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<?xml version="1.0" standalone="yes"?> <Paper uid="C94-2193"> <Title>PRESUPPOSITION & VP-ELLIPSIS*</Title> <Section position="4" start_page="0" end_page="1784" type="metho"> <SectionTitle> 2 DRT-framework </SectionTitle> <Paragraph position="0"> In this section I will outline a proper framework that integrates anaphora resolution, presupposition projection, and ellipsis resolution. Basically, we will extend Kamp's Discourse Representation Theory slightly, by integrating the treatment of presupposition of Van der Sandt and reference to abstract entities by Asher. What is new is the combination of these three formalisms into one, leading to interesting results concerning the analysis of VP-ellipsis.</Paragraph> <Paragraph position="1"> \])RT focuses on the semantic interpretation of discourses. A major aspect of I)RT is the use of Discourse Representation Structures that hold the seinantic content of sentences as a pair < U, C >, in which U is a set of discourse markers (referents) and C a set of conditions upon them. The full syntax of DRSs is given in Definition 1.</Paragraph> <Paragraph position="2"> Definition 1: DRS Syntax 1. If U is a set of reference markers, C a set of conditions, then the pair < Uq~,CC/ > is a 1)RS I~; 2. If P is n-place predicate constant and tl ... t~ are terms, then P(tl ... tn) is a condition; 3. If (i) and g~ are DRSs, then ~ (P, * => qJ and (I) V * are conditions 4. If (I) is a I)RS, P a predicative I)RS, tl, t2 are terms, then ~(h,t2):(I), cP(h) and h:O are conditions.</Paragraph> <Paragraph position="3"> Clause (2) forms atomic conditions. Clause (3) states negation, universal quantification, and disjunction. Clause (4) defines anaphoric, elliptical material, and propositions and deserves more attention because it deviates from Kamp's original proposal. In our framework we introduce the alfa-condition (~:~) which functions to indicate that the information in \])\]IS ~ must be anaphorically Linked to previously established discourse markers. It has two additional arguments, one for indicating the prhlcipal referent of the anaphoric construction, and (optional) one for stating the antecedent. So a condition c~(x,y):~ states that y is the antecedent for x~ under restriction of (I). In the case of pronouns, e0 only contains discourse markers and no conditions. But in the case of, for example, definite descriptions, (I) carries the restrictions in its conditions for linking the discourse marker associated to the definite description to an earlier introduced marker.</Paragraph> <Paragraph position="4"> Referential constructions such as ellipsis and event-type anaphora, are not linked to discourse markers but, instead, refer to portions of discourse, and are indicated by e: P(t), where P is an abstracted piece of the previous DRS. Resolution of epsilon-conditions is done by applying the abstracted DRS P to its argument t.</Paragraph> <Paragraph position="5"> Alfa- and epsilon conditions do not c~rry any subordination relations with respect to other DRSs, and neither do propositional conditions. They are, in contrast to the sub-DRSs formulated under clause (3), accessible for anaphoric relations and inherit the subordination relations of the I)RS in which they are situated.</Paragraph> <Paragraph position="6"> Ellipsis resolution is done by a process called C-Abstraction (cf. Asher 1993, p. 249). It is stated in a simplified form as: (Asher) 1. If c:P(t) is a condition in DRS K and is derived from auxiliary do, then P may be identiffed with Ay.K*, where K* is an alphabetic variant of a part of K.</Paragraph> <Paragraph position="7"> 2. K* is underspecified for alfa- and epsilon null conditions.</Paragraph> <Paragraph position="8"> While parsing a sequence of sentences, we aSsume tile following: firstly, we have got ~ pro per I)RS of the sentences that we have parsed so far, and secondly, a compositional bottom-up construction procedure that returns the DRS of the actual sentence, which is called the sentence-l)RS (henceforth s-I)RS).</Paragraph> <Paragraph position="9"> An s-DRS is in a sense underspecified, because all anaphoric material that it includes is still unresol-. ved. On the representationM level this is marked by leaving the optionM slot in the Mfu-condition for the antecedent untilled. Anaphoric material contains, besides the 'normal' anaphors, also all presuppositioual information of the sentence under consideration. Accordingly all presupposition inducers are marked as such in the lexicon.