On the Concurrent Computational Content of Intermediate Logics

We provide a proofs-as-concurrent-programs interpretation for a large class of intermediate logics that can be formalized by cut-free hypersequent calculi. Obtained by adding classical disjunctive tautologies to intuitionistic logic, these logics are used to type concurrent λ-calculi by Curry–Howard correspondence; each of the calculi features a specific communication mechanism, enhanced expressive power when compared to the λ-calculus, and implements forms of code mobility. We thus confirm Avron's 1991 thesis that intermediate logics formalizable by hypersequent calculi can serve as basis for concurrent λ-calculi.