Λ-normal forms in an intensional logic for English

Studia Logica 39 (2-3):311 - 324 (1980)
Abstract
Montague [7] translates English into a tensed intensional logic, an extension of the typed -calculus. We prove that each translation reduces to a formula without -applications, unique to within change of bound variable. The proof has two main steps. We first prove that translations of English phrases have the special property that arguments to functions are modally closed. We then show that formulas in which arguments are modally closed have a unique fully reduced -normal form. As a corollary, translations of English phrases are contained in a simply defined proper subclass of the formulas of the intensional logic.
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References found in this work BETA
Peter B. Andrews (1971). Resolution in Type Theory. Journal of Symbolic Logic 36 (3):414-432.
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