<?xml version="1.0" standalone="yes"?>
<Paper uid="E95-1032">
  <Title>Ellipsis and Quantification: A Substitutional Approach</Title>
  <Section position="4" start_page="229" end_page="233" type="metho">
    <SectionTitle>
2 Ellipsis Substitutions
</SectionTitle>
    <Paragraph position="0"> This section illustrates the substitutional treatment of ellipsis through a small number of examples. For presentation purposes we only sketch the intended semantics of the simplified QLF notation used, and a more detailed discussion is deferred until section 3.</Paragraph>
    <Section position="1" start_page="229" end_page="230" type="sub_section">
      <SectionTitle>
2.1 Simple VP E1Hpsis
</SectionTitle>
      <Paragraph position="0"> A simple, uninteresting example to fix some notation: null (2) John slept. So did Mary We represent the first sentence, ignoring tense, as a  (resolved) QLF (3) \[+j\]: sleep( term(+j, ~, )ly.name(y, 'John'),</Paragraph>
      <Paragraph position="2"> The noun phrase John gives rise to an existentially quantified term, uniquely identified by the index -I-j. The texan expression has four arguments: an index, a determiner/quantifier, an explicit restriction, and an additional contextually derived restriction. In this case, the quantifier ranges over objects that are named 'John' and are further restricted to be identical to some (contextually salient) individual, denoted by j.smith. Prior to reference resolution, the contextual restriction on the term would be an uninstantiated meta~variable; resolution consists of instantiating mete-variables to contextually 1This is similar to' Nerbonne's (1991) constraint-based semantics, except that he builds descriptions of logical forms, not semantic compositions.</Paragraph>
      <Paragraph position="3"> appropriate values. The scope of the term is indicated by the scope node I-l-j\] : prefixing the formula sleep(term(+j,...)). Again, prior to resolution this scope node would be an uniustantiated mete-variable.</Paragraph>
      <Paragraph position="4"> A generalized quantifier representation equivalent to the above is</Paragraph>
      <Paragraph position="6"> The index in the scope node means that to semantically evaluate the QLF, you get hold of the quantitier, restriction and contextual restriction of the corresponding term. This forms a (generalized) quantifier expression, whose body is obtained by discharging all occurrences of the term and it index to a variable, and abstracting over the variable. Terms and indices not dischargeable in this manner lead to uninterpretable QLFs (Alshawi and Crouch, 1992).</Paragraph>
      <Paragraph position="7"> We represent the elliptical sentence, again abbreviated, as a (partially resolved) QLF:</Paragraph>
      <Paragraph position="9"> ?P is an unresolved mete-variable. To resolve the ellipsis, it needs to be instantiated to some contextually salient predicate.</Paragraph>
      <Paragraph position="10"> Along similar lines to DSP, we can set up an equation to determine possible values for ?p2:</Paragraph>
      <Paragraph position="12"> That is, we are looking for a predicate that when applied to the subject term of the ellipsis antecedent returns the antecedent. The interpretation of the ellipsis is then given by applying this predicate to the subject of the ellipsis.</Paragraph>
      <Paragraph position="13"> The equation (6) is solved by setting ?P to something that takes a term T as an argument and substitutes T for tema(+j,...) and the index of T for +j throughout the ellipsis antecedent (the RHS of (6)):</Paragraph>
      <Paragraph position="15"> Here T^(...) is a form of abstraction; for now it will do no harm view it as a form of ~abstraction, though this is not strictly accurate.</Paragraph>
      <Paragraph position="16"> The substitutions are represented using the notation I {oldlnew,...}. Applying this value for ?P in the ellipsis (5), we</Paragraph>
      <Paragraph position="18"> Ellipsis resolution thus amounts to selecting an antecedent and determining a set of substitutions to apply to it. For reasons that will be explained shortly, it is important that resolution does not actually carry out the application of the substitutions.</Paragraph>
      <Paragraph position="19"> 2Terms shown abbreviated, i.e. tex~(Tj .... ) instead of tern(Wj, 3, ~y.name(y,'John'), ~y.y = j_maith).</Paragraph>
      <Paragraph position="20">  However, were we to do this in this particular case, where the antecedent (3) is fully resolved, we would successfully capture the intended interpretation of the ellipsis, namely:</Paragraph>
