believes(R1, P1),
|
||
|
||
|
||
P1:<U:{R2, R3},
|
||
|
||
C:{pretty(R2),
|
||
|
||
<20>K',
|
||
|
||
K':<C:{pretty(R3)}> }> }>
|
||
|
||
|
||
|
||
These extensions to DRT give it considerable power, but are
|
||
|
||
far from giving it the power necessary to represent adequately
|
||
|
||
the full range of meanings available in natural language. In the
|
||
|
||
|
||
next section we attempt to apply DRT to a selection of natural
|
||
|
||
language in order to discover further extensions that will be
|
||
|
||
necessary if DRT is to become an adequate theory for the
|
||
|
||
representation of natural language.
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
9
|
||
|
||
|
||
|
||
|
||
|
||
|
||
3. Application of DRT
|
||
|
||
|
||
The passage to be analyzed here was treated extensively in
|
||
|
||
Smith 1977 in order to determine the types of information that
|
||
|
||
|
||
must be added to the text in order to obtain a complete
|
||
|
||
representation of the situation reported by the text. The text
|
||
|
||
is a narrative passage that has been normed at sixth-grade
|
||
|
||
readability (ETS 1969). It is particularly interesting because
|
||
|
||
|
||
it forces the reader to treat certain items as if they were in
|
||
|
||
K0.
|
||
|
||
In order to represent this passage, it is necessary to
|
||
|
||
postulate ad hoc extensions to DRT. Although these extensions
|
||
|
||
|
||
work for this passage, they should be regarded as suggestions
|
||
|
||
only and not as fully developed extensions; some will reveal
|
||
|
||
their weaknesses as the representation is developed.
|
||
|
||
The DRS K for the passage will be developed incrementally,
|
||
|
||
|
||
the DRS for each portion being added to the existing DRS. The
|
||
|
||
clean-up of redundant discourse markers, however, is assumed to
|
||
|
||
take place before the DRSs are combined. Additional symbols will
|
||
|
||
be explained as they are introduced. As before, discourse
|
||
|
||
|
||
sentences will be presented in the company of the DRSs that they
|
||
|
||
add to K; since these sentences, unlike those in previous
|
||
|
||
examples, have a cumulative effect, they will be denoted with the
|
||
|
||
prefix N.
|
||
|
||
|
||
In order to treat reference adequately, the items shown
|
||
|
||
below must be included in DRS K0. These items are, in effect,
|
||
|
||
imposed on the reader as possible referents. The marker Now
|
||
|
||
indicates the time of reading.
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
10
|
||
|
||
|
||
(N0) K:<U0:{R1, R2, Now, R10, R15},
|
||
|
||
C0:{}>
|
||
|
||
|
||
(N1a) The cave widened out as he went
|
||
|
||
|
||
U := U0 + {E1, E2}
|
||
|
||
C := C0 + {cave(R1),
|
||
|
||
E1:widen_out(R1),
|
||
|
||
E2:go(R2),
|
||
|
||
|
||
E2 o E1,
|
||
|
||
E2 << Now }
|
||
|
||
|
||
The symbol o indicates that E2 overlaps E1; << indicates
|
||
|
||
|
||
that E2 (and therefore E1) precedes the time of reading.
|
||
|
||
'widened out' is treated as a unit verb; the 'out' is actually
|
||
|
||
redundant. Since 'the cave' is definite, its referent must exist
|
||
|
||
prior to (N1); for this reason R1 is included in U0, and the same
|
||
|
||
|
||
is true of 'he' and R2.
|
||
|
||
|
||
(N1b) and the bottom seemed to drop away little by little
|
||
|
||
U := U + {R3, E3, P1}
|
||
|
||
|
||
C := C + {bottom(R3),
|
||
|
||
part-of(R3, R1),
|
||
|
||
E3:seem(P1),
|
||
|
||
P1:<U:{E4},
|
||
|
||
|
||
C:{E4:drop_away(R3),
|
||
|
||
little_by_little(E4)
|
||
|
||
E4 =< E3}>
|
||
|
||
E2 o E3}
|
||
|
||
|
||
|
||
R3, 'the bottom,' has no apparent antecedent and might have
|
||
|
||
been included in U0. It seems more likely, however, that it
|
||
|
||
existed implicitly and that a meaning rule (such as 'Every
|
||
|
||
|
||
physical object has a bottom') resolves the reference. E3 is
|
||
|
||
true if P1 seems to be true, even if P1 is actually false. Since
|
||
|
||
E4 is controlled by 'seem,' it is a subset ( =< ) of E3. (I am
|
||
|
||
not sure that this is what Guenthner et al. mean by subset, since
|
||
|
||
|
||
they offer no examples, but it works here.)
