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<?xml version="1.0" standalone="yes"?> <Paper uid="E93-1018"> <Title>A unification-based approach to multiple VP Ellipsis resolution*</Title> <Section position="4" start_page="139" end_page="139" type="metho"> <SectionTitle> SEM like:\[j,m\] \] \] IN _ OUT \[like:\[m\]\] </SectionTitle> <Paragraph position="0"> With regard to VPE resolution, two points are relevant. First the IN value is a don't-care-value (symbolized here by the anonymous variable), thus signaling the fact that incoming anaphoric information is irrelevant in the case of non-elliptical clauses. Second, the OUT value contains the information associated with the sentence main VP thus signalling the fact that non elliptical clauses update the current outgoing context with new information. Note that anaphoric information concerning VPs is here assumed not to be cumulative, that is the OUT value of \[\] is not &quot;added&quot; to the IN value - rather it constitutes the sole output of (a) independent of the preceding context. The intuition formalised here is that the discourse entity providing the interpretation of an elided VP is not as persistent as an individual discourse entity and thus should remain local to the discourse constituent that introduced it (although in some particular cases such as e.g. parallelism, anaphoric information pertaining to VPs can be percolated by the discourse grammar rules). For more details on this point, the reader is referred to \[Gardent 1991\], pages 141-142.</Paragraph> <Paragraph position="1"> Now consider the category assigned by the discourse grammar to the elliptical clause (c). Again ignoring irrelevant attributes, this category can be represented as:</Paragraph> </Section> <Section position="5" start_page="139" end_page="140" type="metho"> <SectionTitle> SEM R:\[p\[ As\] \] \[E IN \[R:AS\] OUT \[R:As\] </SectionTitle> <Paragraph position="0"> where R and As are unification variables over relations and arguments respectively. The important point to note here is that the variables R and As are shared by the IN value on the one hand, and by the SEM value on the other. This in effect implements VPE resolution. To see this, suppose that we have a discourse rule of the following form (AND abbreviates the category for and): Seml\] \[S M Sem2\] Application of this rule to the categories of (a), (b) and (c) above will trigger the unification of Outl with \[like:\[m\]\] on the one hand, and \[R:As\] on the other. Thus \[R:As\] is unified with \[like:\[m\]\] and the semantic representation R:\[p I As\] of (c) will become like:\[p,m\], just as required.</Paragraph> </Section> <Section position="6" start_page="140" end_page="141" type="metho"> <SectionTitle> 3 Discourse structure and Multiple VPE resolution </SectionTitle> <Paragraph position="0"/> <Section position="1" start_page="140" end_page="140" type="sub_section"> <SectionTitle> 3.1 Some data </SectionTitle> <Paragraph position="0"> The claim this paper makes about multiple VPE resolution is that the same discourse relation must hold between the multiple VP ellipses on the one hand and the multiple antecedents on the other. The present section has for object to substantiate this claim. As a first case in point, consider the following example.</Paragraph> <Paragraph position="1"> (5) I never go swimming because I don't look good in a swimming suit. (causal) a. I might ifI did. (causal) b. If I did, I probably would. (causal) c. Sarah does and so she does. (causal) d. ? I might after I did. (temporal) e. ? I might but I did. (contrast) Example (5) gives a case of a-clauses which are related by a causal relation. Several possible continuations are then given, some of them are acceptable, some of them are not. The relevant observation is that in those cases where the relation holding between e-clauses also is a causal one, the continuation is acceptable; however, in those cases where the relation holding between e-clauses is of a different nature, the continuation is inacceptable.</Paragraph> <Paragraph position="2"> As a second case in point, consider example (6): (6) I was thin then and the trousers looked good on me and I should have bought them,</Paragraph> <Paragraph position="4"> Here the antecedent discourse unit consists of three clauses, the first two can be said to be related by a causal relation (because I was thin, the trousers looked good on me) whereas the third clause is conjoined to the first two. Again, several possible continuations are given, some of them are acceptable, some of them are not. This time, the observation is that in the case where no causal relation can be established between the appropriate e-clauses (i.e. when those clauses corresponding to the cause and to the result of the cause are not adjacent), the continuation is unacceptable 3. That is, in the case where an identical relational pattern cannot be established 3This observation was originally made in \[Stainton-Ellis 1988\], page 75.