Propositions in Linear Multirole Logic as Multiparty Session Types

Abstract: We identify multirole logic as a new form of logic and formalize linear multirole logic (LMRL) as a natural generalization of classical linear logic (CLL). Among various meta-properties established for LMRL, we obtain one named multi-cut elimination stating that every cut between three (or more) sequents (as a generalization of a cut between two sequents) can be eliminated, thus extending the celebrated result of cut-elimination by Gentzen. We also present a variant of $\pi$-calculus for multiparty sessions that demonstrates a tight correspondence between process communication in this variant and multi-cut elimination in LMRL, thus extending some recent results by Caires and Pfenning (2010) and Wadler (2012), among others, along a similar line of work.