Making computational sense of Montague's intensional logic

Abstract

Montague's difficult notation and complex model theory have tended to obscure potential insights for the computer scientist studying Natural Language. Despite his strict insistence on an abstract model-theoretic interpretation for his formalism, we feel that Montague's work can be related to procedural semantics in a fairly direct way. A simplified version of Montague's formalism is presented, and its key concepts are explicated in terms of computational analogues. Several examples are presented within Montague's formalism but with a view toward developing a procedural interpretation. We provide a natural translation from intensional logic into lisp. This allows one to express the composition of meaning in much the way Montague does, using subtle patterns of functional application to distribute the meanings of individual words throughout a sentence. The paper discusses some of the insights this research has yielded on knowledge representation and suggests some new ways of looking at intensionality, context, and expectation.