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Salguero Lamillar, Francisco J.

idUS. Depósito de Investigación Universidad de Sevilla

279DRT’s treatment of inference and presupposition asa source of semantic enrichmentFrancisco J. Salguero LamillarUniversidad de Sevillasalguero@cica.es1 Inferential semantic enrichment in discourse interpretationThe Discourse Representation Theory (DRT) (Kamp & Reyle 1993) provides an expla-nation of the semantic enrichment processes that are present in discourse, by means of thestructure of the successive representations associated to a concrete sequence of utterances.In the case of pronominal anaphora or indefinites, interpretation is just possible in relationwith those elements present in discourse or in associated databases. Each Discourse Repre-sentation Structure (DRS) can be seen as a database within which certain information aboutthe world is codified. So, when the speaker codifies a message, we can think on a selectionof lexical elements suitable for representing the referred individuals and the properties theyhave, the relations they hold in a concrete description of the world and even the propertiesand relations between this description of the world and other ones. All these elements arecombined using certain rules; so the hearer obtains from the speaker a series of linguisticdata to which he must apply his grammatical, logical and encyclopaedic knowledge in orderto be able of decodifying the complete information. In a very general way, the followingscheme could be an illustration of discourse interpretation process:Rules of grammar Rules of logic Knowledge of theworldDiscourse interpretationFigure 1Grammar, logic and encyclopaedic knowledge appear in this scheme as separate mod-ules with a unique and final relation: the interpretation of the speaker utterances. Neverthe-less, there are enough reasons to think that the established relations among these modulesare closer. Without discussing questions about syntactic or morphological iconicity andthose logical aspects that are more evident in natural language grammar, we can consider280that the interpretation of any linguistic utterance rests on the application of all these knowl-edge modules to the intermediate representations of discourse that are necessary for evalu-ating the speaker utterances. Consider the scheme in Figure 2, more complex than the for-mer one:Rules of Grammar(Linguistic Knowledge)Rules of LogicMeaning postulatesRules of lexical informationSituation &Context(Knowledgeof the world)Anaphoric variable instantiationrulesDiscourse(Previous information)Utterance InterpretationFigure 2As it can be seen, the instantiation of anaphoric variables is considered as an intermedi-ate module for the interpretation of utterances. Therefore, the interpretation of anaphora(pronouns, indefinite noun phrases, definite descriptions, relative clauses, spatial or tempo-ral deictic terms, tense and aspect of verbs, etc.) is the common element for the confluenceof the other modules. Hence the importance of anaphoric inference in DRT and anotherdynamic frames of discourse interpretation.In the interpretation of discourse, it is rare to have a unique database for establishing itsglobal meaning. Several related databases are usually needed to obtain a model. The givenrelations among representations or necessary databases for the evaluation of discourse ut-terances are far away from those in classical model theory. Conceived in this manner aslinguistic databases, the different representations of discourse are similar to possibleworlds. So they can be seen as moments, giving a temporal interpretation to discourse rep-resentations; or they can be seen as successive states of the speaker/hearer’s mind, and thenwe have that discourse representations are similar to Kripke’s information states. Whateverthe case could be, the representations of discourse are interpreted as partial models of real-ity, and therefore they can be treated as Hintikka sets (Salguero 1994).This perspective allows us dealing with discourse interpretation as a sort of logical cal-culus, a series of inferences on the successive representations of discourse that take the281hearer to the meaning of its constituent utterances. Such inferences depend on the rules ofthe grammatical and logical modules, and on the hearer’s knowledge of the world. Butthere is even another decisive factor that intervenes in these inferences: presuppositions.2 Presuppositions and DRTThe notion of presupposition has been discussed since Antiquity, without havingreached a consensus about its linguistic or logical nature up to the day. We can see it as asemantic