On Axiomatization of Non-Cartesian Logics

Abstract

Nowadays it is generally accepted as a kind of truism by a significant part of logicians that Belnap's four-valued logic B4 (the definition see below) is a good logical system, which is both useful in practice and fruitful in theory. Lots of papers and monographs deal with the syntactic analogue of B4, which is a well-known system of First Degree Entailment (FDE), and with its algebraic correlate, id est the class of De Morgan algebras.