An algebraic study of the first order version of some implicational fragments of the three-valued Lukasiewicz logic

2020/10/23 by Aldo Figallo-Orellano, Figallo-Orellano, Aldo, Juan Sebastián Slagter +1
Computer Science · #Advanced Algebra and Logic #FOS: Computer and information sciences #Logic in Computer Science (cs.LO)

paper · pdf · doi:10.48550/arxiv.2011.09868

openalex publication_date 2020/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

MV-algebras are an algebraic semantics for Lukasiewicz logic and MV-algebras generated by a finite chain are Heyting algebras where the Godel implication can be written in terms of De Morgan and Moisil's modal operators. In our work, a fragment of trivalent Lukasiewicz logic is studied. The propositional and first-order logic is presented. The maximal consistent theories are studied as Monteiro's maximal deductive systems of the Lindenbaum-Tarski algebra, in both cases. Consequently, the adequacy theorem with respect to the suitable algebraic structures is proven.

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