A treatment of plurals and plural quantifications based on a theory of collections

Minds and Machines 3 (4):453-474 (1993)
Collective entities and collective relations play an important role in natural language. In order to capture the full meaning of sentences like The Beatles sing Yesterday, a knowledge representation language should be able to express and reason about plural entities — like the Beatles — and their relationships — like sing — with any possible reading (cumulative, distributive or collective).In this paper a way of including collections and collective relations within a concept language, chosen as the formalism for representing the semantics of sentences, is presented. A twofold extension of theA–C concept language is investigated: (1) special relations introduce collective entities either out of their components or out of other collective entities, (2) plural quantifiers on collective relations specify their possible reading. The formal syntax and semantics of the concept language is given, together with a sound and complete algorithm to compute satisfiability and subsumption of concepts, and to compute recognition of individuals.
Keywords Plurals  concept languages  generalized quantifiers  part-whole relation
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DOI 10.1007/BF00974106
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Fred Landman (1989). Groups, I. Linguistics and Philosophy 12 (5):559 - 605.
Emmon Bach (1986). The Algebra of Events. Linguistics and Philosophy 9 (1):5--16.

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