Contents 1 Introduction: grammatical reasoning 1 2 Linguistic inference: the Lambek systems 5 2.1 Modelinggrammaticalcomposition ............................ 5 2.2 Gentzen calculus, cut elimination and decidability . . . . . . . . . . . . . . . . . . . . 9 2.3 Discussion: options for resource management . . . . . . . . . . . . . . . . . . . . . . 13 3 The syntax-semantics interface: proofs and readings 16 3.1 Term assignment for categorial deductions . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2 Natural language interpretation: the deductive view . . . . . . . . . . . . . . . . . . . 21 4 Grammatical composition: multimodal systems 26 4.1 Mixedinference:themodesofcomposition........................ 26 4.2 Grammaticalcomposition:unaryoperations ....................... 30 4.2.1 Unary connectives: logic and structure . . . . . . . . . . . . . . . . . . . . . . . 31 4.2.2 Applications: imposing constraints, structural relaxation

This paper focuses on the semantics of interrogative sentences and has three main parts

this paper I treat conditionals using material implication, ignoring the well-known semantic/pragmatic problems concerning their correct interpretation. Of course, one may doubt whether (7a), which is verified by any situation in which there is one woman who did not come to the party, reflects correctly the wide scope reading of the indefinite in (7). Obviously, this problem is independent of the scope problem of indefinites. For this reason and because antecedents of conditionals are one of the simplest and most striking cases of scope islands, I use such examples freely, counting on the reader to substitute her favorite theory of conditionals for material implication. This claim has been challenged in Farkas (1981), Rooth & Partee (1982:fn.6) and, more recently, in Ruys (1992) and Abusch (1994). These works all show cases where Fodor & Sag's claim is argued to be incorrect. The empirical debate will be reviewed later in this paper (subsection 3.4.2). Ruys and Abusch both conclude that Fodor & Sag's "referential" approach is inadequate. To handle the facts, Ruys proposes an indexing mechanism of indefinites within a DRT-like interpretation of LF. Abusch proposes to enrich DRT with a storage mechanism that changes the syntactic position of the N' predicate (= the restriction of the indefinite) at the representational level. Both Ruys and Abusch therefore accept the assumption of DRT about a distinct syntactic representational level for meaning. This level (sometimes called Logical Form') is additional to the syntactic level that undergoes semantic interpretation (GB's Logical Form, other theories' Surface Structure). Indefinites in Ruys and Abusch's treatments are not quantifiers. Instead, they involve the familiar treatment of DRT using free variables. I henceforth c...

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ver sets of atoms. We can describe these features using the notation Q and S. Flexibility operators shift meanings between the four kinds of denotations that these two features describe. The boolean theory of coordination The basic fact about coordination in many languages is its cross-categorial behaviour: morphemes like and and or can appear in coordinate structures of many dierent categories, as (partly) illustrated by the following simple sentences. (1) Mary sang and/or Sue danced. (2) Mary and/or Sue sang. (3) Mary sang and/or danced. Early versions of Transformational Grammar assumed that this property of coordination could be explained by assuming that at deep structure coordinators are sentential only, like the connectives of rst order logic. A Conjunction 1 Reduction transformation was assumed to relate phrasal coordinations

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One elegant and linguistically powerful guideline for a semantic theory of coordination will be referred to here as the Boolean assumption. According to this assumption conjunctive coordinators like and are described using the cross-categorial Boolean operator of Generalized Conjunction (GC). Symmetrically, disjunctive coordinators

this paper I would like to oppose both views. A central technical point to be shown is that in the generalized quantifiers framework, and conjunctions can standardly be treated as uniformly "intersective" to account also for the truth conditions of collective predications like in (3). One general conclusion drawn from this fact is that conservative type theoretical semantics should be able to handle the problem of and in a natural way. Thus, a comprehensive theory of coordination can eliminate the ambiguity stipulation in the first approach above as well as the massive technical and ontological revisions necessitated by the second. Following this observation, we extend the semantic theory of coordinations whose "building blocks" are singular NP's. Traditionally, conjunction and disjunction are treated symmetrically using the standard Boolean definitions. The collective interpretation of sentences like (3) is obtained as a result of type shifting in the denotation of the NP. Type transition, following Partee & Rooth's notion of flexibility, is motivated by type mismatch, here between distributive generalized quantifiers and collective predicates. The shifting operator is shown to be a generalization of the existential determiner, being a part of a "natural" hierarchy of type shifting principles, in the sense of Partee(1986) and van Benthem(1986,1991). This reveals a connection between the phenomena of "free" existential quantification and collective predication in natural languages. The paper is organized as follows. Section 2 presents some background: a brief discussion of previous proposals and a few conceptual and technical preliminaries for the alternative solution developed. Section 3 deals with coordinations of proper names. Section 4 discusses the hierarchy of ope...