The logic of quasi MV star algebras

Abstract

Quasi-MV* algebras were introduced as generalizations of MV*-algebras and quasi-MV algebras. The recent investigation into quasi-MV* algebras shows that they are closely related to quantum computational logic and complex fuzzy logic. In this paper, we aim to study the logical system associated with quasi-MV* algebras in detail. First, we introduce quasi-Wajsberg* algebras as the term equivalence of quasi-MV* algebras and investigate the related properties of quasi-Wajsberg* algebras. Then we establish the logical system associated with quasi-Wajsberg* algebras using fewer deduction rules. Finally, we discuss the soundness of this logical system.