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

Abstract

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. An advantage of this formalism is the possibility of reasoning and stepwise refining in the presence of scoping ambiguities. Moreover, many phenomena covered by the Generalized Quantifiers Theory are easily captured within this framework. In the final part a way to include a theory of parts (mereology) is suggested, allowing for a lattice-theoretical approach to the treatment of plurals.