      <Paragraph position="22"> Note that the substitutions are not applied in the conventional order; viz. first replace +j by +m throughout (3) and then replace term(+j .... ) by term(+m,...). The first substitution would ensure that there was no term(+j,...) for the second substitution to replace. The order in which substitutions apply instead depends on the order in which the expressions occur when making a top down pass through (3), such as one would do when applying semantic evaluation rules to the formula.</Paragraph>
      <Paragraph position="23"> Note also that the term index substitution applies to the scope node, so that \[+j\]: is replaced by \[+in\]:. This ensures that the term for Mary in the ellipsis gets a parallel scope to the term for John in the antecedent. Scope parallelism may not be significant where proper names are concerned, but is important when it comes to more obviously quantificational terms (section 2.3).</Paragraph>
    </Section>
    <Section position="2" start_page="230" end_page="230" type="sub_section">
      <SectionTitle>
2.2 Evaluative Substitutions
</SectionTitle>
      <Paragraph position="0"> The meaning of an ellipsis is composed in essentially the same way, and from the same components, as the meaning of its antecedent. However, some changes need to be made in order to accommodate new material introduced by the ellipsis. The substitutions specify what these changes are. In the example discussed above, the meaning of the ellipsis is built up in the same way as for the antecedent, except that whenever you encounter a term corresponding to 'John' or something dependent/co-indexed with it, you it is treated as though it were the term for 'Mary' or dependent/co-indexed with it.</Paragraph>
      <Paragraph position="1"> This means that the substitutions act as directives controlling the way in which QLF expressions within their scope are evaluated. They are not syntactic operations on QLF expressions -- they are part of the QLF object language.</Paragraph>
      <Paragraph position="2"> The reason that substitutions are not 'applied' immediately upon ellipsis resolution is as follows. At the time of deciding on the ellipsis substitutions, the precise composition of the antecedent may not yet have been determined. (For instance the scopes of quantifiers or the contextual restrictions on pronouns in the antecedent may not have been resolved; this will correspond to the presence of uninstantiated meta-variables in the antecedent QLF.) The ellipsis should follow, modulo the substitutions, the same composition as the antecedent, whatever that composition is eventually determined to be. It makes no sense to apply the substitutions before the antecedent is fully resolved, though it does make sense to decide what the appropriate substitutions should be.</Paragraph>
      <Paragraph position="3"> In practical terms what this amounts to is exploiting re-entraney in QLFs. The elliptical QLF will contain a predicate formed from the antecedent QLF plus substitutions. Any uninstantiated recta-variables in the antecedent are thus re-entrant in the ellipsis. Consequently, any further resolutions to the antecedent are automatically imposed on the ellipsis.</Paragraph>
      <Paragraph position="4"> This would not be the ease if the substitutions were treated as syntactic operations on QLF to be applied immediately: some re-entrant meta-variables would be substituted out of the ellipsis, and those remaining would not be subject to the substitutions (which would have already been applied) when they were eventually instantiated.</Paragraph>
    </Section>
    <Section position="3" start_page="230" end_page="231" type="sub_section">
      <SectionTitle>
2.3 Scope Parallelism
</SectionTitle>
      <Paragraph position="0"> It was noted above that substitutions on term indices in scope nodes ensures scope parallelism. This is now illustrated with a more interesting example (adapted from Hirshbfihler as cited by DSP).</Paragraph>
      <Paragraph position="1"> (10) A Canadian flag hung in front of every house, and an American flag did too.</Paragraph>
      <Paragraph position="2"> The antecedent has two possible seopings: a single Canadian flag in front of all the houses, or each house with its own flag. Whichever seeping is given to the antecedent, a parallel seeping should be given to the ellipsis.</Paragraph>