</Paragraph> <Paragraph position="5"> for e- and a-clauses, multiple VPE becomes hard to understand, if not unacceptable.</Paragraph> <Paragraph position="6"> In what follows, I take these examples to suggest that the same discourse relation must hold between a- and e-clauses resepctively. I characterise this observation in terms of parallelism, make this notion precise and show how it interacts with other grammar components (e.g. syntax and semantic) to determine multiple VPE resolution. It should be stressed however that the approach can only be as precise as the definition of discourse relations and unfortunately, this notion is notoriously elusive. Nonetheless the hope is that this paper captures an important intuition about multiple VPE resolution namely, the intuition that parallelism constitutes one of the (many) factors affecting multiple VPE acceptability and interpretation.</Paragraph> </Section> <Section position="2" start_page="140" end_page="141" type="sub_section"> <SectionTitle> 3.2 Formal analysis </SectionTitle> <Paragraph position="0"> Assuming a discourse grammar of the type described in section (2), the claims this paper makes about multiple VPE resolution are (i) that whenever a discourse contains multiple VPEs, the clauses containing the VPEs and those containing the antecedent VPs form two complex discourse constituents which are related together by the relation of parallelism and (ii) that parallelism constrains VPE resolution in that each VPE will resolve to the &quot;parallel VP&quot; in the complex discourse constituents formed by the aclauses. We now make these claims precise. First, we define the semantic representation language PS used by the grammar described in section (2). PS: consists of the wffs described by the following syntax:</Paragraph> <Paragraph position="2"> The intuition is that PS is a quantifier free lan: guage where variables are unification variables and polarity (i.e. absence or presence of negation) is always explicit (that is, non-negated wffs are described as positive i.e. marked with 1). Thus for instance, the expression 0:and:\[0:p, 1:( d is a wff of /~, which one can think of as the more traditional propositional logic formula-~(-,pAq). We call PROP the set of wffs of the form polarity:predicate:\[argl ... argn\] 4. Given this language PS, the discourse relation of parallelism is said to hold between two propositions represented by the/: wffs * and * (written, parallelism((I), ql)) iff (I) is structurally identical with * . Structural identity is defined as follows: 4Note that contrary to tradition negated propositions are assumed to be atomic wffs.</Paragraph> <Paragraph position="3"> Definition 1 (Structural identity between L:</Paragraph> <Paragraph position="5"> That is, structural identity is identity up to propositional level (where negation is taken to be part of propositional information). To give two simple examples: null l:p=,0:q and 1: implies\[l: p, 0: q\] =, 1: implies\[l: r, 0: s\] To state the constraint regulating multiple VPE resolution, we first define the notion of a yield. Thus the yield of an PS wit C/ consists of the sequence of atomic propositions contained in C/. Finally, we state the constraint as follows: Definition 3 (Constraint on multiple VPE resolution) Let C/ be the semantic representation associated with the discourse segment formed by the a-clauses and el be that associated with the e-clauses. Then, if</Paragraph> <Paragraph position="7"> then for 1 < i < n, 0i = 79i and ssi = tti.</Paragraph> <Paragraph position="8"> That is, each elided predicate 0i and argument list tti 5 in 3;(el) resolves to the parallel predicate :Pi and argument list ssi in 31(q~). To see how this constraint works, consider example (1). Suppose that the discourse grammar assigns to the a- and the e- part of this discourse the following (simplified) semantic representations: A-clauses: 0:and:\[ 0:OM:\[i\], l:GtM:\[i\]\] E-clauses: l:and:\[ 0:rh:\[il, 0:R2:\[i\]\] ject NP and is thus ignored.