Classical Linear Logic of Implications

Abstract

We give a simple term calculus for the multiplicative exponential fragment of Classical Linear Logic, by extending Barber and Plotkin’s system for the intuitionistic case. The calculus has the nonlinear and linear implications as the basic constructs, and this design choice allows a technically managable axiomatization without commuting conversions. Despite this simplicity, the calculus is shown to be sound and complete for category-theoretic models given by *-autonomous categories with linear exponential comonads.KeywordsCategorical ModelEquational TheoryLinear LogicSpringer Lecture NoteLambda CalculusThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.