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
11
|
||
|
||
|
||
|
||
|
||
|
||
|
||
(N1c) and then, with no warning, it split in two directions,
|
||
|
||
U := U + {E5, Set1}
|
||
|
||
C := C + {<7B>K1c
|
||
|
||
K1c:<U:{R4},
|
||
|
||
|
||
C:{warning(R4)}>
|
||
|
||
E5:split_in(R1, Set1),
|
||
|
||
E3 << E5,
|
||
|
||
direction(Set1)}
|
||
|
||
|
||
|
||
Since there is no warning, R4 is not visible to the top-
|
||
|
||
level K. 'directions' introduces what is perhaps the major
|
||
|
||
weakness in current versions of DRT, a means of representing
|
||
|
||
|
||
plural nouns. The ad hoc solution offered here is to use set
|
||
|
||
markers, following a suggestion in Guenthner et al. The
|
||
|
||
proposition direction(Set1) is a notational shorthand for a
|
||
|
||
complex sub-DRS representing "All members of Set1 are
|
||
|
||
|
||
directions."
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
12
|
||
|
||
|
||
|
||
(N1d) one path leading straight ahead and one off to the
|
||
|
||
left.
|
||
|
||
U := U + {E6, R5, R6, E7, R7, R8}
|
||
|
||
|
||
C := C + {path(R5),
|
||
|
||
E6:lead(R5, R6),
|
||
|
||
R6 <- Set1,
|
||
|
||
straight_ahead(R6),
|
||
|
||
|
||
E6 =< E5,
|
||
|
||
path(R7),
|
||
|
||
E7:lead(R7, R8),
|
||
|
||
R8 <- Set1,
|
||
|
||
|
||
to_the_left(R8)
|
||
|
||
E7 =< E5}
|
||
|
||
|
||
The cohesion of R5 and R7 with R1 is indicated by the fact
|
||
|
||
|
||
that R6 and R8 are members of ( <- ) Set1.
|
||
|
||
|
||
(N2) "If I were an opening to this cave, where would I be?"
|
||
|
||
he asked himself.
|
||
|
||
|
||
U := U + {E8, P2, R9}
|
||
|
||
C := C + {E8:ask(R2, R2, P2)
|
||
|
||
P2:K2a -> K2b,
|
||
|
||
K2a:<U:{R9}
|
||
|
||
|
||
C:{opening(R9),
|
||
|
||
part-of(R9, R1),
|
||
|
||
R2 = R9,
|
||
|
||
R2 \= R9}>
|
||
|
||
|
||
K2b:<C:{location(R2, ?)}>
|
||
|
||
E7 << E8 }
|
||
|
||
|
||
(N2) is, on the one hand, almost ridiculous; its only
|
||
|
||
|
||
contribution to the understanding of the passage is the knowledge
|
||
|
||
that 'he' is lost (Smith 1977), but that knowledge is no more
|
||
|
||
explicit in the DRS than it is in the sentence itself. On the
|
||
|
||
other hand, it is a major headache for DRT. (N2) is an embedded
|
||
|
||
|
||
contra-factual conditional whose antecedent is impossible and
|
||
|
||
whose consequent is a rhetorical question (indicated by the ? as
|
||
|
||
an argument to location). Its embeddedness, in this case, is
|
||
|
||
wrong, in the sense that it is not a matter of 'his' belief, but
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
13
|
||
|
||
|
||
|
||
|
||
|
||
|
||
in another situation it might be. The implication itself is
|
||
|
||
worthless, but another implication might not be. The conclusion
|
||
|
||
that R9 is not R2 (indicated by \= ) is obvious but might be
|
||
|
||
useful in another contrafactual. The whole DRS must be added to
|
||
|
||
|
||
K so that the reader can infer, by conversational implicature,
|
||
|
||
that 'he' does not know the answer to the rhetorical question and
|
||
|
||
that, since he does not know the answer, he is lost.
