Possible-translations algebraization for paraconsistent logics. (English) Zbl 1117.03035

Summary: This note proposes a new notion of algebraizability, which we call possible-translations algebraic semantics, based upon the newly developed possible-translations semantics. This semantics is naturally adequate to obtain an algebraic interpretation for paraconsistent logics, and generalizes the well-known method of algebraization by W. Blok and D. Pigozzi. This generalization obtains algebraic semantics up to translations, applicable to several non-classical logics and particularly apt for paraconsistent logics, a philosophically relevant class of logics with growing importance for applications.


03B53 Paraconsistent logics
03G25 Other algebras related to logic