Abstract:  In 2002, Dalla Chiara and Giuntini observed that there is an interesting way to restrict valuations, which unifies the requirement in the Kripke semantics of intuitionistic propositional logic (IPL) and orthologic (OL). Lately, axiomatization of some logics w.r.t. this unified semantics has been studied.
In this talk, by slightly generalizing their definition, we will give a unified semantics of IPL, OL and Albert Visser's basic propositional logic. Working in language {⊥,∧,→} and {⊥,∧,∨,¬} respectively, we will provide axiomatization of the logic w.r.t. this semantics.