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<Paper uid="P95-1010">
  <Title>Features and Agreement</Title>
  <Section position="3" start_page="0" end_page="70" type="metho">
    <SectionTitle>
2 Features in Lambek Categorial
Grammar
</SectionTitle>
    <Paragraph position="0"> In LCG semantic interpretation and long distance dependencies are handled independently of the feature system, so agreement phenomena seem to be the major application of a feature system for LCG.</Paragraph>
    <Paragraph position="1"> Since only a finite number of feature distinctions need to be made in all the cases of agreement we know of, we posit only a very simple feature system here. Roughly speaking, features will be treated as atomic propositions (we have no need to separate them into attributes and values), and a simple category will be a Boolean combination of such atomic 'features' (since we have no reason to posit a recursive feature structures either). In fact we are agnostic as to whether more complex feature systems for LCG are linguistically justified; in any event Dorre et. al. (1994) show how a full attribute-value feature structure system having the properties described here can be incorporated into LCG.</Paragraph>
    <Paragraph position="2"> Following the standard formulation of LCG, we regard the standard LCG connectives '/' and 'V as directed implications, so we construct our system so that a//~ fl~ can combine to form a if fl' is logically stronger than/~.</Paragraph>
    <Paragraph position="3"> Formally, we adopt Morrill's treatment (Morrill, 1992) of the (semantically impotent) Boolean connectives '^' and 'v' (Morrill named these 'lq' and '11' respectively). Given a set of atomic features 5, we define the set of feature terms 7- and categories g as follows, where '/' and 'V are the standard LCG forward and backward implication operators.</Paragraph>
    <Paragraph position="5"> In general, atomic categories in a standard categorim grammar will be replaced in our analyses with formulae drawn from 7-. For example, the NP Kim might be assigned by the lexicon to the category np^sg^3, the verb sleeps to the category s\npnsg^3,  and the verb slept (which does not impose person or number features on its subject) to the category s\np.</Paragraph>
    <Paragraph position="6"> To simplify the presentation of the proofs, we formulate our system in natural deduction terms, and specify the properties of the Boolean connectives using the single inference rule P, rather than providing separate rules for each connective.</Paragraph>
    <Paragraph position="7"> ~P where I- in the calculus. 1 C/ C/ propositional The rule P allows us to replace any formula in T with a logically weaker one. For example, since Kim is assigned to the category np^sgA3, then by rule P it will belong to np as well.</Paragraph>
    <Paragraph position="8"> Finally, we assume the standard LCG introduction and elimination rules for the directed implication operators.</Paragraph>
    <Paragraph position="9">  For example, the following proof of the well-formedness of the sentence Kim slept can be derived using the rules just given and the lexical assignments described above.</Paragraph>
    <Paragraph position="10">  This example brings out one of the fundamental differences between the standard treatment of agreement in 'unification-based' grammar and this treatment of agreement in LCG. In the 'unification-based' accounts agreement is generally a symmetric relationship between the agreeing constituents: both agreeing constituents impose constraints on a shared agreement value, and the construction is well-formed iff these constraints are consistent.</Paragraph>
    <Paragraph position="11"> However, in the LCG treatment of agreement proposed here agreement is inherently asymmetric, in 1Because conjunction and disjunction are the only connectives we permit, it does not matter whether we use the classical or intuitionistic propositional calculus here. In fact, if categories such as np and ap are 'decomposed' into the conjunctions of atomic features +nounA--verb and q-noun^+verb respectively as in the Sag et. at. (1985) analysis discussed below, disjunction is not required in any of the LCG analyses below. However, Bayer (1994) argues that such a decomposition is not always plausible.</Paragraph>
    <Paragraph position="12"> that an argument must logically imply, or be subsumed by, the antecedent of the predicate it combines with. Thus in the example above, the rule P could be used to 'weaken' the argument from npAsgA3 to rip, but it would not allow np (without agreement features) to be 'strengthened' to, say, npA SgA 3.</Paragraph>
    <Paragraph position="13"> Abstracting from the details of the feature systems, we can characterize the 'unification-based' approach as one in which agreement is possible between two constituents with feature specifications C/ and C/ iff C/ and C/ are consistent, whereas the LCG approach requires that the argument C/ implies the corresponding antecedent C/ of the predicate (i.e., Interestingly, in cases where features are fully specified, these subsumption and consistency requirements are equivalent. More precisely, say that a formula C/ from a feature constraint language fixes an atomic feature constraint X iff C/ ~ X or C/ -~X- For example, in single-valued feature systems (person) = 1 and (person) = 3 both fix (person) = 1, (person) = 2, (person) = 3, etc., and in general all fully-specified agreement constraints fix the same set of formulae.</Paragraph>
    <Paragraph position="14"> Now let C/ and C/ be two satisfiable formulae that fix the same set of atomic feature constraints. Then A C/ is consistent iff C/ ~ C/. To see this, note that because C/ and C/ fix the same set of formulae, each condition holds iff C/ and C/ are elementarily equivalent (i.e., for each feature constraint X, C/ ~ X iff C/ ~ X)-However, the role of partial agreement feature specifications in the two systems is very different. The following sections explore the empirical consequences of these two approaches. We focus on co-ordination phenomena because this is the one area of the grammar where underspecified agreement features seem to play a crucial linguistic role, and cannot be regarded merely as an abbreviatory device for a disjunction of fully-specified agreement values.</Paragraph>
  </Section>
  <Section position="4" start_page="70" end_page="72" type="metho">
    <SectionTitle>
