2022/07/15 by Chen, Zhicheng
#FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.2207.07306
In this paper, we propose a relational semantics of propositional language, which unifies the relational semantics of intuitionistic logic, Visser's Basic Propositional Logic and orthologic. Working in language \\bot,∧,¬\ and \\bot,∧,→\ respectively, we axiomatize this basic logic as well as stronger ones corresponding to different combinations of frame conditions: reflexivity, symmetry, and transitivity. We also provide translations from these propositional logics into modal logics.