Axioms and models of linear logic

Abstract

Girard's recent system of linear logic is presented in a way that avoids the two-level structure of formulae and sequents, and that minimises the number of primitive function symbols. A deduction theorem is proved concerning the classical implication as embedded in linear logic. The Hilbert-style axiomatisation is proved to be equivalent to the sequent formalism. The axiomatisation leads to a complete class of algebraic models. Various models are exhibited. On the meta-level we use Dijkstra's method of explicit equational proofs.