</Paragraph> <Paragraph position="9"> Then definition 3 adequately predicts that R1 =OM and R2 = GtM. That is, the constraint embodied in definition 3 implements the fact that multiple VPE resolution is sensitive to the semantic- rather than to the surface-ordering of the antecedents.</Paragraph> </Section> <Section position="3" start_page="141" end_page="141" type="sub_section"> <SectionTitle> 3.3 Implementation </SectionTitle> <Paragraph position="0"> The above analysis can be implemented in the discourse grammar described in section (2) as follows.</Paragraph> <Paragraph position="1"> The parallelism rule will be:</Paragraph> <Paragraph position="3"> This rule has two effects. First, it requires that the semantic representations of the constituting discourse constituents be s-identical - this implements the restriction stated in defining parallelism. Second, it unifies the OUT value of the first discourse constituent with the IN value of the second - this ensures that the antecedents provided by the first (possibly complex) discourse constituent are accessible to any VPEs occuring in the second constituent. Now consider the rule for the connective unless (where UNLESS abbreviates the category associated with un- null the surface ordering). This reflects the fact that multiple VPE resolution is sensitive to the logical- rather than the surface-ordering of its antecedents. Application of the UNLESS rule to the a-clauses 6 (I wouldn't go to Manchester unless I open my mat 0 in example (1) will yield the category (recall that irrelevant attributes and attribute values are omitted): Similarly, the e-clauses (I didn't so I didn't) will be assigned the category:</Paragraph> <Paragraph position="5"> \[\[PI: As1\], \[P2:As2\]\] Finally, application of the parallelism rule to these two categories will yield:</Paragraph> <Paragraph position="7"> That is, the uninstantiated variables Pi, P2, ASl and Ass in \[~\] have been assigned a value by means of unification m such a way as to implement the restriction on multiple VPE resolution stated in definition 3, and with the result that the semantic representation of the overall discourse is the expected one.</Paragraph> </Section> </Section> <Section position="7" start_page="141" end_page="144" type="metho"> <SectionTitle> 4 Structural identity and semantic </SectionTitle> <Paragraph position="0"> equivalence The approach proposed above relies on the syntactic notion of structural identity. However it is a well-known fact that syntactically distinct logical formulae may be semantically equivalent. For instance, (7) p ---+ q ~ --,(p A &quot;-,q) _= --,p V q Now given these logical equivalences, it is unclear how the semantics of natural language discourse should be represented. Suppose for instance, that we have a discourse of the form If P, Q. Then there is a choice as to how this discourse should be represented, namely should it be represented as p --+ q, -~(p ^ -~q) or -~p V q (where p and q represent the semantic content of the discourses P and Q related by if) ? Traditionally, it is assumed that such a discourse will translate to what could be called the canonical form i.e p ~ q. However, the data on multiple ellipses (and the analysis proposed here) suggests that this should not always be the only possibility. As a case in point, consider example (8).</Paragraph> <Paragraph position="1"> (8) If he is \[t lucky\], he has \[2 ordered his software from a house that can help\]. If he hasn't 0~, he isn't 01 and may the gods be with him because he will need it.</Paragraph> <Paragraph position="2"> Suppose that both a- and e-clauses translate to the canonical form, we then have the following semantic</Paragraph> <Paragraph position="4"> Definition 3 will then yield the (correct) prediction: null</Paragraph> <Paragraph position="6"> So it seems that a given natural language connective should be allowed to be ambiguous between several semantically equivalent but syntactically distinct discourse relations (for instance, if could be assigned all translations given in (7) above). But if this is so, the question then arises as to how this ambiguity can be resolved. The claim I want to make is that both the resolution of this ambiguity and the resolution of multiple VP ellipses result from a complex interaction between syntax, semantics and pragmatics. The following section provides some evidence in support of this claim.