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

Several algebraic structures (namely HW, BZMV^dM, Stonean MV and MV_Δ 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.