relation between sentences and define it saying that a sentence B presupposesanother sentence A if A implies B or if the truth value of A is a condition for the truth valueof B. It is also usual to understand the notion of presupposition pragmatically as a set ofattitudes and notices, being used by language users in their speech acts. In this case, werefer to speaker/hearer’s presuppositions instead of sentence presuppositions. But there isno opposition between these two perspectives because we can treat presupposition as a onemore part of the interpretation of the utterances that constitute discourse in a concrete rep-resentation of its meaning, and then both perspectives are satisfied: the semantic and thepragmatic one.This signifies that we will not find a well defined notion of presupposition in the spe-cialised literature, but a set of linguistic data that must be explained in a theory about dis-course interpretation (Levinson 1983). Typical examples of these linguistic data are sen-tences like:(1) Have you stopped hitting your wife?(2) The actual king of France is not baldIn (1) we have that the verbal aspect and the possessive your presuppose that the hearerhas a wife and that he hits her. In (2) we are in front of a classical existence presuppositionintroduced by the definite determiner the. Both sentences are classical examples of presup-positions, but they are not the only ones. We can classify the linguistic elements that can bethe source of presuppositions in discourse, following (Beaver 1997):1. Definite noun phrases, introduced by the definite article, demonstratives or posses-sives, proper names or even relative clauses.2. Quantified noun phrases, introduced by a quantificational determiner.3. Factive verbs or verbal nouns and noun phrases related to them, such as reject,know, the fact that, the acquaintance of, etc. In this case we can distinguish be-tween cognitive factives, related to the knowledge of the facts, and emotive fac-tives, related to emotional attitudes towards the facts.4. Clefts (it-, wh- or pseudo-clefts), like It was not John who called you up, presup-posing someone called you up.5. Wh-questions that presuppose the existence of an entity suitable for an answer, likeWhat colour is the snark?, presupposing the existence of a “snark”.6. Counterfactuals, presupposing the falsity of the antecedent.7. Lexical presuppositions. For instance, dog presupposes animal.8. Action verbs, like stop doing something, aspectual or temporal modifiers, like be-fore or after in certain sentences (v. gr.: After having your breakfast, go out toschool, presupposing you are having breakfast).2829. Iterative expressions, like again, or the prefix re-, presupposing some kind of repe-tition.10. Some discourse connectives, like although, but, because.Casuistry is wide and we do not pretend to have a list with every source of presupposi-tion in discourse. But we can see now that presuppositions in the sentences (1) and (2)depend on verbal aspect and tense, studied, for instance, in (Kamp & Reyle 1993:483f.),and on the interpretation of noun phrases and the quantificational scope of the determiners.This last one is the most usual source of existential presupposition in discourse and we willanalyse it in this paper.2.1 Accommodation of presuppositions in DRSsIt is evident, as we have mentioned before, that presuppositions play an important rolein discourse interpretation. They are indeed a part in the semantic and logical structure ofthe discourse utterances and, therefore, they must appear in any representation of thatstructure. So we need a method for making presuppositions explicit in Discourse Repre-sentation Structures (DRSs), since they are the way in which DRT represents discourseinterpretation. We are adopting van der Sandt’s method, consisting in the explicit extensionof discourse context in order to include in the correspondent DRS all the presuppositionsintervening in the interpretation of the utterances (van der Sandt 1992, 1993). This methodis called accommodation.Accommodation consists in the addition of discourse referents and conditions to a DRS.This addition is made in any of the accessible representations that contain the discourseelement that triggers the presupposition. When a trigger element causes a presuppositionwithout an antecedent, accommodation will consist in the transference of discourse markersand conditions of the presupposition from the representation of the trigger to an accessibleDRS. Therefore, we can distinguish among local accommodation (when the addition ismade in the same DRS of the trigger), global accommodation (when the addition is made inthe