</Paragraph> </Section> <Section position="5" start_page="1784" end_page="1784" type="metho"> <SectionTitle> 3 Presupposition Projection </SectionTitle> <Paragraph position="0"> In this section we will show how presupposition projection (aild hence, anaphora resolution) is treated in I)RT. The Mgorithm I present is in essence conform to Van der Sandt's proposal \[Van der Sandt, 1992\]. Van der Sandt's theory is principally based on two mechanisms: binding and accommodation. Compared to classical presupposition theories, the former corresponds by and large to presupposition cancellation (or better: neutralization), while the latter is sort of repairing the discourse in the style of Lewis \[1979\]. The idea of Van der Sandt's work is that &quot;anaphoric expressions are either linked to some previously established antecedent or, if they have enough descriptive content, accommodated at some level of representation&quot; \[Van der Sandt, 1992\]. All anaphoric information is resolved (under normal circumstances), conform the following rules: 1. Try to bind the anaphoric material to an accessible antecedent.</Paragraph> <Paragraph position="1"> 2. If (1) fails, accommodate an antecedent.</Paragraph> <Paragraph position="2"> Accommodation must take place at some accessible level of discourse. It has been argued in the literature that accommodation must take place as global as possible. \[Helm, 1983; Van der Sandt, 1992\]. Rather than using a non-monotone moving operation for accommodation we obey the following algorithm: 1.</Paragraph> <Paragraph position="3"> 2.</Paragraph> <Paragraph position="4"> 3.</Paragraph> <Paragraph position="5"> 4. Ready.</Paragraph> <Paragraph position="6"> If there is a superordinated level then (2) else (4).</Paragraph> <Paragraph position="7"> Copy the presupposed information to this level, but only if this does not lead to semantic contradictions (unbound variables or inconsistencies) or pragmatic violations, else (4). Repeat step (1).</Paragraph> <Paragraph position="8"> We will not elaborate in detail on the issue which constrains constitute the elimination of possible accommodation sites. The interested reader should consult Van der Sandt's paper (1992) for proposals.</Paragraph> <Paragraph position="9"> We exemplify the projection algorithm with (3) and (4). The former presupposes John as a (tog owner, the latter, in contrast, does not presuppose that, although it contains the same presupposition inducer. This is named the the projection problem. (3) John beats his dog.</Paragraph> <Paragraph position="10"> (4) If John has a dog, he beats his dog.</Paragraph> <Paragraph position="11"> The result of the compositional semantic construction process for (4), given that presuppositions are marked in the lexicon as anaphorical, is the follo-</Paragraph> <Paragraph position="13"> This s-DRS is merged with the DRS of the previous discourse, which is in this case an empty one. The next step is to examine the newly acquired conditions and see if there are any anaphoric DRSs among them.</Paragraph> <Paragraph position="14"> In the first place we find the condition for the proper name John, which is treated as a presupposition. We cannot bind this expression to a referent, since there is none available, so we accommodate the information in the principle DRS) Accommodation is simply fulfilled by copying an alphabetic variant of the anaphoric DRS to the main DRS.</Paragraph> <Paragraph position="15"> Linking is possible for the personal pronoun x3 to the (closest) referent of John.</Paragraph> <Paragraph position="16"> The other anaphoric DRS in the conseqnent of tile implication paraplirases his dog has an embedded anaphoric DRS, which has to be resolved first. In this case the referent x5 can be linked to xl. Finally we can resolve x4 to x2 because their corresponding conditions do not conflict and yield:</Paragraph> <Paragraph position="18"> This DRS is fully specified and paraphrases the meaning of (4) correctly: There is a male person called John, and if John owns a dog, he beats it.</Paragraph> <Paragraph position="19"> For (3), our algorithm would accommodate the information that John owns a dog.