Intuitionistic modal logic made explicit
Michel Marti, Thomas Studer · BORIS (University Library Bern)
Previous intuitionistic justification logics included explicit justifications for all admissible rules of intuitionistic logic in order to get completeness with respect to provability semantics. We present the justification logic iJT4, which does not have these additional justification terms. We establish that iJT4 is complete with respect to modular models and that there is a realization of intuitionistic S4 into iJT4. Hence iJT4 can be seen as an explicit version of intuitionistic S4.