Nested Sequents for Intuitionistic Logics

Abstract

Relatively recently nested sequent systems for modal logics have come to be seen as an attractive deep-reasoning extension of familiar sequent calculi. In an earlier paper I showed that there was a strong connection between modal nested sequents and modal prefixed tableaux. In this paper I show that the connection continues to intuitionistic logic, both standard and constant domain, relating nested intuitionistic sequent calculi to intuitionistic prefixed tableaux. Modal nested sequent machinery generalizes one-sided sequent calculi—intuitionistic nested sequents similarly generalize two-sided sequents. It is noteworthy that the resulting system for constant domain intuitionistic logic is particularly simple. It amounts to a combination of intuitionistic propositional rules and classical quantifier rules, a combination that is known to be inadequate when conventional intuitionistic sequent systems are used.