Strong quasi-MV* algebras and their logics

In this paper, we introduce the subvariety of quasi-MV* algebras in order to characterize the logic which is related to complex fuzzy logic. First, we give the definitions of strong quasi-MV* algebra and strong quasi-Wajsberg* algebra and show that they are term equivalence. Second, we present the representation theorem and the standard completeness of strong quasi-MV* algebras. Moreover, we discuss the properties of terms in the language of Wajsberg* algebras and strong quasi-Wajsberg* algebras. Finally, we establish the logical system associated with strong quasi-Wajsberg* algebra and prove that the logical system is sound and complete.