Open Access
VOL. 2 | 1998 An Introduction to Linear Logic: Expressiveness and Phase Semantics
Mitsuhiro Okada

Editor(s) Mariangiola Dezani-Ciancaglini, Mitsuhiro Okada, Masako Takahashi

MSJ Memoirs, 1998: 255-295 (1998) DOI: 10.2969/msjmemoirs/00201C070


We first point out some nature of linear logic, in comparison with tra- ditional logics, in Introduction (§ 1), then give the syntax and the intuitive meaning of the syntax in § 2. We give phase semantics of linear logic and a phase semantic proof for the completeness and cut-elimination theorems (at once) in § 3. We formulate a concurrent process calculus as a conservative subsystem of linear logic and give some examples of concurrent process specification by linear logic in § 4. In § 5 we give a simplified phase semantics and the completeness for a fragment of linear logic, in which some concurrent process models such as Petri nets can be formulated.


Published: 1 January 1998
First available in Project Euclid: 17 January 2014

zbMATH: 0935.03030
MathSciNet: MR1728764

Digital Object Identifier: 10.2969/msjmemoirs/00201C070

Rights: Copyright © 1998, The Mathematical Society of Japan

Vol. 2 • 1 January 1998
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