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λ-Normal Forms in an Intensional Logic for English

Joyce Friedman and David S. Warren
Studia Logica: An International Journal for Symbolic Logic
Vol. 39, No. 2/3 (1980), pp. 311-324
Published by: Springer
Stable URL: http://www.jstor.org/stable/20014988
Page Count: 14
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λ-Normal Forms in an Intensional Logic for English
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Abstract

Montague [7] translates English into a tensed intensional logic, an extension of the typed λ-calculus. We prove that each translation reduces to a formula without λ-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 λ-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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