Categorical abstract algebraic logic categorical algebraization of first-order logic without terms

Archive for Mathematical Logic 44 (4):473-491 (2004)

Abstract
An algebraization of multi-signature first-order logic without terms is presented. Rather than following the traditional method of choosing a type of algebras and constructing an appropriate variety, as is done in the case of cylindric and polyadic algebras, a new categorical algebraization method is used: The substitutions of formulas of one signature for relation symbols in another are treated in the object language. This enables the automatic generation via an adjunction of an algebraic theory. The algebras of this theory are then used to algebraize first-order logic
Keywords Algebraic logic  Equivalent deductive systems  Algebraizable logics  Institutions  Equivalent institutions  Algebraizable institutions  Algebraic theories  Monads  Triples  Adjunctions  First-order logic  Cylindric algebras  Polyadic algebras
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Reprint years 2005
DOI 10.1007/s00153-004-0266-7
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References found in this work BETA

Protoalgebraic Logics.W. J. Blok & Don Pigozzi - 1986 - Studia Logica 45 (4):337 - 369.
Equivalential Logics (I).Janusz Czelakowski - 1981 - Studia Logica 40 (3):227 - 236.
Equivalential logics.Janusz Czelakowski - 1981 - Studia Logica 40 (3):227-236.

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Algebraic Semantics for Deductive Systems.W. J. Blok & J. Rebagliato - 2003 - Studia Logica 74 (1-2):153 - 180.

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