Tense Operators on MV-Algebras and Lukasiewicz-Moisil Algebras

We introduce the tense LMn-algebras and the tense MV algebras as algebraic structures for some tense many-valued logics. A representation theorem for tense LMn-algebras is proved and the polynomially equivalence between tense LM3-algebras (resp. tense LM4-algebras) and tense MV3-algebras (resp. tense MV4-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.