</Paragraph> <Paragraph position="20"> XNote that proper names, treated as presuppositions, arc always accommodated to the top level DRS this way, or linked to previously established markers.</Paragraph> <Paragraph position="21"> We will explain our analysis of VP-ellipsis by example (5). R.ecM1 that (5)is ambiguous in whether 'Ibrn is beating John's dog (the strict interpretation) or Tom is beating TonPs dog (the sloppy reading).</Paragraph> <Paragraph position="22"> (5) John kicked Ms {log. 'Ibm did, too.</Paragraph> <Paragraph position="23"> Our analysis heavily relies on the interpretation of focusing particles. No existing approach to VP-ellipsis does so, Mthough absence of presupposition introducers makes interpretation of elided VPs impossible (6). The set of presupposition triggers I am referriug to includes particles like too, also, so, either, discourse connectives before; after, and, but and other presupposition inducers such as certain focusing constructions.</Paragraph> <Paragraph position="24"> (6) ? John kicked his dog. Tom did.</Paragraph> <Paragraph position="25"> We will emi}hasize on the interpretation of focllsing particles, especially, the adverb too. Discourse particles function to enhance the cohere.nee of discourse. They do not add anything to the meaning of the propositi{}us they modify, but rather judge whether at propositions tits within the previous {:ontext or not;. This feature characterizes them as eliminators of possible readings in a given context. It makes it impossible to understand (5) as 3ohn kicked Bill's dog, and '/bin kicked 51bra's dog, for example.</Paragraph> <Paragraph position="26"> The particle too typically is sensitive to fi)cused objects. It, words, too(qS), C/ a propositk, n, pre supposes '~/), with gJ a proposition derived froln C/ with the focused items in C/ replaced by their alternatives. We follow Rooth \[Rooth, 1985\] in taking the fm, ction of focus to be evoking alternative sets. Focus determines in that respect an additional semzmtic wflue H 1. Ordinary semantic values ~.\]o are not affected by focus.</Paragraph> <Paragraph position="27"> (7) \[ qbmfa kicked his1 dog\] j = the set of pro positions of the forln &quot;x kicked x's dog&quot; (8) ~ 'Ibm/,1 kicked his2 dog~ / = the set of propositions of the form &quot;x kicked his~ dog&quot; (9) \[ !l'om/, 1 kicked his1 dog~ deg = the proposition &quot;John1 kicked his1 dog&quot; Note that pronouns with focused antecedents (7) get a referential interpretation, and pronouns with an unfocused antecedent get a bound interpretation. The semantics of too, stated in terms of Rooth's alternative semantics is consequently: (lO) too({I}): \[{iqdeg(D I7~~ (k~-I~\]\] ') The merge operation (D takes two DRSs and returns a new one. The merging of I)RSs consists in simply taking the union of the sets of discourse markers and the sets of conditions separately.</Paragraph> <Paragraph position="28"> The alfa-condition in (10) introduces the presupposition of too. In order to preserve {:oordinafion be.tweeu this presupposition and the asserLion, it is necessary 1;o perform ellipsis and anaphora resolutiou befi}re the interpretation of proposition modilying particles (;an take place.</Paragraph> <Paragraph position="29"> We will work out an example in detail to make clear how resolution is restrained by presupposition. l)iscourse markers of type x, are used to range over individuals, markers of type Pl range over propositions. Consider (5), paraphrased in the following DRS:</Paragraph> <Paragraph position="31"> By C-At}str;~ction (Def. 2) we derive the following predicative I)RS for kicked his dog', wt, ich will be ~pplied to the argument of tile epsilon-condition in (11), x4.</Paragraph> <Paragraph position="33"> Note that (12) is underspecified for anaphoric relations. It will become part of a context distinct from its original one, and therefore other discourse markers may play the role of antecedents. The discourse marker x6, standing for his, can be either linked to the marker corresponding to Tom, or to the marker corresponding to John. In the former case we get a referential reading in the presupposition because the antecedent is in focus position, in the latter case we get a bound reading. However, these possible readings 2 are checked for being allowed by the presupposition introduced by too.