main DRS that includes all the other representations), and intermediate accommodation(when the addition is made in another DRS, different from the main one and accessiblefrom the DRS where the trigger element appears) (van der Sandt 1992).Triggers are seen as anaphoric elements in discourse interpretation because these ele-ments cannot be interpreted with independence of the structural relation established be-tween the position in which they are represented in a DRS and the place where the repre-sentations of their antecedents are: an accessible DRS, like in the case of pronominalanaphora’s antecedents. Let us see an example taken from (Beaver 1997):(3) Mary doesn’t realise that somebody is escaping.The correspondent DRS (DRS1) includes the presupposition somebody is escaping, thatwill be represented within a double line box. This presupposition marks the existence in thediscourse universe of an individual z and verifies the condition is_escaping(z). The markerw can be instantiated as z because the presupposition is accessible from its DRS. We cancompare (DRS1) with the interpretation of the sentence (4), represented by (DRS2):(4) Fred is escaping but Mary doesn’t realise somebody is escaping.283(DRS1)yMary(y)zis_escaping(z) wrealises(y, is_escaping(w) )(DRS2)x,yFred(x)is_escaping(x)Mary(y)zis_escaping(z) wrealises(y, is_escaping(w) )The main DRS in (DRS2) is accessible from the negated DRS, so the marker z can beinstantiated by means of the marker x. Therefore, the universe of the presupposition can be284reached from the global universe of discourse, as the condition of the presupposition isaccessible like a global condition. This means that the presupposition has an antecedentand, therefore, as it does not play another role in (DRS2), it could be eliminated salva in-terpretatione. When we eliminate a presupposition by means of its resolution into an ante-cedent as in (DRS2), or when we accommodate it into a DRS accessible from the trigger’srepresentation, we say that the presupposition is cancelled. But, how does the accommoda-tion method work in relation with the presuppositions in a DRS? Consider the followingsentence:(5) If Mary chose the Sherry then she realises it is a good wine.In the following DRSs, we will simplify the discourse markers using individual con-stants m and s, denoting Mary and Sherry respectively, and the bidimensional structure willbe represented linearly for saving space in the page. Then, in (DRS3) the signs [ and ] aresingle line box limits and the signs { and } are double line box limits. An empty box [  ]means that there is no individual marker for that representation.(DRS3) [ [m,s] [ [  ] chose(m,s)]   [ [  ] { [  ] good_wine(s) } realises(m, [ [  ]good_wine(s) ] ) ] ]In order to have a DRS where no presupposition appears without an antecedent, wemust move the DRS representing the presupposition towards any of the sites that are acces-sible from the trigger’s DRS, that is to say: from the representation of the sentence Maryrealises that the Sherry is a good wine. This movement produces three different DRSsdepending on the accommodation type:Global accommodation: The Sherry is a good wine and if Mary chose it, she realises it isa good wine.(DRS4) [ [m,s] good_wine(s) [ [  ] chose(m,s)]   [ [  ] realises(m, [ [  ] good_wine(s) ] ) ] ]Intermediate accommodation: If the Sherry is a good wine and Mary chose it then sherealises it is a good wine(DRS5) [ [m,s] [ [  ] good_wine(s) chose(m,s)]   [ [  ] realises(m, [ [  ] good_wine(s) ] ) ] ]Local accommodation: If Mary chose the Sherry then it is a good wine and she realises itis a good wine.(DRS6) [ [m,s] [ [  ] chose(m,s)]   [ [  ] good_wine(s) realises(m, [ [  ] good_wine(s) ] ) ] ]Each one of these three DRSs supposes a different interpretation of the existing relationbetween the sentence (5) and the presupposed sentence The Sherry is a good wine. Now wecan ask what kind of accommodation is the best one for the interpretation of an uterrancelike (5) and try to establish a priority. First, we must try to instantiate the presuppositionmarkers in the actual accommodation. That is what is called resolution. But resolution ispossible only when we have accessible markers for the instantiation, from the DRS con-taining the presupposition trigger up to the main DRS. When we cannot find markers forthe resolution then we must appeal to accommodation, but now going in the reverse way:285from the main DRS up to the trigger’s DRS. This means the priority is resolution and then,when resolution is not possible, global accommodation, intermediate accommodation andfinally local accommodation. This process has certain constraints