      <Paragraph position="3"> A simplified QLF for (10) is  (11) ?SI: and(?S2: hang(term(+c, B,...), ter~(+h,V,...)), 3, ...)))  where the indices +c, +a and +h are mnemonic for Canadian flag, American flag and house. Taking the first conjunct as the antecedent, we can set up an</Paragraph>
      <Paragraph position="5"> the solution to which iss</Paragraph>
      <Paragraph position="7"> This make the elliptical conjunct equivalent to</Paragraph>
      <Paragraph position="9"> The scope node, ?S2 can be resolved to \[+h, +el ('every house' takes wide scope), or \[+e,+h\] ('a Canadian flag' takes wide scope). Whichever resolution is made, the substitution of +a for +e ensures parallel scoping in the ellipsis for 'an American flag'.</Paragraph>
      <Paragraph position="10"> Cashing out the substitutions for the first case, we  (15) D:and(\[+h, +c\]:hang(tera(+c, 3,...), term(+h,V,...)), \[+h, +a\]:hang(t erm(+a, 3,...), term(-bh,V,...))) There is another scoping option which instantiates ?$1 to \[q-h\], i.e. gives 'every house' wide scope over both antecedent and ellipsis. In this case the two terms, term(+h...) in ellipsis and antecedent are both discharged (i.e. bound) at the scope node ?$1, rather than being separately bound at the two copies of ?$2 (16) \[+h\]:and(\[+c\]:hang(term(+c, 3,...), term(+h,V,..</Paragraph>
      <Paragraph position="11"> \[-ka\]:hang(t erm(-ka, 3,.. :/!' (This has equivalent truth-conditions to (15)). 4 Besides illustrating scope parallelism, this is an example where DSP have to resort to higher-order unification beyond second-order matching. But no such increase in complexity is required under the present treatment.</Paragraph>
    </Section>
    <Section position="4" start_page="231" end_page="232" type="sub_section">
      <SectionTitle>
2.4 Strict and Sloppy Identity
</SectionTitle>
      <Paragraph position="0"> The notion of strict and sloppy identity is usually confined to pronominal items occurring in antecedents and (implicitly) in ellipses. 5 A standard example is (17) John loves his mother, and Simon does too. On the strict reading, Simon and John both love John's mother. The implicit pronoun has been strictly identified with the pronoun in the antecedent to pick out the same referent, John. On the sloppy reading Simon loves Simon's mother. The implicit pronoun has been sloppily identified with its antecedent to refer to something matching a similar description, i.e. the subject or agent of the loving relation, Simon.</Paragraph>
      <Paragraph position="1"> The sentence (18) John read abook he owned, and so did Simon. has three readings: John and Simon read the same book; John and Simon both read a book belonging to John, though not necessarily the same one; John reads one of John's books and Simon reads one of Simon's books.</Paragraph>
      <Paragraph position="2"> Intuitively, the first reading arises from strictly identifying the elliptical book with the antecedentbook. The second arises from strictly identifying the pronouns, while sloppily identifying the books.  lipsis, the QLF is rendered uninterpretable, which is as required. As detailed in section 3, scoping +c discharges the term and its index by substituting a variable for it. But the ellipsis substitution overrides this, substituting a new term and index, -Fa. But there is no way of discharging them.</Paragraph>
      <Paragraph position="3"> s Also to pronouns of laziness.</Paragraph>
      <Paragraph position="4"> The third from sloppily identifying both the books and the pronouns. In the literature, the first reading would not be viewed as a case of strict identity. But this view emerges naturally from our treatment of substitutions, and is arguably a more natural characterisation of the phenomena.</Paragraph>
      <Paragraph position="5"> We need to distinguish between parallel and non-parallel terms in ellipsis antecedents. Parallel terms, like John in the example above, are those that correspond terms appearing explicitly in the ellipsis. Non-paraUel terms are those that do not have an explicit parallel in the ellipsis. (Determining which terms are parallel/non-parallel is touched on in section 4.) For parallel terms, we have no choice about the ellipsis substitution. We replace both the term and its index by the corresponding term and index from the ellipsis. But for all non-parallel terms we have a choice between a strict or a sloppy substitution, s A sloppy substitution involves substituting a new term index for the old one. This has the effect of reindexing the version of the term occurring in the ellipsis, so that it refers to the same kind of thing as the antecedent term but is not otherwise linked to it.</Paragraph>
