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Revisiting the Adequacy Theorem for Fragments of Łukasiewicz Logic

Bulletin of the Section of Logic
A. V. Figallo introduced the 3-valued Super Łukasiewicz logic expanded with the Δ operator, denoted as C3↣,Δ, in 1990. This operator is used in the definition of 3-valued Łukasiewicz algebras, and it is not possible to recover Δ through implication and ...
Miguel Pérez-Gaspar +2 more
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A HENKIN-STYLE PROOF OF COMPLETENESS FOR FIRST-ORDER ALGEBRAIZABLE LOGICS

The Journal of Symbolic Logic, 2015
AbstractThis paper considers Henkin’s proof of completeness of classical first-order logic and extends its scope to the realm of algebraizable logics in the sense of Blok and Pigozzi. Given a propositional logic L (for which we only need to assume that it has an algebraic semantics and a suitable disjunction) we axiomatize two natural first-order ...
Petr Cintula, Carles Noguera
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A note on the hierarchy of algebraizable logics

, 2021
Peer ...
Cintula, Petr, Noguera, Carles
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Definitional equivalence and algebraizability of generalized logical systems

Annals of Pure and Applied Logic, 1999
The author introduces and studies a concept of algebraizable sequential logic, a generalized notion of a logical system that covers, on a uniform basis, sequential systems and the quasi-equational theories of quasivarieties in Mal'tsev's sense. The author defines a concept of equivalence between generalized logics so that a logic is considered to be ...
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A Logical Modeling of Severe Ignorance. [PDF]