Algebraic Structures Related to Many Valued Logical Systems. Part II: Equivalence Among some Widespread Structures

Article type: Research Article

Authors: Cattaneo, Gianpiero | Ciucci, Davide | Giuntini, Roberto | Konig, Martin

Affiliations: Dipartimento di Informatica Sistemistica e Comunicazione, Università di Milano – Bicocca, Via Bicocca degli Arcimboldi 8, 20126 Milano, Italia | Dipartimento di Scienze Pedagogiche e Filosofiche, Università di Cagliari, Via Is Mirrionis 1, 09123 Cagliari, Italia

Abstract: Several algebraic structures (namely HW, BZMVdM, Stonean MV and MVΔ algebras) related to many valued logical systems are considered and their equivalence is proved. Four propositional calculi whose Lindenbaum–Tarski algebra corresponds to the four equivalent algebraic structures are axiomatized and their semantical completeness is given.

Journal: Fundamenta Informaticae, vol. 63, no. 4, pp. 357-373, 2004