that can be found in (vander Sandt 1992) or in (Beaver 1997).2.2 Existential presuppositions and DRSsWe can now recover the classical example by Bertrand Russell to illustrate the treat-ment of existence presuppositions in DRT:(2) The actual king of France is not baldThe problem for Predicate Logic is whether this sentence is true or false because there isno entity in the domain of discourse that could be considered as a good instantiation for theindividual variable in order to satisfy the predicate to_be_the_king_of_france. Nevertheless,Russell said that the logical form of this sentence presupposes the existence of such anindividual:[2]  x(king_of_france(x)  bald(x))It is evident that if [2] is true then we can infer [2’], that is to say: There is a king ofFrance; but if [2] is false then we can infer [2”], that is to say: All the kings of France arebald.[2’]  x(king_of_france(x))[2”]  x(king_of_france(x) bald(x)),To avoid this kind of undesirable presuppositions, Russell proposed his theory of defi-nite descriptions, introducing a logical operator   as a descriptor. In this theory, two possi-ble scopes were postulated for negation: a restricted scope [2*] (corresponding to the globalaccommodation of the presupposition) and a general scope [2+] (corresponding to the localaccommodation):[2*]  x[king_of_france(x)](  bald(x))[2+]  ( x[king_of_france(x)](bald(x)))(DRS7) Global accommodation: (DRS8) Local accommodation:xking_of_france(x) x king_of_france(x) bald(x) bald(x)286In ordinary discourse, to avoid the undesirable effect produced by the existential pre-supposition in (2), we can enrich our utterance with an explanation in the following way:(6) The actual king of France is not bald. There is no actual king of France.The corresponding DRS to (6) must include, however, the existential presupposition anddeal with it in the adequate manner, resolving its discourse markers or accommodating it inthe corresponding site inside the DRS:(DRS9) [ [  ]  [ [  ] bald(x) { [x] king_of_france(x) } ]  [ [y] king_of_france(y) ] ]The two possible accommodations for the presupposition in (DRS9), after leaving thepossibility of resolution of the marker x aside, are the following ones:(DRS10) [ [x] king_of_france(x)  [ [  ] bald(x) ]  [ [y] king_of_france(y) ] ](DRS11) [ [  ]  [ [x] bald(x) king_of_france(x) ]  [ [y] king_of_france(y) ] ](DRS10) represents the global accommodation of the presupposition and (DRS11) rep-resents the local accommodation. But, between both options, we must prefer the local ac-commodation (DRS11), because the global accommodation (DRS10) contains a contradic-tion since we can resolve the marker y instantiating it in the marker x that appears in anaccessible representation. Then, the existential presupposition is cancelled in (DRS11).The addition of van der Sandt’s accommodation theory to DRT to deal with presuppo-sitions gives us certain advantages over other alternative theories. It includes, for instance, aresolution mechanism for anaphora we cannot find in the theory of definite descriptions.Moreover, it offers a criterion for distinguishing between different scopes of the presuppo-sition and choosing the most adequate one in each case to cancel it. It also offers the possi-bility of treating in a different way the different presuppositions appearing in discourse,depending on the relations with their trigger elements and their sites inside the global DRSthat represents their meaning.ReferencesBEAVER, D. (1997). “Presupposition”, in BENTHEM, J. van & MEULEN, A. ter (eds.)(1997), Handbook of Logic and Language, North-Holland, Amsterdam, pp.: 939-1008.KAMP, H. & REYLE, U. (1993). From Discourse to Logic, Kluwer, Dordrecht.LEVINSON, S. (1983). Pragmatics. Cambridge University Press, Cambridge.SALGUERO LAMILLAR, F. J. (1994). “Anaphoric instantiation problems in an inferentialmodel of utterance representation”, in MARTÍN VIDE, C. (ed.) (1994), Current issuesin mathematical linguistics, North-Holland, Amsterdam, pp.: 39-48.SANDT, R. van der (1992). “Presupposition projection as anaphora resolution”. Journal ofSemantics, 9: 333-377.SANDT, R. van der (1993). “Resolution and accomodation”, in KAMP, H. (ed.) (1993),Presupposition, DYANA-2. Dynamic Interpretation of Natural Language. ESPRIT Ba-sic research project 6852. Deliverable R2.2.A, Part II, pp.: 233-242.

DRT’s treatment of inference and presupposition as a source of semantic enrichment

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DRT’s treatment of inference and presupposition as a source of semantic enrichment

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idUS. Depósito de Investigación Universidad de Sevilla