|
||
|
||
|
||
|
||
(N3) Luke wasn't frightened.
|
||
|
||
U := U + {Sit1}
|
||
|
||
C := C + {Luke(R2),
|
||
|
||
<20>Sit1,
|
||
|
||
|
||
Sit1:<C:{frightened(R2)}>
|
||
|
||
Sit1 o E8}
|
||
|
||
|
||
(N3) introduces a situation (more accurately, a non-
|
||
|
||
|
||
situation) whose duration is vague but which at least overlaps
|
||
|
||
E8.
|
||
|
||
|
||
(N4a) Oh, he knew there were such things in this world as
|
||
|
||
|
||
bottomless caves,
|
||
|
||
U := U + {Sit2, P3}
|
||
|
||
C := C + {Sit2:know(R2, P3),
|
||
|
||
Sit2 o Sit1,
|
||
|
||
|
||
P3:<U:{Sit3, Set2, R10}
|
||
|
||
C4:{bottomless_caves(Set2),
|
||
|
||
world(R10),
|
||
|
||
Sit3:exist_in(Set2, R10),
|
||
|
||
|
||
Sit3 o Sit2}> }
|
||
|
||
|
||
P3 is like an external anchor, in that it is a fact about
|
||
|
||
the world, but Kamp 1985 does not allow for propositions as
|
||
|
||
|
||
external anchors. It could be treated as an internal anchor, but
|
||
|
||
it is explicit in the discourse. Both Sit2 and Sit3 are true
|
||
|
||
throughout the discourse, so they are irrelevant as temporal
|
||
|
||
markers, but either might have changed during the discourse and
|
||
|
||
|
||
the representation must allow for that possibility.
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
14
|
||
|
||
|
||
(N4b) where people fell in and were never heard of again,
|
||
|
||
C4 := C4 + {K4a -> <20>K4b,
|
||
|
||
K4a:<U:{Set3, R11, R12, E9}
|
||
|
||
C:{people(Set3),
|
||
|
||
|
||
R11 <- Set2,
|
||
|
||
R12 <- Set3,
|
||
|
||
fall-in(R12, R11)},
|
||
|
||
K4b:<U:{R13, E10},
|
||
|
||
|
||
C:{R13 <- Set3,
|
||
|
||
R13 \= R12,
|
||
|
||
E10:hear_of(R13, R12),
|
||
|
||
E9 << E10}> }
|
||
|
||
|
||
|
||
This is a continuation of the sub-DRS begun in (N4a); it is
|
||
|
||
interpreted as a universal: 'No person who falls in such a cave
|
||
|
||
is ever heard of again.' Since this universal is embedded in a
|
||
|
||
|
||
belief, it does not matter whether such persons exist or not; if
|
||
|
||
it were not, it would be necessary to replace R11 with a set of
|
||
|
||
at least two members.
|
||
|
||
|
||
|
||
(N4c) but if there had been any such thing around the cottage
|
||
|
||
he would have heard about it.
|
||
|
||
U := U + {Set2}
|
||
|
||
C := C + {K4c -> K4d,
|
||
|
||
|
||
cottage(R15),
|
||
|
||
K4c:<U:{R14, Sit4},
|
||
|
||
C:{R14 <- Set2,
|
||
|
||
Sit4:exist_around(R14, R15),
|
||
|
||
|
||
<20>exist_around(R14, R15)}>
|
||
|
||
K4d:<U:{E11},
|
||
|
||
C:{E11:hear_about(R2, R14),
|
||
|
||
E11 << E1}> }
|
||
|
||
|
||
|
||
It is not clear whether (N4c) should be treated as a
|
||
|
||
continuation of the belief initiated in (N4a), as a different
|
||
|
||
belief, or as a top-level condition. Viewed objectively, it is a
|
||
|
||
|
||
belief (and an illogical one at that), yet it does not seem to be
|
||
|
||
syntactically embedded in 'know,' or any other verb of belief.
