Multirole logic and multiparty channels

Abstract

We identify multirole logic as a new form of logic in which conjunction/disjunction is interpreted as an ultrafilter on the power set of some underlying set (of roles), and the notion of negation is generalized to endomorphisms on this underlying set. In this talk, we present linear multirole logic (LMRL) as a natural generalization of classical linear logic (CLL). Among various meta-properties established for LMRL, we obtain one named multiparty cut-elimination stating that every cut involving one or more sequents (as a generalization of a binary cut involving exactly two sequents) can be eliminated, thus extending the celebrated result of cut-elimination by Gentzen. An immediate application of LMRL can be found in a formulation of session types for channels that support multiparty communication in distributed programming. Guided by LMRL, we give an interesting interpretation to linear multiplicative conjunction/disjunction as session type constructors that encompasses certain seemingly contradictory ones found in the literature