A lexical extension of Montague semantics

This paper presents a model theory of lexical semantics that is compatible with theories in the Montagovian tradition. Lexical expressions are modeled as subsets or "subspaces " in a "semantic space". A unique representation is defined for subspaces of the semantic space. Tms unique representation is called the "normal form " of the lexical denotation. A Boolean algebra of normal forms is developed, in wmch lexical entailment is Boolean inclusion. The presentation in the body of the paper is informal, making use of exam-ples to illustrate the theory and to indicate the range of applicability. Formal definitions and proofs in support of the presentation are given in the Appendix