Chu spaces as a semantic bridge between linear logic and mathematics

AbstractThe motivating role of linear logic is as a “logic behind logic”. We propose a sibling role for it as a logic of transformational mathematics via the self-dual category of Chu spaces, a generalization of topological spaces. These create a bridge between linear logic and mathematics by soundly and fully completely interpreting linear logic while fully and concretely embedding a comprehensive range of concrete categories of mathematics. Our main goal is to treat each end of this bridge in expository detail. In addition, we introduce the dialectic lambda-calculus, and show that dinaturality semantics is not fully complete for the Chu interpretation of linear logic