Negation and Implication in Quasi-Nelson Logic

Quasi-Nelson logic is a recently-introduced generalization of Nelson’s constructive with strong negation to non-involutive setting. In the present paper we axiomatize negation-implication fragment quasi-Nelson (QNI-logic), which constitutes in sense algebraizable core logic. We introduce finite Hilbert-style calculus for QNI-logic, showing completeness and algebraizability respect variety QNI-algebras. Members latter class, also introduced investigated recent paper, are precisely subreducts algebras. Relying on our result, show how fragments intuitionistic may both be obtained as schematic extensions QNI-logic.