Implicit connectives of algebraizable logics

Studia Logica 78 (1-2):155 - 170 (2004)
An extensions by new axioms and rules of an algebraizable logic in the sense of Blok and Pigozzi is not necessarily algebraizable if it involves new connective symbols, or it may be algebraizable in an essentially different way than the original logic. However, extension whose axioms and rules define implicitly the new connectives are algebraizable, via the same equivalence formulas and defining equations of the original logic, by enriched algebras of its equivalente quasivariety semantics. For certain strongly algebraizable logics, all connectives defined implicitly by axiomatic extensions of the logic are explicitly definable.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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Reprint years 2005
DOI 10.1007/s11225-005-5170-6
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References found in this work BETA
Weakly Algebraizable Logics.Janusz Czelakowski & Ramon Jansana - 2000 - Journal of Symbolic Logic 65 (2):641-668.
An Algebraic Approach to Intuitionistic Connectives.Xavier Caicedo & Roberto Cignoli - 2001 - Journal of Symbolic Logic 66 (4):1620-1636.

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The Logic Ł•.Marta S. Sagastume & Hernán J. San Martín - 2014 - Mathematical Logic Quarterly 60 (6):375-388.
Axiomatizability by {{\ Forall}{\ Exists}!}-Sentences.Miguel Campercholi & Diego Vaggione - 2011 - Archive for Mathematical Logic 50 (7-8):713-725.

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