|
||
|
||
If it is a different belief, or a top-level condition (as it is
|
||
|
||
treated here), Set2 must be promoted from P3 to the top-level so
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
15
|
||
|
||
|
||
|
||
|
||
|
||
|
||
that it can be visible to other sub-DRSs. R15 must be added to
|
||
|
||
K0; it is a definite description whose referent cannot be deduced
|
||
|
||
in the way 'bottom' can be deduced as 'part-of' a cave. As with
|
||
|
||
K2a, it would seem reasonable to elevate the negation of the
|
||
|
||
|
||
antecedent of a contrafactual to the top-level, but in that case
|
||
|
||
R14 would not be accessible (it would exist in a subordinate
|
||
|
||
universe). Since Sit4 is a general proposition, no temporal
|
||
|
||
relation is assigned; the same is true of Sit5, Sit6, and Sit7
|
||
|
||
|
||
below.
|
||
|
||
|
||
(N5a) This was just a plain, ordinary cave--deeper than most,
|
||
|
||
but that was all--
|
||
|
||
|
||
U := U + {Sit5, Sit6, Set4}
|
||
|
||
C := C + {Sit5:plain_cave(R1),
|
||
|
||
Sit6:ordinary_cave(R1),
|
||
|
||
just(Sit5),
|
||
|
||
|
||
just(Sit6),
|
||
|
||
cave(Set4),
|
||
|
||
<20>K5,
|
||
|
||
K5:<U:{Set5, R16},
|
||
|
||
|
||
C:{Set5 =< Set4,
|
||
|
||
cardinality(Set5) >
|
||
|
||
cardinality(Set4)/2,
|
||
|
||
R16 <- Set5,
|
||
|
||
|
||
R1 <-\- Set5,
|
||
|
||
deeper_than(R16, R1)}> }
|
||
|
||
|
||
From a logical point of view, most of (N5a) is redundant;
|
||
|
||
|
||
the only useful part is 'deeper than most,' and that belief lacks
|
||
|
||
credibility. Nevertheless, it poses several problems: handling
|
||
|
||
the adjective-common noun combination, handling 'just,' and
|
||
|
||
accounting for 'most' in a manner suitable for logic. The
|
||
|
||
|
||
adjectives 'plain' and 'ordinary' (unlike 'red,' e.g.) have
|
||
|
||
little meaning until applied to a particular domain-- caves, in
|
||
|
||
this case. The adverb 'just' means something like 'not other
|
||
|
||
than' in this case, but how is that meaning determined? It does
|
||
|
||
|
||
not seem to be a syntactic matter, but a DRS is composed from a
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
16
|
||
|
||
|
||
syntactic parse. K5 is an attempt to handle 'most'; the symbols
|
||
|
||
< and / have their usual mathematical meanings; <-\- indicates
|
||
|
||
'not a member of.'
|
||
|
||
|
||
|
||
(N5b) and some place there had to be an opening to it.
|
||
|
||
U := U + {R17, R18, Sit7, P4}
|
||
|
||
C := C + {place(R17),
|
||
|
||
opening(R18),
|
||
|
||
|
||
part-of(R18, R1),
|
||
|
||
Sit7:necessary(P4),
|
||
|
||
P4:<C:{located(R18, R17)}> }
|
||
|
||
|
||
|
||
The truth of (N5b) is doubtful, but given its truth, R17 and R18
|
||
|
||
must exist at the top-level. It is possible that R18 is
|
||
|
||
identical to R9, now raised to top-level. Sit7 suggests one way
|
||
|
||
to handle modal auxiliaries.
|
||
|
||
|
||
|
||
(N6) There was, though, one big difference about this cave:
|
||
|
||
it was Luke's.
|
||
|
||
U := U + {Sit8, Sit9}
|
||
|
||
|
||
C := C + {Sit8:difference(R1, Set5, Sit9),
|
||
|
||
Sit9:own(R2, R1),
|
||
|
||
Sit8 o E1,
|
||
|
||
Sit9 o Sit8}
|
||
|
||
|
||
|
||
The noun 'difference' entails two things that are different
|
||
|
||
(this cave and other caves) and the thing that distinguishes them
|
||
|
||
(Sit9). However, only Sit9 is syntactically specified.
