Monadic GMV-algebras

Abstract

Monadic M V -algebras are an algebraic model of the predicate calculus of the Lukasiewicz infinite valued logic in which only a single individual variable occurs. GM V -algebras are a non-commutative generalization of M V -algebras and are an algebraic counterpart of the non-commutative Lukasiewicz infinite valued logic. We introduce monadic GM V -algebras and describe their connections to certain couples of GM V -algebras and to left adjoint mappings of canonical embeddings of GM Valgebras. Furthermore, functional M GM V -algebras are studied and polyadic GM Valgebras are introduced and discussed.

Operators on Pavelka's algebras induced by fuzzy relations

“…There exist several generalizations of monadic operators for another structures [27,28] but monadic operators on structures with no double negation law lost natural Galois connections and obtained results are weaker.…”

Monadic NM-algebras

“…Inspired by this, monadic Heyting algebras, an algebraic model of the one-variable fragment of the intuitionistic predicate logic, were introduced and developed in [1,14,15]. Subsequently, monadic MV-algebras, an algebraic model of the one element fragment of Lukasiewicz predicate logic, were introduced and studied in [7,18,19]. After then, monadic BL-algebras, monadic residuated lattices, monadic basic algebras and monadic residuated ℓ-monoids were introduced and investigated in [10,20,6,21].…”

Tense Polyadic N × M-Valued Łukasiewicz–Moisil Algebras

“…This subject caused great interest and led several authors to deepen and generalized the algebras defined by Halmos, to such an extent that research is still being conducted in this direction. For instance, the classes of polyadic Heyting algebras ( [25]), polyadic MV-algebras ( [30]), polyadic BL-algebras ( [12]), polyadic θ-valued Lukasiewicz-Moisil algebras ( [1]), polyadic GMV-algebras ( [23]), to mention a few.…”