TL;DR
This paper extends intuitionistic tense logics to multi-modal systems with new axiomatizations, providing soundness and completeness proofs for these generalized frameworks.
Contribution
It introduces a novel framework for intuitionistic grammar logics, including axiomatizations for base and extended systems with seriality and path axioms.
Findings
Axiomatizations for base intuitionistic grammar logics
Extensions with seriality and path axioms
Soundness and completeness proofs via canonical models
Abstract
We generalize intuitionistic tense logics to the multi-modal case by placing grammar logics on an intuitionistic footing. We provide axiomatizations for a class of base intuitionistic grammar logics as well as provide axiomatizations for extensions with combinations of seriality axioms and what we call "intuitionistic path axioms". We show that each axiomatization is sound and complete with completeness being shown via a typical canonical model construction.
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