Modal logics and bivalent modalities

In this talk, I will introduce modalities which interpret the predicates "it is logically valid that" and "it is logically consistent that" in many-valued logics. Such modalities are defined in such a way that the truth of []F and <>F takes only into consideration whether F receives or not designated values, reflecting the two-valuedness of many-valued logics. In this analysis, we aim to establish what are the most general principles of validity in this family of logics.