</Paragraph> <Paragraph position="34"> Applying (10) to the resolved propositional DRS P2 with the referential reading gives us the presupposition in (13) which allows the sloppy interpretation of Tom does, too:</Paragraph> <Paragraph position="36"> The presupposition Pa can be linked to Pl in (11) and is therefore not rejected. The resolved DRS with the bound reading in the presupposition gives us the strict interpretation of the elided VP.</Paragraph> <Paragraph position="37"> The presupposition stemming from too for this case is (14) and can also be linked to Pl.</Paragraph> <Paragraph position="39"> Given DRS (11), no other presuppositions can be satisfied and therefore these two readings are exhaustive. Because linking of presuppositions has 2Which number would be larger, if there were more suitable antecedents for x6, more possible antecedents VPs, or more alternatives for the focused object Tom. tlowevcr, none of these readings would fulfil the requirement to be an anaphoric presupposition! in our framework a higher priority than accommodation, readings like '/bm kicked x's donkey, where x does not equal John or Tom, are not allowed. null Finally, note that, for the definite description his dog, in the second case presupposition neutralization by anaphoric binding took place, while in the first case the presupposition was accommodated (by &quot;assertion&quot;).</Paragraph> </Section> <Section position="6" start_page="1784" end_page="1784" type="metho"> <SectionTitle> 5 Comparison to other Approa- </SectionTitle> <Paragraph position="0"> ches I classify previous approaches to VP-ellipsis resolution as 1) approaches that take the antecedent VP as ambiguous, 2) approaches that pursue a copying-and-renaming mechanism, and 3) approaches that rely on discourse relations. None of the approaches to be mentioned use presupposition as means to restrain VP-ellipsis resolution.</Paragraph> <Section position="1" start_page="1784" end_page="1784" type="sub_section"> <SectionTitle> Source-clause Ambiguity Approaches </SectionTitle> <Paragraph position="0"> The first class of approaches to VP-ellipsis is characterized by claiming that the semantics of the elided VP is identical to another VP salient in discourse. They treat the source clause as ambiguous in cases where there is both a strict and sloppy interpretation possible. For illustration, our example (5) would allow only one of the two possible properties for the antecedent VP, respectively the referential and the bound interpretation.</Paragraph> <Paragraph position="1"> (15) a) Ax. kicked(x,dog_of(x)) b) Ax. kicked(x,dog_of(john)) Resolution is simply done by choosing one of the possible sources given in (15) and apply it to the subject of the elliptical VP. This analysis is proposed in \[Sag, 1976\], \[Williams, 1977\], \[Klein, 1987\], \[Roberts, 1987\] and \[Gawron and Peters, 1990\] and are also termed &quot;identity-of-relations&quot; approaches in the literature.</Paragraph> <Paragraph position="2"> The most serious problem that these approaches face is &quot;the postulation of wild ambiguity in the source clause, one derivation for each possible case of subsequent ellipsis.&quot; \[Dalrymple et al., 1991\]. Furthermore, it turns out to be impossible to hold on to this analysis for cases like (16): (16) With Betty, John visited her parents, and with MARY, he did, too.</Paragraph> <Paragraph position="3"> Example (16) also shows the strict/sloppy ambiguity. Our analysis predicts this, since the focused object is Mary, and the presupposition stemming from too is either with x, John did visit x's parents (sloppy reading) or with x, John did visit Betty's parents (strict reading).</Paragraph> </Section> <Section position="2" start_page="1784" end_page="1784" type="sub_section"> <SectionTitle> Copying-and-Renaming Approaches </SectionTitle> <Paragraph position="0"> On the other hand, there are the 'sloppy-identity', qmn-identity', or ~flexible-copying' approaches to the problem of ellipsis, which abandon the assumption that the source clause is ambiguous.</Paragraph> <Paragraph position="1"> Instances of these analyses are the higher order unification and equationM analysis \[DMrymple et al., 1991\], role-based copying methods \[Kehler, 1993\], and few posited in Discourse Representation Theory \[B~uerle, 1988\]; \[Sem, 1993\]; and Kainp (Personal communication of Kamp to Gawron & Peters \[Gawron and Peters, 1990\]).