Finite basis theorem for Filter-distributive protoalgebraic deductive systems and strict universal horn classes

Studia Logica 74 (1-2):233 - 273 (2003)
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Abstract

We show that a finitely generated protoalgebraic strict universal Horn class that is filter-distributive is finitely based. Equivalently, every protoalgebraic and filter-distributive multidimensional deductive system determined by a finite set of finite matrices can be presented by finitely many axioms and rules.

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Citations of this work

Correspondences between Gentzen and Hilbert Systems.J. G. Raftery - 2006 - Journal of Symbolic Logic 71 (3):903 - 957.
Order algebraizable logics.James G. Raftery - 2013 - Annals of Pure and Applied Logic 164 (3):251-283.
The Beth Property in Algebraic Logic.W. J. Blok & Eva Hoogland - 2006 - Studia Logica 83 (1-3):49-90.
Contextual Deduction Theorems.J. G. Raftery - 2011 - Studia Logica 99 (1-3):279-319.

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References found in this work

Protoalgebraic logics.W. J. Blok & Don Pigozzi - 1986 - Studia Logica 45 (4):337 - 369.
Equivalential logics.Janusz Czelakowski - 1981 - Studia Logica 40 (3):227-236.
On distributivity of closure systems.Wojciech Dzik & Roman Suszko - 1977 - Bulletin of the Section of Logic 6 (2):64-66.

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