Tense Operators on MV-Algebras and Łukasiewicz-Moisil Algebras

Article type: Research Article

Authors: Diaconescu, Denisa | Georgescu, George

Affiliations: Faculty of Mathematics and Informatics, University of Bucharest, Str. Academiei Nr. 14, Bucharest, Romania. E-mail: ddenisuca@yahoo.com; georgescu@funinf.cs.unibuc.ro

Abstract: We introduce tense LM_n-algebras and tense MV-algebras as algebraic structures for some tense many-valued logics. A representation theorem for tense LM_n-algebras is proved and the polynomial equivalence between tense LM_3-algebras (resp. tense LM_4-algebras) and tense MV_3-algebras (resp. tense MV_4-algebras) is established. We study the pairs of dually-conjugated operations on MV-algebras and we use their properties in order to investigate how the axioms of tense operators are preserved by the Dedekind-MacNeille completion of an Archimedean MV-algebra. A tense many-valued propositional calculus is developed and a completeness theorem is proved.

Keywords: tense Łukasiewicz-Moisil algebra, tense MV-algebra, tense Moisil logic

Journal: Fundamenta Informaticae, vol. 81, no. 4, pp. 379-408, 2007