Quasi-N4-lattices and their logic

Abstract

The variety of quasi-N4-lattices (QN4) was recently introduced as a non-involutive generalization of N4-lattices (algebraic models of Nelson's paraconsistent logic). While research on these algebras is still at a preliminary stage, we know that QN4 is an arithmetical variety which possesses a ternary as well as a quaternary deductive term, enjoys equationally definable principal congruences and the strong congruence extension property. We furthermore have recently introduced an algebraizable logic having QN4 as its equivalent semantics. In this contribution we report on the results obtained so far on this class of algebras and on its logical counterpart.