Tense Operators on MV-Algebras and Łukasiewicz-Moisil Algebras

  • Authors:

  • Denisa Diaconescu;George Georgescu

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

  • Venue:
  • Fundamenta Informaticae
  • Year:
  • 2007

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Abstract

We introduce tense LM_n-algebras and tense MV-algebras asalgebraic structures for some tense many-valued logics. Arepresentation theorem for tense LM_n-algebras is proved and thepolynomial equivalence between tense LM_3-algebras (resp. tenseLM_4-algebras) and tense MV_3-algebras (resp. tenseMV$_4$-algebras) is established. We study the pairs ofdually-conjugated operations on MV-algebras and we use theirproperties in order to investigate how the axioms of tenseoperators are preserved by the Dedekind-MacNeille completion of anArchimedean MV-algebra. A tense many-valued propositional calculusis developed and a completeness theorem is proved.