The aim of this paper is to discuss the motivation for a new general algebraic semantics for deductive systems, to introduce it, and to present an outline of its main features. Some tools from the theory of abstract logics are also introduced, and two classifications of deductive systems are analysed: one is based on the behaviour of the Leibniz congruence (the maximum congruence of a logical matrix) and the other on the behaviour of the Frege operator (which associates to every theory the interderivability...
In [4] Blok and Pigozzi prove syntactically that RM, the propositional calculus also called R-Mingle, is algebraizable, and as a consequence there is a unique quasivariety (the so-called equivalent quasivariety semantics) associated to it. In [3] it is stated that this quasivariety is the variety of Sugihara algebras. Starting from this fact, in this paper we present an equational base for this variety obtained as a subvariety of the variety of R-algebras, found in [7] to be associated in the same...
We present the basic theory of the most natural algebraic counterpart of the ℵ-valued Lukasiewicz calculus, strictly logically formulated. After showing its lattice structure and its relation to C. C. Chang's MV-algebras we study the implicative filters and prove its equivalence to congruence relations. We present some properties of the variety of all Wajsberg algebras, among which there is a representation theorem. Finally we give some characterizations of linear, simple and semisimple algebras....
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