A unified relational semantics for BPL, IPL and OL -- axiomatization without disjunction
Abstract
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 \,,\ and \,,\ 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.
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