An Introduction to Linear Logic: Expressiveness and Phase Semantics

Abstract

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.