      <Paragraph position="6"> A strict substitution substitutes the term by its index. In this way, the version of the term occurring in the ellipsis is directly linked to antecedent term. To illustrate, an abbreviated QLF for the antecedent John read a book he owned is</Paragraph>
      <Paragraph position="8"> Here, we have left the scope node as an uninstantinted meta-variable ?S. The pronominal term +h occurs in the restriction of the book term +b. The pronoun has been resolved to have a contextual restriction, rft(+j), that co-indexes it with the subject term. Here, 'fit(.)' is a function that when applied to an entity-denoting expression (e.g. a variable or constant) returns the property of being identical to that entity; when it applies to a term index, it returns an E-type property contextually linked to the term.</Paragraph>
      <Paragraph position="9"> The ellipsis can be represented as (20) ?P(term(+s, 3, Ay.name(y,'Simon'),...)) which is conjoined with the antecedent.</Paragraph>
      <Paragraph position="10"> The three readings of (18) are illustrated below, listing substitutions to be applied to the antecedent SThis is true of the non-paraliel tera(-Fh .... ) in example (11); but this added complication does not affect the basic account of scope parallelism given earlier.</Paragraph>
      <Paragraph position="11">  and cashing out the results of their application, though omitting scope.</Paragraph>
      <Paragraph position="12">  the strict substitution on the term in which it occurs, it makes no difference whether the pronoun is given a strict or a sloppy substitution. (b) Strict substitution for the book leaves behind an occurrence of the index +b in the ellipsis. For the QLF to be interpretable, it is necessary to give the antecedent book term wide scope over the ellipsis in order to discharge the index.</Paragraph>
      <Paragraph position="13">  (22) Sloppy book, strict pronoun</Paragraph>
      <Paragraph position="15"> As above, the antecedent pronoun is constrained to be given wide scope over the ellipsis, on pain of the index +h being undischargeable. (Pronouns, like proper names, are treated as contextually restricted quantifiers, where the contextual restriction may limit the domain of quantification to one indi-</Paragraph>
      <Paragraph position="17"> The index substitution from the primary term reindexes the contextual restriction of the pronoun. It becomes coindexed with +s instead of +j.</Paragraph>
      <Paragraph position="18"> DSP's account of the first reading of (18) is significantly different from their account of the last two readings. The first reading involves scoping the book quantifier before ellipsis resolution. The other two readings only scope the quantifier after resolution, and differ in giving the pronoun a strict or a sloppy interpretation. In our account the choice of strict or sloppy substitutions for secondary terms can constrain permissible quantifier scopings. 7 But the making of these choices does not have to be interleaved in a precise order with the scoping of quantifiers. null Moreover, the difference between strict and sloppy readings does not depend on somehow being able to distinguish between primary and secondary occurrences of terms with the same meaning. In DSP's representation of the antecedent of (18), both NPs 'John' and 'he' give rise to two occurrences of the same term (a constant, j). The QLF representation is able to distinguish between the primary and the secondary, pronominal, reference to John.</Paragraph>
    </Section>
    <Section position="5" start_page="232" end_page="233" type="sub_section">
      <SectionTitle>
2.5 Other Phenomena
</SectionTitle>
      <Paragraph position="0"> Space precludes illustrating the substitutional approach through further examples, though more are discussed in (Alshawi et al., 1992; Cooper et al., 1994b). The coverage is basically the same as DSP's: Antecedent Contained Deletion: A sloppy substitution for every person that Simon did in the sentence John greeted every person that Simon did results in re-introducing the ellipsis in its own resolution. This leads to an uninterpretable cyclic QLF in much the same way that DSP obtain a violation of the occurs check on sound unification.</Paragraph>
