Disjunctive Axioms and Concurrent $\lambda$-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 messageexchange, and enhanced expressive power w.r.t. 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.