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A Class of Simpler Logical Matrices for the Variable-Sharing Property

100%

Robles G. , Méndez J. M.

tom 20

nr 3

241-249

In our paper “A general characterization of the variable-sharing property by means of logical matrices”, a general class of so-called “Relevant logical matrices”, RMLs, is defined. The aim of this paper is to define a class of simpler Relevant logical matrices RMLs′ serving the same purpose that RMLs, to wit: any logic verified by an RML′ has the variable-sharing property and related properties predicable of the logic of entailment E and of the logic of relevance R.

On the Leibniz congruences

63%

Font J. M.

tom 28

nr 1

17-36

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 relation modulo the theory). For protoalgebraic deductive systems the class of algebras associated in general turns out to be the class of algebra reducts of reduced matrices, which is the algebraic counterpart usually considered for this large class of deductive systems; but in the general case the new class of algebras shows a better behaviour.