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 spaces”. A unique representation is defined for subspaces of the semantic space. This unique representation is called the "normal form" of the lexical denotation. A Boolean algebra of normal forms is developed, in which lexical entailment is Boolean inclusion. The presentation in the body of the paper is informal, making use of examples 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.
Purdy, William C., "A Lexical Extension of Montague Semantics" (1990). Electrical Engineering and Computer Science Technical Reports. 69.