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
17
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
(N7) He had found it and it was his own secret place.
|
||
|
||
U := U + {E12, Sit10, R19}
|
||
|
||
C := C + {E12:find(R2, R1),
|
||
|
||
|
||
E12 << E1,
|
||
|
||
secret_place(R19),
|
||
|
||
R19 = R1,
|
||
|
||
Sit10:own(R2, R19)
|
||
|
||
|
||
E12 << Sit10}
|
||
|
||
|
||
The representation of (N7) is straight-forward; R19 is R1,
|
||
|
||
but to replace it by R1 in Sit10 is to make Sit10 a copy of Sit9.
|
||
|
||
|
||
This application of DRT has pointed out several needed
|
||
|
||
extensions to the theory. One of the most obvious is the means
|
||
|
||
of representing plural NPs, including those with quantifiers that
|
||
|
||
are less specific than 'all' but more specific than 'some' (e.g.
|
||
|
||
|
||
'most'). Another needed extension is a means of handling terms
|
||
|
||
that modify conditions: verbs that take verbals as complements
|
||
|
||
(modals and verbs such as 'seem') and adjectives whose meanings
|
||
|
||
depend on the particular nouns that they modify. A third
|
||
|
||
|
||
extension is a formalism for specifying arguments that
|
||
|
||
are not syntactically indicated (such as those for 'difference').
|
||
|
||
Whether or not the second and third extensions are feasible
|
||
|
||
without appealing to semantic analysis prior to constructing the
|
||
|
||
|
||
DRS remains to be seen; perhaps the needed machinery is available
|
||
|
||
in the lexicon.
|
||
|
||
|
||
Conclusion
|
||
|
||
|
||
|
||
DRT has been successful in representing a small subset of
|
||
|
||
natural language, and is being extended to increase the size of
|
||
|
||
that subset. As we have seen in Part 3 of this report, other
|
||
|
||
|
||
extensions will be necessary before it can handle the full range
|
||
|
||
of natural language expressions. If those extensions can be
|
||
|
||
accomplished without appeal to semantics, DRT will prove to be
|
||
|
||
quite powerful. However, DRT is intended to provide a bridge
|
||
|
||
|
||
between syntactic parses and model theoretic semantics; if
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
18
|
||
|
||
|
||
semantic analysis is necessary before a DRS can be constructed,
|
||
|
||
the purpose of DRT has been lost, or at least seriously modified.
|
||
|
||
|
||
|
||
|
||
REFERENCES
|
||
|
||
|
||
ETS. 1969. Sequential Tests of Educational Progress. Princeton:
|
||
|
||
Educational Testing Service.
|
||
|
||
|
||
Goodman, D. 1988. An Implementation of an extension to discourse
|
||
|
||
representation theory: Translating natural language to
|
||
|
||
discourse representation structures to Prolog clauses.
|
||
|
||
Unpublished master's thesis, The University of Georgia,
|
||
|
||
|
||
Athens.
|
||
|
||
Guenthner, F. 1987. Linguistic meaning in discourse
|
||
|
||
representation theory. Synthese 73:569-98.
|
||
|
||
Guenthner, F., H. Lehman, and W. Schonfeld. 1986. A Theory for
|
||
|
||
|
||
the representation of knowledge. IBM Journal of Research
|
||
|
||
and Development 30:1.39-56.
|
||
|
||
Kamp, H. 1981. A Theory of truth and semantic representation.
|
||
|
||
In J. Groenendijk, T. Janssen, and M. Stokhof (eds.) Formal
|
||
|
||
|
||
Methods in the Study of Language, 277-322. University of
|
||
|
||
Amsterdam.
|
||
|
||
Kamp, H. 1983. SID without time or questions. Ms. Stanford, CA.
|
||
|
||
Kamp, H. 1985. Unpublished discourse representation theory
|
||
|
||
|
||
project description, University of Texas, Austin.
|
||
|
||
Pinkal, M. 1986. Definite noun phrases and the semantics of
|
||
|
||
discourse. COLING-86, 368-373. University of Bonn.
|
||
|
||
Spencer-Smith, R. 1987. Semantics and discourse representation.
|
||
|
||
|
||
Mind and Language 2:1.1-26.
|
||
|
||
Smith, W. 1977. Types of information addition in the
|
||
|
||
psycholinguistic process of reading. Unpublished doctoral
|
||
|
||
thesis, The University of Georgia, Athens.
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|