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THE JUDGEMENT CALCULUS FOR INTUITIONISTIC LINEAR LOGIC: PROOF THEORY AND SEMANTICS

✍ Scribed by Silvio Valentini

Publisher: John Wiley and Sons
Year: 1992
Tongue: English
Weight: 958 KB
Volume: 38
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.19920380105

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✦ Synopsis

Abstract

In this paper we propose a new set of rules for a judgement calculus, i.e. a typed lambda calculus, based on Intuitionistic Linear Logic; these rules ease the problem of defining a suitable mathematical semantics. A proof of the canonical form theorem for this new system is given: it assures, beside the consistency of the calculus, the termination of the evaluation process of every well‐typed element. The definition of the mathematical semantics and a completeness theorem, that turns out to be a representation theorem, follow. This semantics is the basis to obtain a semantics for the evaluation process of every well‐typed program. 1991 MSC: 03B20, 03B40.

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