λ-Normal forms in an intensional logic for English

✍ Scribed by Joyce Friedman; David S. Warren

• Publisher: Springer Netherlands
• Year: 1980
• Tongue: English
• Weight: 916 KB
• Volume: 39
• Category: Article
• ISSN: 0039-3215
• DOI: 10.1007/bf00370327

✦ Synopsis

Montague [7]

translates English into a tensed intensional logic, an extension of the typed J-calculus. We prove that each translation reduces to a for-m~da without J-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 A-normal form. As a corollary, translations of English phrases are contained in a simply defined proper subclass of the formulas of the intensional logic.