Nested Sequents for Intuitionistic Logics

Nested sequent systems for modal logics were introduced by Kai Brünnler, and have come to be seen as an attractive deep reasoning extension of familiar sequent calculi. In an earlier paper I showed there was a connection between modal nested sequents and modal prefixed tableaus. In this paper I extend the nested sequent machinery to intuitionistic logic, both standard and constant domain, and relate the resulting sequent calculi to intuitionistic prefixed tableaus. Modal nested sequent machinery generalizes one sided sequent calculi—the present work similarly generalizes 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.