Résume | In the literature there are several papers on the study of quantifiers in non-classical logics. Part of these works consists of considering the fragment corresponding to the study of monadic logic, that is, the fragment where the predicate symbols depend only on a fixed variable or a constant symbol. Although the connectives of propositional logic are non-classical, quantifiers are interpreted in the classical sense. The purpose of this paper is to introduce different notions of quantifiers in the particular case of the infinite valued logic (IVL) developed by Lukasiewicz. The algebraic models of this theory turn out to be MV algebras endowed with an additional operator, where MV-algebras are the algebraic models corresponding to the logic IVL. When quantifiers are interpreted classically, these structures are called monadic MV-algebras and are generalizations of the well known monadic Boolean algebras introduced by Halmos [Ha62].
References:
[Ha62] P. Halmos, Algebraic Logic, Chelsea Publishing Company, 1962.
[Sch77] Schwartz, D., Theorie der polyadischen MV-algebren endlicher Ordnung, Math. Nachr., 78 (1977) 131--138.
[Sch80] Schwartz, D., Polyadic MV-algebras, Zeitschrift f\"*u*r Math. Logik und Grundla\-gen der Mathematik, 26 (1980) 561--564 . |