Algebraic Semantics for Quasi-Nelson Logic

摘要

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 QN of quasi-Nelson logic, and show that QN is regularly BP-algebraizable with respect to its algebraic counterpart obtained by the Blok-Pigozzi algorithm, namely the class of Q-algebras. Finally, we show that the class of Q-algebras coincides with the class of quasi-Nelson algebras.