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September 14, 2020

Four-valued logics of truth, non-falsity, and material equivalence

The purpose of this talk is to demonstrate how to work with quasivarieties (universal Horn classes) in a relational signature which consists of more than one predicate symbol. While universal algebraists work with the binary equality predicate, and algebraic logicians work with the unary truth predicate, the four-valued Belnap–Dunn logic provides a natural setting where two unary predicates arise (namely the truth and non-falsity predicates), as well as an equality predicate. We show how to axiomatize the logic of truth and non-falsity, as well as the logic of truth and equality, determined by the four-valued algebraic semantics of Belnap and Dunn.