On Plural Anaphora

Language, Information and Computation (PACLIC12), 18-20 Feb, 1998, 184-194 On Plural Anaphora Kiyoshi ISHIKAWA Hosei University ishikawagcogsci.L.chiba-u.ac.jp Abstract In order to formulate truth-conditionally - satisfactor* semantics in a composi- tional. manner, - model-iiieoretic semanticists sometimes posit morphology-semantics mismatches. Among them are Kamp and Reyle (1993), who occasionally ignore English plural morphology in constructing their analysis of anaphora. Our goal in this paper is to demonstrate that natural language morphology is a better guide for a compositional semantics than Kamp and Ryle assume. By refining the semantics of plurality put forth in Ishikawa (1995a), we construct an analysis of plural anaphora in a way that respects English plural morphology. Our results suggest that natural language morphology is not as redundant as usually assumed. 1 Introduction One of the research goals of modeltheoretic semantics is to derive the truth condition of (an utterance of) an arbitrary (declarative) sentence compositionally. Surface grammar (morphology and syntax) is sometimes felt not to get along well with compositional se- mantics, in which case the fine details of surface grammar are often ignored. For example, Kamp and Reyle (1993) treat plural anaphora by ignoring plural morphology of English nouns and verbs. Their treatment has the implication that English plural morphology has no semantic contribution to make and hence redundant (or even an obstacle for a compositional semantics). We have two purposes in this paper. The first is to revise Ishikawa's (1995a) semantics of plurality by modifying its lattice-theoretic structure of situation theoretic structured objects.' The second is to offer an alternative to Kamp and Reyle's treatment that respects English number morphology, by combining the revised version of Ishikawa's se- mantics of plurality with what we call the Resolution Principle. By doing the latter, we attempt to suggest that natural language surface grammar is, in fact, a better guide to compositional semantics than Kamp and Reyle assume.2 3 2 An Extended Lattice-theoretic Theory of Plurality 2.1 The Basics Following Link (1983), we assume lattice-theoretic ontology of individuals. Assuming Situation Semantics, we extend lattice-theoretic structure to situations and propositions in a way to be explained below. Just as one would analyze (la) as something like (1b) under the thesis of direct reference of names (Kaplan 1989), we analyze (la) as something like (1c), and (2a) as (2b).4 (1) a. John and Mary b. j e m 1See also Bach (1986) and Krifka (1989). Rea2For arguments that number agreement in English is not semantically redundant, see Hoeksema (1983), Reid (1991), Pollard and Sag (1994), Ishikawa (1995b). this paper we exclude generalized quantifiers from our consideration. An attempt to analyze plural generalized quantifiers in a similar spirit can be found in Ishikawa 11997), with which I'm not completely satisfied. 4For the assumption that even proper names exploit resource situation, see Ishikawa (1995c, 1996, To appear). See also Bach (1987). 184 Language; Information and Computation (PACLIC12), 18-20 Feb, 1998, 184-194 c. Xp where p=(r =<< member, x, X >> A < member, y, X >> A << John, x >> A << …

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