</Paragraph> <Paragraph position="7"> The interaction of parallelism with other levels of linguistic information So far I have argued that multiple VPE resolution is subject to the discourse constraint that the propositions expressed by e- and a-clauses must be related by the discourse relation of parallelism. I have then&quot; shown that due to semantic equivalence, there might be several parallel configurations potentially holding between a- and e-clauses. However the actual data shows little ambiguity: in most cases, the hearer can single out the (unique) intended reading. In this section, I argue that the discourse constraint of parallelism interacts with other sources of linguistic information to determine this unique reading. In particular, I argue that syntax, semantics and pragmatics all contribute to solve the ambiguity raised by semantic equivalences between discourse relations.</Paragraph> <Paragraph position="8"> rTo improve readibility, I use here (and in the rest of this section) an informal notation to describe the semantics of discourse. ~i represent the semantics of VPEs where i indicates surface ordering.</Paragraph> <Section position="1" start_page="143" end_page="143" type="sub_section"> <SectionTitle> 5.1 Syntax </SectionTitle> <Paragraph position="0"> Consider again example (8) where the discourse formed by the e-clauses is of the form If P, Q and the associated semantic representation may be either p --* q or --q --* --p. Now look at the syntax of antecedent and elliptical VPs. The first elliptical VP is the perfective auxiliary has and thus subcategorises for a past participle whereas the second ellipsis consists of copula be and thus selects a predicative phrase. Correspondingly, the antecedent VPs are (1) a predicative phrase (lucky) and (2) a past participle (ordered his software from a house that can help). If we assume that VPE acceptability is sensitive to the syntactic information associated with the antecedent, then the above observations explain why the discourse relation holding between aand e-clauses must be --q --~ --p rather than p ---, q.</Paragraph> <Paragraph position="1"> For in the first case hasn't indeed resolves to a past participle (namely ordered his software from a house that can help) and isn't to a predicative phrase (i.e.</Paragraph> <Paragraph position="2"> lucky); whereas in the second case, the subcategorisation requirements of the auxiliaries are systematically violated. Thus if we assume that the (or at least some) syntactic properties of the antecedent VPs are relevant in determining VPE acceptability, then we can account for the fact that despite of the ambiguity introduced by semantic equivalences between discourse relations, there is only one reading for (8) i.e. the reading which is compatible both with the discourse requirement of parallelism between a- and e-clauses and with the syntactic constraints betweeen antecedent and elliptical VP. As already mentioned (cf. section 2), the present discourse grammar makes precisely this assumption since it takes anaphoric information to be sequences of VP categories i.e feature structures containing inter alia syntactic information about admissible antecedent VPs.</Paragraph> </Section> <Section position="2" start_page="143" end_page="143" type="sub_section"> <SectionTitle> 5.2 Semantics </SectionTitle> <Paragraph position="0"> \[Sag 1980\] argues that VPE is subject to a constraint on semantic representations, which is dubbed the alphabetical variant constraint. The analysis is convincing in that it accounts for a wide range of facts about VPE and its interaction with other linguistic phenomena such as quantification, extraction, pseudo-clefts, ready constructions and equisentences. For instance, the alphabetic variant constraint will account for the inacceptability of (9)8: (9) If every boy thinks that Mary is in love with him, the party will be a success. ~ If they don't, it won't.</Paragraph> <Paragraph position="1"> Note that in this case, discourse parallelism does hold between a- and e-clanses. So if discourse parallelism (as defined in this paper) was taken to be the only constraint regulating VPE acceptability, this 8To be compared with the well formed: If every boy brings a bottle, the party will be a success. If they don't, it won't.</Paragraph> <Paragraph position="2"> (ill formed) discourse could not be rejected by the grammar. However, if Sag's constraint is assumed then the ill-formedness of (9) can be accounted for as follows. Sag's constraint states that VPE is acceptable iff the semantic representation of the antecedent VP (which he assumes to be a lambda abstraction over individuals) is identical tip to renaming of bound variables with the semantic representation of the ellipsis and furthermore, all occurences of a free variable occuring both in the representation of the antecedent and of the ellipsis are bound by the same operator. Given this, the ill-formedness of (9) is explained by the fact that the pronoun him is represented by a variable (say, y) which is free in the semantic representation associated with the antecedent VP (i.e.)