      <Paragraph position="1"> Cascaded Ellipsis: The number of readings obtained for John revised his paper before the teacher did, and then Simon did was used as n benchmark by DSP. The approach here gets the four readings identified by them as most plausible. With slight modification, it gets a fifth reading of marginal plausibility. The modification is to allow (strict) substitutions on terms not explicitly appearing in the ellipsis antecedent -- i.e. the implicit his paper in the second ellipsis when resolving the third ellipsis.</Paragraph>
      <Paragraph position="2"> We do not get a sixth, implausible reading, provided that in the first clause his is resolved as being coindexed with the term for John; i.e. that John and his do not both independently refer to the same individual. Kehler blocks this reading in a similar manner. DSP block the reading by n more artificial restriction on the depth of embedding of expressions in logical forms; they lack the means for distinguishing between coindexed and merely co-referential expressions. null Multiple VP Ellipsis Multiple VP ellipsis (Gardent, 1993) poses problems at the level of determining which VP is the antecedent of which ellipsis. But at the level of incorporating elliptical material once TThe converse also holds. Giving aa antecedent term wide scope over the ellipsis renders the choice of a strict or &amp; sloppy substitution for it in the ellipsis immaterial. During semantic evaluation of the QLF, dischaxgo ing the antecedent through scoping will substitute out all occurrence of the term Lad its index before ellipsis substitutions are applied. Note though that this order dependence applies at the level of evaluating QLFs, not constructing and resolving them.</Paragraph>
      <Paragraph position="3">  the antecedents have been determined, it appears to offer no special problems.</Paragraph>
      <Paragraph position="4"> Other Forms of Ellipsis: Other forms of eb lipsis, besides VP-ellipsis can be handled substitutionally. For example, NP-ellipsis (e.g. Who slept? John.) is straightforwardly accommodated. PPellipsis (e.g. Who left on Tnesdayf And on Wednesday?) requires substitutions for form constructions in QLF (not described here) representing prepositional phrases.</Paragraph>
    </Section>
    <Section position="6" start_page="233" end_page="233" type="sub_section">
      <SectionTitle>
2.6 Comparisons
</SectionTitle>
      <Paragraph position="0"> The use of terms and indices has parallels to proposals due to Kehler and Kamp (Kehler, 1993a; Gawron and Peters, 1990). Kehler adopts an analysis where (referential) arguments to verbs are represented as related to a Davidsonian event via thematic role functions, e.g. agent(e)--john). Pronouns typically refer to these functions, e.g. he-agent(e). In VP ellipsis, strict identity corresponds to copying the entire role assignment from the antecedent. Sloppy identity corresponds to copying the function, but applying it to the event of the ellided clause.</Paragraph>
      <Paragraph position="1"> For Kamp, strict identity involves copying the discourse referent of the antecedent and identifying it with that of the ellided pronoun. Sloppy identity copies the conditions on the antecedent discourse referent, and applies them to the discourse referent of the ellided pronoun.</Paragraph>
      <Paragraph position="2"> Neither Kamp nor Kehler extend their copying/substitution mechanism to anything besides pronouns, as we have done. In Kehler's case, it is hard to see how his role assignment functions can be extended to deal with non-referential terms in the desired manner. DRT's use of discourse referents to indicate scope suggests that Kamp's treatment may be more readily extended in this manner; lists of discourse referents at the top of DRS boxes are highly reminiscent of the index lists in scope nodes.</Paragraph>
    </Section>
  </Section>
  <Section position="5" start_page="233" end_page="234" type="metho">
    <SectionTitle>
3 Semantic Evaluation
</SectionTitle>
    <Paragraph position="0"> Figure 1 defines a valuation relation for the QLF fragment used above, derived from (Alshawi and Crouch, 1992; Cooper et al., 1994a). If a QLF expression contains uninstantiated recta-variables, the valuation relation can associate more than one value with the expression. In the case of formulas, they may be given both the values true and false, corresponding to the formula being true under one possible resolution and false under another. A subsumption ordering over QLFS, ~, is employed in the evaluation rules, in effect to propose possible instantiations for meta-variables (the rule fragment only allows for scope meta-variables, but (Cooper et al., 1994a) describes the more general case where other kinds of meSa-variable are permitted). A partially instantiated QLF therefore effectively specifies a set of possible evaluations (or semantic compositions).</Paragraph>
