\Sigma\Pi-polycategories, additive linear logic, and process semantics

Abstract

We present a process semantics for the purely additive fragment of linear logic in which formulas denote protocols and (equivalence classes of) proofs denote multi-channel concurrent processes. The polycategorical model induced by this process semantics is shown to be equivalent to the free polycategory based on the syntax (i.e., it is full and faithfully complete). This establishes that the additive fragment of linear logic provides a semantics of concurrent processes. Another property of this semantics is that it gives a canonical representation of proofs in additive linear logic. This arXived version omits Section 1.7.1: "Circuit diagrams for polycategories" as the Xy-pic diagrams would not compile due to lack of memory. For a complete version see "http://www.cpsc.ucalgary.ca/~pastroc/".