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This paper describes how meanings are represented in a semantic grammar for a fragment of English in the logic programming language Prolog. The conventions of Definite Clause Grammars are used. Previous work on DCGs with a semantic component has used essentially first-order formulas for representing meanings. The system described here uses formulas of the typed λ-calculus. The first section discusses general issues concerning the use of first-order logic or the λ-calculus to represent meanings. The second section describes how λ-calculus meaning representations can be constructed and manipulated directly in Prolog. This 'programmed' representation motivates a suggestion, discussed in the third section, for an extension to Prolog so that the language itself would include a mechanism for handling the λ-formulas directly.

Using λ-calculus to represent meanings in logic grammars