~z.think(z, love(m, y))) and cannot be bound by the same operator (i.e. the universal quantifier introduced by the subject NP every boy) when occuring in the semantic representation of the elliptical VP (because it occurs outside the scope of every).</Paragraph> <Paragraph position="3"> Here again, the assumption that the antecedent of a VPE is represented by a monostratal category means that Sag's alphabetic variant constraint can easily be integrated in the present account. This can be done in two ways. The first possibility consists in adopting Sag's view and adding a constraint in the category associated with VP ellipsis auxiliaries to the effect that the semantic representation of the antecedent VP and that of the ellided VP must be alphabetic variants of each other. This has the inconvenience of requiring a global check over the semantic representation of the whole discourse segment containing a- and e-clauses, a check which is essentially non compositional in nature 9. A second possibility is to adopt a dynamic semantics (i.e. a semantics where meaning is taken to be a relation between contexts and where a context contains information about pronoun denotations). Under such an assumption, it can be shown that the inacceptability of any discourse violating the alphabetic variant constraint comes out as a failure to interpret this discourse (model theoretic interpretation simply fails) so that the semantic representation of a- and e-clauses need not be checked upon. Such an approach is described in \[Gardent 1990\] and could easily be integrated in the present framework: it suffices to replace the static semantics whose syntax is described in 3, by the dynamic semantics given in \[Gardent 1990\].</Paragraph> </Section> <Section position="3" start_page="143" end_page="144" type="sub_section"> <SectionTitle> 5.3 Pragmatics </SectionTitle> <Paragraph position="0"> Just as syntax and semantics, pragmatics can interact with discourse constraints to determine multiple VPE acceptability. A particularly clear illustration of this interaction comes from the pragmatics of discourse connectives i.e. words such as but, unless, etc.</Paragraph> <Paragraph position="1"> Consider for instance the discourse in (10).</Paragraph> <Paragraph position="2"> (10) I gave her some questions to ask you if you rang her.</Paragraph> <Paragraph position="3"> a. I did but she didn't.</Paragraph> <Paragraph position="4"> b. , I did but she did.</Paragraph> <Paragraph position="5"> Although both continuations can be viewed as parallel to the a-clauses (cf. section 6), only continuation (a) is acceptable. Continuation (b) is inacceptable because the pragmatics of but (which requires some contrastive relation to hold between the propositions it relates) is violated.</Paragraph> <Paragraph position="6"> The discourse grammar sketched here does not integrate pragmatic information and thus cannot account for the difference in acceptability between (a) and (b). Whether it can be extended to do so remains an open question although recent work in pragmatics (such as \[Elhadad and McSeown 1990\]) suggests that the monostratal, unification based approach to discourse grammar is fully compatible with a comprehensive treatment of the semantics and pragmatics of discourse connectives.</Paragraph> </Section> </Section> <Section position="8" start_page="144" end_page="145" type="metho"> <SectionTitle> 6 Taking stock </SectionTitle> <Paragraph position="0"> While section (3) argues that multiple VPE resolution is subject to the discourse constraint of parallelism, section (5) shows that it is also sensitive to other linguistic components such as syntax and semantics. The present section (i) discusses how the resulting overall analysis accounts for the examples given so far, (ii) introduces some additional data and (iii) summarises how the various linguistic modules interact in determining VPE acceptability for the set of cases presented throughout the paper.</Paragraph> <Paragraph position="1"> We start by examining the examples given so far.