Protoalgebraic logics

Studia Logica 45 (4):337 - 369 (1986)
Abstract
There exist important deductive systems, such as the non-normal modal logics, that are not proper subjects of classical algebraic logic in the sense that their metatheory cannot be reduced to the equational metatheory of any particular class of algebras. Nevertheless, most of these systems are amenable to the methods of universal algebra when applied to the matrix models of the system. In the present paper we consider a wide class of deductive systems of this kind called protoalgebraic logics. These include almost all (non-pathological) systems of prepositional logic that have occurred in the literature. The relationship between the metatheory of a protoalgebraic logic and its matrix models is studied. The following results are obtained for any finite matrix model U of a filter-distributive protoalgebraic logic : (I) The extension U of is finitely axiomatized (provided has only finitely many inference rules); (II) U has only finitely many extensions.
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DOI 10.1007/BF00370269
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References found in this work BETA
Multiple-Conclusion Logic.D. J. Shoesmith - 1978 - Cambridge University Press.
Reduced Products of Logical Matrices.Janusz Czelakowski - 1980 - Studia Logica 39 (1):19 - 43.
Equivalential Logics (I).Janusz Czelakowski - 1981 - Studia Logica 40 (3):227 - 236.

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Citations of this work BETA
Fregean Logics.J. Czelakowski & D. Pigozzi - 2004 - Annals of Pure and Applied Logic 127 (1-3):17-76.
Weakly Algebraizable Logics.Janusz Czelakowski & Ramon Jansana - 2000 - Journal of Symbolic Logic 65 (2):641-668.
Equivalential and Algebraizable Logics.Burghard Herrmann - 1996 - Studia Logica 57 (2-3):419 - 436.
Taking Degrees of Truth Seriously.Josep Maria Font - 2009 - Studia Logica 91 (3):383-406.
Correspondences Between Gentzen and Hilbert Systems.J. G. Raftery - 2006 - Journal of Symbolic Logic 71 (3):903 - 957.

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