3 Coordination and agreement
</SectionTitle>
    <Paragraph position="0"> asymmetries Interestingly, the analysis of coordination is the one place where most 'unification-based' accounts abandon the symmetric consistency-based treatment of agreement and adopt an asymmetric subsumption-based account. Working in the GPSG framework Sag et. al. (1985) proposed that the features on a conjunction must be the most specific category which subsumes each conjunct (called the generalization by Shieber (1992)). Shieber (1986) proposed a weaker condition, namely that the features on the conjunction must subsume the features on each conjunct, as expressed in the annotated phrase struc- null VP bec~rae wealthy and a Republican wealthy a Republican and np ap P became npvap eonj npvap vp/npvap npvap vp  sis of (2b).</Paragraph>
    <Paragraph position="1"> ture rule below (Shieber, 1992).2 In all of the exampies we discuss below, the features associated with a conjunction is the generalization of the features associated with each of its conjuncts, so our conclusions are equally valid for both the generalization and subsumption accounts of coordination.</Paragraph>
    <Paragraph position="3"> Consider the sentences in (2). Decomposing the categories N(oun) and A(djective) into the Boolean-valued features {(noun) = +,(verb) = -} and {(noun) = +, (verb) = +} respectively, the fact that became can select for either an NP or an AP complement (2a) can be captured by analysing it as subcategorizing for a complement whose category is underspecified; i.e., its complement satisfies (noun) = +, and no constraint is imposed on the verb feature.</Paragraph>
    <Paragraph position="4"> (2) a. Kim \[v became \] \[hv wealthy \] / \[NP a Republican \] b. Kim \[vP \[v became \] lAP wealthy \] and \[NP a Republican \] \] Now consider the coordination in (2b). Assuming that became selects the underspecified category (noun) = +, the features associated with the coordination subsume the features associated with each coordinate, as required by rule (1), so (2b) has the well-formed structure shown in Figure 1.</Paragraph>
    <Paragraph position="5"> On the other hand, a verb such as grew which selects solely AP complements (3a) requires that its complement satisfies (noun) = +, (verb) = +.</Paragraph>
    <Paragraph position="6"> Thus the features on the coordinate structure in (3b) must include (verb) = + and so do not subsume the  (verb) = - feature on the NP complement, correctly predicting the ungrammatieality of (3b).</Paragraph>
    <Paragraph position="7"> (3) a. Kim grew lAP wealthy\]/*\[Np a Republican\] 2Note that the LFG account of coordination provided by Kaplan and Maxwell (1988) differs significantly from both the generalization and the subsumption accounts of coordination just mentioned, and does not generate the incorrect predictions described below.</Paragraph>
    <Paragraph position="8"> wealthy a Republican ap and np .p p  Our LCG account analyses these constructions in a similar way. Because the LCG account of agreement has subsumption 'built in', the coordination rule merely requires identity of the conjunction and each of the conjuncts.</Paragraph>
    <Paragraph position="9">  in any conjunct. 3 We provide an LCG derivation of (2b) in Figure 2. Roughly speaking, rule P allows both the AP wealthy and the NP a Republican to 'weaken' to npvap, so the conjunction satisfies the antecedent of the predicate became. (This weakening also takes place in non-coordination examples such as Kim became wealthy). On the other hand, (3b) is correctly predicted to be ill-formed because the strongest possible category for the coordination is npvap, but this does not imply the 'stronger' ap antecedent of grew, so the derivation in Figure 3 cannot proceed to form a vp.</Paragraph>
    <Paragraph position="10"> Thus on these examples, the feature-based subsumption account and the LCG of complement co-ordination constructions impose similiar feature constraints; they both require that the predicate's feature specification of the complement subsumes the features of each of the arguments. In the feature-based account, this is because the features associ- null associated with each conjunct, while in the LCG account the features associated with the complement specification in a predicate must subsume those associated with the complement itself.</Paragraph>
    <Paragraph position="11"> Now consider the related construction in (4) involving conjoined predicates as well conjoined arguments. Similar constructions, and their relevance to the GPSG treatment of coordination, were first discussed by Jacobson (1987). In such cases, the feature-based subsumption account requires that the features associated with the predicate conjunction subsume those associated with each predicate conjunct. This is possible, as shown in Figure 4. Thus the feature structure subsumption account incorrectly predicts the well-formedness of (4).</Paragraph>
    <Paragraph position="12"> (4) *Kim \[ grew and remained \] \[ wealthy and a Republican \].</Paragraph>
    <Paragraph position="13"> Because the subsumption constraint in the LCG analysis is associated with the predicate-argument relationship (rather than the coordination construction, as in the feature-based subsumption account), an LCG analysis paralleling the one given in Figure 4 does not exist. By introducing and withdrawing a hypothetical ap constituent as shown in Figure 5 it is possible to conjoin grew and remained, but the resulting conjunction belongs to the category vp/ap, and cannot combine with the wealthy and a Republican, which belongs to the category npvap.</Paragraph>
    <Paragraph position="14"> Informally, while rule P allows the features associated with an argument to be weakened, together with the introduction and elimination rules it permits the argument specifications of predicates to be strengthened (e.f. the subproof showing that remained belongs to category vp/ap in Figure 5). As we remarked earlier, in LCG predicates are analysed as (directed) implicational formulae, and the argument features required by a predicate appear in the antecedent of such formulae. Since strengthening the antecedent of an implication weakens the implication as a whole, the combined effect of rule P and the introduction and elimination rules is to permit the overall weakening of a category.</Paragraph>
  </Section>
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