Disjunctive Axioms and Concurrent $λ$-Calculi: a Curry-Howard Approach
We add to intuitionistic logic infinitely many classical disjunctive tautologies and use the Curry--Howard correspondence to obtain typed concurrent $λ$-calculi; each of them features a specific communication mechanism, including broadcasting and cyclic message-exchange, and enhanced expressive power with respect to the $λ$-calculus. Moreover they all implement forms of code mobility. Our results provide a first concurrent computational interpretation for many propositional intermediate logics, classical logic included.
math.LO↗