Algebraic Semantics for Quasi-Nelson Logic

Quasi-Nelson logic is a generalization of Nelson logic in the sense that the negation is not necessary involutive. In this paper, we give a Hilbert-style presentation \(\mathbf {QN}\) of quasi-Nelson logic, and show that \(\mathbf {QN}\) is regularly BP-algebraizable with respect to its algebraic counterpart obtained by the Blok-Pigozzi algorithm, namely the class of \(\mathsf {Q}\)-algebras. Finally, we show that the class of \(\mathsf {Q}\)-algebras coincides with the class of quasi-Nelson algebras.