Studia Logica 45 (4):337 - 369 (1986)
AbstractThere 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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References found in this work
Multiple Conclusion Logic.D. J. Shoesmith & Timothy Smiley - 1978 - Cambridge, England / New York London Melbourne: Cambridge University Press.
Matrix Approach in Methodology of Sentential Calculi.Ryszard Wójcicki - 1973 - Studia Logica 32 (1):7 - 39.
George Grätzer. Universal Algebra. D. Van Nostrand Company, Inc., Princeton Etc. 1968, Xvi + 368 Pp. [REVIEW]Kirby A. Baker - 1973 - Journal of Symbolic Logic 38 (4):643-644.
Investigations Into the Sentential Calculus with Identity.Roman Suszko & Stephen L. Bloom - 1972 - Notre Dame Journal of Formal Logic 13 (3):289-308.