Definitional equivalence and algebraizability of generalized logical systems (Q1302288)

The author introduces and studies a concept of algebraizable sequential logic, a generalized notion of a logical system that covers, on a uniform basis, sequential systems and the quasi-equational theories of quasivarieties in Mal'tsev's sense. The author defines a concept of equivalence between generalized logics so that a logic is considered to be algebraizable whenever it is equivalent to the quasi-equational theory of a quasivariety. The author presents also a general algebraic approach to a rather wide class of sentential logics containing all intermediate logics and many interesting non-algebraizable logics.