    <Paragraph position="1"> Definition of \])(QLF, M, g, Subs, v) where QLF is a QLF expression M is a model, (O, F) g is an assignment of values to variables Subs is a set of substitutions v is a value assigned to the QLF expression  1. Constant symbols, c: V( c, M, g, Subs, v) iff F(c) = v (where F is the interpretation function for non-logical constants provided by M) 2. Variables, z: V(z, M, g, Subs, v) iff g(z) = v 3. Reinterpretation: )2(QLF,, M, g, Subs, v) iff V(QLF~, M, g, Subs, v) where QLF1/ QLF 2 E Subs 4. Merging reiaterpretations: V( QL~Subsl, M, g, Subs~, v) if V( QLF, M, g, Subs1 ~ Subs~, v) 5. Abstraction: V()~z.~b, M, g, Subs, h) if ~b _~ ~b' and h is such that Y(~*, M, g~k, Subs, v) iff h(k, .) 6. Application:  V(p(,,, ..... ,,.), M, g, Subs, P(A1 ..... A.)) if p(~, ..... ,,.) _~ p'(,d ..... ,.% i)(p', M, g, Subs, P), V(a'~, M, g, Subs, At), ..., and V(a'n, M, g, Subs, A,) 7. a-Application: r(X^~b (T), M, g, Subs, v) if ~}(~b I {X/T}, M, g, Subs, v) 8. Scoped formula: V( Scope:~, M, g, Subs, v) if &amp;quot;IJ( Q'( R', ~'), M, g, Subs, v)  where a)~ is a formula containing the term, To,</Paragraph>
    <Paragraph position="3"> As the QLF becomes more instantiated, the set of possible evaluations narrows towards a singleton.</Paragraph>
    <Paragraph position="4"> It is also possible for a QLF to be uninterpretable; to specify no possible evaluation. Thus, no rules are given for evaluating terms or their indices in isolation. They must first be discharged by the scoping rule, which substitutes the terms and indices by A-bound variables. Inappropriate scoping may leave undischarged and hence uninterpretable terms and indices (which accounts for the so-called free-variable and vacuous quantification constraints on scope (Alshawi and Crouch, 1992)). The substitutions employed by the evaluation rule for scoping achieve a similar effect to the introduction and discharging of quantifier assumptions in Pereira's (1990) categorial semantics.</Paragraph>
    <Paragraph position="5"> The non-deterministic nature of evaluation and the role of substitutions draws us to conclude that ellipsis substitutions operate on (descriptions of) the semantic compositions, not the results of such compositions. null</Paragraph>
  </Section>
  <Section position="6" start_page="234" end_page="234" type="metho">
    <SectionTitle>
4 Parallelism and Inference
</SectionTitle>
    <Paragraph position="0"> Selecting ellipsis antecedents and parallel elements within them is an open problem (Priist, 1992; Prfist et al., 1994; Kehler, 1993b; Grover et al., 1994). Our approach to parallelism is perhaps heavy-handed, but in the absence of a clear solutions, possibly more flexible. The QLFs shown above omitted category information present in terms and ~orms. s Categories are sets of feature value equations containing syntactic information relevant to determining how uninstantiated meta-variables can be resolved.</Paragraph>
    <Paragraph position="1"> Tense in VP-ellipsis illustrates how categories can be put to work. In (24) I enjoyed it. And so will you the ellipsis is contained within a form expression whose category is vp_ellipsis It ense=inf ,modalffivill ,perf ectffi_, progressive=_,pol=pos .... \] This states the syntactic tense, aspect and polarity marked on the ellipsis (underscores indicate lack of specification). The category constrains resolution to look for verb phrase/sentence sources, which come wrapped in forms with categories like \[t ease=past, modalffino, pexf ectffino, progressive--no ,polffipos .... \] Heuristics simi\]ar to those described by Hardt (1992) may be used for this. The category also says that, for this kind of VP match 9, the term in the antecedent whose category identifies it as being the subject should be treated as parallel to the explicit term in the ellipsis.</Paragraph>
    <Paragraph position="2"> As this example illustrates, tense and aspect on ellipsis and antecedent do not have to agree. When Sforns axe described in (Alshawi and Crouch, 1992). 9Not all VP ellipses have VP antecedents.</Paragraph>