</Paragraph> <Paragraph position="2"> Their shortcomings are, generally stated, first that they are forced to put additional, intricate constraints on resolution to omit overgeneration of readings. Second, these approaches do not include a detection of parMlelism. They take the identification of parallel objects for granted, or assume that the subjects of the source and target clauses are parallel (which is not necessarily the case, see e.g. (16)). A proper treatment of ellipsis requires the integration of parallelism detection between the source and target clause.</Paragraph> <Paragraph position="3"> Our approach can also be classified as a copying-and-renaming approach, with the difference that it uses presupposition neutralization as a naturn constraint rather than using &quot;artificial&quot; constraints to restrict resolution. Copying-andrenaming analyses generally have better predictions than source-clause-ambiguity approaches.</Paragraph> <Paragraph position="4"> The following example, for instance, is judged to have five readings: (17) John revised his paper before the teacher did, and Bill did, too.</Paragraph> <Paragraph position="5"> Our analysis generates (assuming that before introduces a similar presupposition as too), when the embedded elided VP is strictly interpreted, two readings (the corresponding presuppositions are x revised x's paper before t revised t's paper, and x revised j's paper before the t revised t's paper) and three readings when the embedded elided VP is sloppily interpreted (here the corresponding presuppositions are: x revised x's paper before t revised x's paper, x revised j's paper before t revised j's paper, and x revised x's paper before t revised j's paper). These are exactly the same readings as \[l)alrylnple et al., 1991\], \[Kehler, 1993\] and \[Sem, 1993\] get in their analysis.</Paragraph> </Section> <Section position="3" start_page="1784" end_page="1784" type="sub_section"> <SectionTitle> Analyses using Discourse Relations </SectionTitle> <Paragraph position="0"> A quite distinct class of approaches to VP-ellipsis are those that use discourse structure to restrain resolution lasher, 1993; Gardent, 1993; Priist and Scha, 1990\]. These merely built on fi'ameworks stemming from AI of whom the most famous one is Grosz & Sidner's Discourse Structure Theory \[Grosz and Sidner, 1986\]. In order to identify the underlying segments of discourse and their relations that hold between them, interpretation of clue words (finguistic expressions that indicate boundaries between discourse segments) and the purpose of the speaker is taken into account. Also, one inight need knowledge of the world in the analysis of segmentation.</Paragraph> <Paragraph position="1"> A general problem that these approaches face is that they heavily rely on discourse relations.</Paragraph> <Paragraph position="2"> There definition is &quot;notoriously elusive&quot; \[Gardent, 1993\], and an exhaustive classification is still sub-ject to future research. Although cue phrases play an important role ill signalling topic changes in discourse, in general another mechanism might be needed to find connections which are not clearly stated. The use of speaker's intentions might be necessary but in general there is no finite set of possible intentions available \[Grosz and Sidner, 1986\]. Another problem is the difficulty of finding a general way to incorporate world knowledge in a working system.</Paragraph> <Paragraph position="3"> It is unclear in how far one needs discourse information for ellipsis resolution. An interesting future research topic is how far presupposition, as proposed in this paper, can support this task.</Paragraph> <Paragraph position="4"> Take for example: (18) If John beat his donkey, Bill will too, but if he doesn't, Bill won't either.</Paragraph> <Paragraph position="5"> Although source-clause-ambiguity approaches predict the right two readings for (18), it is unclear how copying~and-renaming analyses would eliminate any mixed strict/sloppy readings without using discourse relations like contrast and parallelism.</Paragraph> </Section> </Section> class="xml-element"></Paper>