</Paragraph> <Paragraph position="2"> Examples (2) and (ha) are simple cases of discourse parallelism where a- and e-clauses translate to the same canonical LF and no extraneous factor blocks resolution so that each VPE resolves to the parallel element in the antecedent discourse constituent. Example (3) is more intricate and can actually be explained in two different ways. A first possibility is to assume that I should have bought them and but I didn't form a discourse constituent and, I was really thin and ... the ski-pants looked really good on me and now I'm not and they wouldn't another (the intuition here would be that discourse constituents reflect the temporal structure of discourse, that is, temporally related events must be part of the same discourse constituent). Under this first hypothesis, we have on the one hand a case of (single) VP ellipsis where but I didn't resolves to I didn't buy them and on the other hand a simple case of parallelism between complex discourse constituents 1deg. The second possibility is to consider that the three a-clauses form a discourse constituent which is parallel with the discourse constituent formed by the three e-clauses. In 1degThanks to an anonymous referree for pointing out this poSSsible interpretation.</Paragraph> <Paragraph position="3"> this case, the semantic representations of a- and e-clauses can be symbolised as: A-clauses: (T ---* LG) A BT E-clauses: 01 A (02 ---* 03) This clearly does not obey parallelism. In this case, syntax imposes the choice of an equivalent LF (i.e. (02 --~ 03) A 01 ). As in (8), this syntactic constraint stems from the subcategorisation requirement of a VPE auxiliary, namely 'm not which requires a predicative phrase as antecedent.</Paragraph> <Paragraph position="4"> For completeness, consider now the following additional examples.</Paragraph> <Paragraph position="5"> (11) I gave her some questions to \[1 ask you\] if you \[2 rang her\]. I did 02 but she didn't 01.</Paragraph> <Paragraph position="6"> (12) It was preposterous. It \[1 couldn't possibly work\]. There \[2 must have been some other precautions\]. But there weren't 02 and it did 01.</Paragraph> <Paragraph position="7"> (13) Xenophobia pestis, like the hard native perennial it is, bourgeons as lordly young Mediterranean male cyclists sail into oncoming traffic with such signorial arrogance that even as we swear and skid, we look round wildly for street signs to see if he \[1 's right\], and we \[2 are wrong\] and the one-way system \[3 's undergone one of its periodic reversals\]. (He isn't 01. We aren't 02. It hasn't 0s.) (11) illustrates a case where parallelism constrains the choice of an alternative semantic representation with the result that the a-clauses semantics is represented by a wff of the form --(p A --q) rather than the canonical semantic translation for discourses of the form If P, Q i.e. p ---* q. Example (12) provides one more illustration of the interaction of syntax with discourse in determining multiple VPE resolution whereas example (13) illustrates a simple case of discourse parallelism.</Paragraph> <Paragraph position="8"> The following table summarises these observations. The first column (Ex.) indicates the number of the example being referred to together with a mention of the linguistic module, if any, which forced&quot; the choice of an equivalent semantic representation: D stands for Discourse and S for syntax. The second column (Canonical LF) indicates the &quot;canonical&quot; semantic representations (or Logical Forms) of a- and e-clauses: a-clauses are represented by capital letter abbreviations which are mnemonic for their propositional content, whereas the semantics of elliptical clauses is represented by 0i where i reflects surface ordering. Finally, the third column indicates an equivalent semantic representation for both e- or a-clauses (or none when this is superfluous). The intuition is that this column also indicates anaphoric dependencies whereby it indicates for each ellipsis which is the parallel element in the final semantic representation of the a-clauses. To take an example, consider the discourse in (1). For this discourse the table indicates that discourse forces the choice of a non-canonical semantic representation for the a-clauses. That is, the choice of the non-canonical semantic representation is determined in this case by the discourse requirement that a- and e-clauses stand in a parallelism relation. As a result, each ellipsis will resolve to its parallel element in the equivalent LF (rather than the canonical one) i.e. 01 resolves to OM (i.e. open a big stack of mai 0 and ~)2 to GtM (i.e. go to Manchester).</Paragraph> </Section> class="xml-element"></Paper>