    <Paragraph position="3"> this is so, the antecedent and ellipsis categories are both used to determine what fozm should be substituted for the antecedent form. This comprises the restriction of the antecedent form and a new category constructed by taking the features of the antecedent category, unless overridden by those on the ellipsis--a kind of (monotonic) priority union (Grover et ai., 1994) except using skeptical as opposed to credulous default unification (Carpenter, 1993). When a new category is constructed for the antecedent, any tense resolutions also need to be undone, since the original ones may no longer be appropriate for the revised category. One thus merges the category information from source and antecedent to determine what verb phrase form should be substituted for the original. In this case, it will have a category vp \[tensefinf, modalfeill, perfectffino, progressive=no ,polfneg .... \] A more general question is whether all ellipses involve recompositions, with variants, of linguistic antecedents. There are cases where a degree of inference seems to be required: (25) We spent six weeks living in France, eating French food and speaking French, as we did in Austria the year before.</Paragraph>
    <Paragraph position="4"> (one must apply the knowledge that Austrians speak German to correctly interpret the ellipsis). Pulman's (1994) equational treatment of context-dependency suggests one method of dealing with such cases. But it remains to be seen how readily the equations used for ellipsis here can be integrated into Pulman's framework.</Paragraph>
  </Section>
  <Section position="7" start_page="234" end_page="235" type="metho">
    <SectionTitle>
5 Conclusions: Interpretation as
Description
</SectionTitle>
    <Paragraph position="0"> The substitutional treatment of ellipsis presented here has broadly the same coverage as DSP's higher-order unification treatment, but has the computational advantages of (i) not requiring order-sensitive interleaving of different resolution operations, and (ii) not requiring greater than second-order matching for dealing with quantifiers. In addition, it cures a slight overgeneration problem in DSP's account.</Paragraph>
    <Paragraph position="1"> It has been claimed that these advantages arise from viewing semantic interpretation as a process of building descriptions of semantic compositions.</Paragraph>
    <Paragraph position="2"> To conclude, a few further arguments for this view, that are independent of any particular proposals for dealing with ellipsis.</Paragraph>
    <Paragraph position="3"> Order-Independence: One of the reasons for the computational success of unification-based syntactic formalisms is the order-independence of parser/generator operations they permit. If one looks at the order-sensitive nature of the operations of semantic compositions, they provide a poor starting point for a treatment of semantics enjoying similar computational success. But semantic interpreta~  tion, viewed as building a description of the intended composition, is a better prospect.</Paragraph>
    <Paragraph position="4"> Context-Sensitivity: The truth values of many ~ ?) sentences undeniably depend on context.</Paragraph>
    <Paragraph position="5"> ntext-dependence may enter either at the interpretive mapping from sentence to meaning and/or the evaluative mapping from meaning (and the world) to truth-values.</Paragraph>
    <Paragraph position="6">  The more that context-dependence enters into the interpretive mapping (so that meanings are correspondingly more context-independent), the harder it is to maintain a principle of strict compositionality in interpretation. The syntactic structure underspecifies the intended composition, so that the meanings of some constituents (e.g. pronouns) and the mode of combination of other (e.g. quantifiers) are not fully specified. Further contextual information is required to fill the gaps. Again, interpretation seen as description building sits easily with this.</Paragraph>
    <Paragraph position="7"> Preserving Information: Focusing exclusively on the results of semantic composition, i.e. meanings, can ignore differences in how those meanings were derived that can be linguistically significant (e.g. co-referential vs co-indexed terms). If this information is not to be lost, some way of referring to the structure of the compositions, as well as to their results, seems to be required.</Paragraph>
  </Section>
class="xml-element"></Paper>