Standard theories of scope are semantically blind. They employ a single logico-syntactic rule of scope assignment quantifying in Quantifier Raising, storage, or type change etc which roughly speaking prefixes an expression \aplha.

Sentences with multiple occurrences of plural definites give rise to certain effects suggesting that distributivity should be modeled by polyadic operations. Yet in this paper it is argued that the simpler treatment of distributivity using unary universal quantification should be retained. Seemingly polyadic effects are claimed to be restricted to definite NPs. This fact is accounted for by the special anaphoric (dependent) use of definites. Further evidence concerning various plurals, island constraints, and cumulative quantification is shown to support this claim. (...) In addition, it is shown that the evidence against a simple atomic version of unary distributivity is not decisive either. In the (uncommon) cases where distributivity with definites is not strictly atomic, they can be analyzed as dependent on implicit quantifiers. (shrink)

Recent developments in the semantics of natural language seem to lead to a genuine synthesis of ideas from linguistics and logic, producing novel concepts and questions of interest to both parent disciplines. This book is a collection of essays on such new topics, which have arisen over the past few years. Taking a broad view, developments in formal semantics over the past decade can be seen as follows. At the beginning stands Montague's pioneering work, showing how a rigorous semantics can (...) be given for complete fragments of natural language by creating a suitable fit between syntactic categories and semantic types. This very enterprise already dispelled entrenched prejudices concerning the separation of linguistics and logic. Having seen the light, however, there is no reason at all to stick to the letter of Montague's proposals, which are often debatable. Subsequently, then, many improvements have been made upon virtually every aspect of the enterprise. More sophisticated grammars have been inserted (lately, lexical-functional grammar and generalized phrase structure grammar), more sensitive model structures have been developed (lately, 'partial' rather than 'total' in their com position), and even the mechanism of interpretation itself may be fine-tuned more delicately, using various forms of 'representations' mediating between linguistic items and semantic reality. In addition to all these refinements of the semantic format, descriptive coverage has extended considerably. (shrink)

A unified theory is offered to account for three types of definite descriptions: with singular, plural, & mass predicates, & to provide an account for the word the in descriptions. It is noted that B. Russell's analysis ("On Denoting," Mind, 1905, 14, 479-493) failed to account for plural & mass descriptions. The proposed theory differs from Russell's only by the substitution of the notation (less than or equal to) for Russell's =. It is suggested that for every predicate G there (...) is an appropriate "part of" or "some of" relation on the extension of G. For singular predicates, (less than or equal to) becomes just the identity relation =. The predicate G is formulated as "the G" & analyzed with the formula ((schwa)x) (Gx . (Gy (includes) yy (less than or equal to) x)), which accounts for all cases of definite descriptions. It is suggested that the primary use of the is not to indicate uniqueness, but totality. C. Ornatowski. (shrink)

Language in Action demonstrates the viability of mathematical research into the foundations of categorial grammar, a topic at the border between logic and linguistics. Since its initial publication it has become the classic work in the foundations of categorial grammar. A new introduction to this paperback edition updates the open research problems and records relevant results through pointers to the literature. Van Benthem presents the categorial processing of syntax and semantics as a central component in a more general dynamic logic (...) of information flow, in tune with computational developments in artificial intelligence and cognitive science. Using the paradigm of categorial grammar, he describes the substructural logics driving the dynamics of natural language syntax and semantics. This is a general type-theoretic approach that lends itself easily to proof-theoretic and semantic studies in tandem with standard logic. The emphasis is on a broad landscape of substructural categorial logics and their proof-theoretical and semantic peculiarities. This provides a systematic theory for natural language understanding, admitting of significant mathematical results. Moreover, the theory makes possible dynamic interpretations that view natural languages as programming formalisms for various cognitive activities. (shrink)

Barry Schein proposes combining a second-order treatment of plurals with DonaldDavidson's suggestion that there are positions for reference to events in ordinary predicates inorder to account for several of the more puzzling features of ...

Precursors. 2.1 Introduction Thus far I have presented an approach to the semantics of plurals in the form of two rather similar grammars for a fragment of English. And I have given a few examples of the kinds of things one can say within this ...

This dissertation is based on the compositional model theoretic approach to natural language semantics that was initiated by Montague (1970) and developed by subsequent work. In this general approach, coordination and negation are treated following Keenan & Faltz (1978, 1985) using boolean algebras. As in Barwise & Cooper (1981) noun phrases uniformly denote objects in the boolean domain of generalized quanti®ers. These foundational assumptions, although elegant and minimalistic, are challenged by various phenomena of coordination, plurality and scope. The dissertation solves (...) these problems by developing a ¯exible process of meaning composition, as ®rst proposed by Partee & Rooth (1983). Flexible interpretation involves semantic operations without any phonological counterpart, which participate in the interpretation process and change meanings of overt expressions. The dissertation introduces a novel ¯exible system where a small number of operations describe the behaviour of complex phenomena such as `non-boolean' and, the scope of inde®nites and the semantics of collectivity with quanti®cational NPs. The proposed theory is based on a distinction between two features of meanings in natural language. (shrink)