Petri nets, horn programs, linear logic, and vector games

Abstract

Linear Logic was introduced by Girard as a resource-sensitive refinement of classical logic. Linear Logic is of considerable interest for Computer Science. In this paper we focus on the correlations between natural fragments of Linear Logic and a number of basic concepts related to different branches of Computer Science such as Concurrency Theory, Theory of Computations, Horn Programming, and Game Theory. In particular, such a complete correspondence allows us to introduce several new semantics for Linear Logic and to clarify many results on the complexity of natural fragments of Linear Logic.