Residuated lattices as algebraic semantics for paraconsistent Nelson logic

Abstract

The class of NPc-lattices is introduced as a quasivariety of commutative residuated lattices, and it is shown that the class of pairs $(\A, A^+)$ such that $\A$ is an NPc-lattice and $A^+$ is its positive cone, is a matrix semantics for Nelson paraconsistent logic.

Published: Journal of Logic and Computation (2009), doi: 10.1093/logcom/exp028.