The B5-Modalized Propositional Logic

摘要

A B₅-modalized propositional logic will be proposed in this paper which there are five modalities [t], [T], [⊥], [a], [f] to represent the five values t, T, ⊥, a, f in B₅, respectively, and a Gentzen-typed deduction system will be given so that the system is sound and complete with the B₅-valued semantics of the logic.