The main aim of this talk is twofold. Firstly, to present an elementary method based on Farkas’ lemma for rationals how to embed any finite partial subalgebra of a linearly ordered MV-algebra into Q [0; 1] and then to establish a new elementary proof of the completeness of the Lukasiewicz axioms for which the MV-algebras community has been looking for a long time. Secondly, to present a direct ...

In this paper, we introduce a new of BH-algebra and pseudo BH-algebra. We call covid-19 Also, give the concepts ( BH-algebra, ). And study some relationships between them.

This paper is an attempt at developing a theory of algebraic systems that would correspond in a natural fashion to the N0-valued prepositional calculus^). For want of a better name, we shall call these algebraic systems MV-algebras where MV is supposed to suggest many-valued logics. It is known that the classical two-valued logic gives rise to the study of Boolean algebras and, as can be expect...

MV-algebras were introduced by Chang as an algebraic counterpart of the Lukasiewicz infinite-valued logic. D. Mundici proved that the category of MV-algebras is equivalent to the category of abelian l-groups with strong unit. A. Di Nola and A. Lettieri established a categorical equivalence between the category of perfect MV-algebras and the category of abelian l-groups. In this paper we investi...

We consider a non-associative generalization of MV-algebras. The underlying posets of our non-associative MV-algebras are not lattices, but they are related to so-called λ-lattices. c ©2007 Mathematical Institute Slovak Academy of Sciences 1. Non-associative MV-algebras As known, MV-algebras were introduced in the late-fifties by C . C . C h a n g as an algebraic semantics of the Lukasiewicz ma...

In his classical paper 1 , Chang invented the notion of MV-algebra in order to provide an algebraic proof of the completeness theorem of infinite valued Lukasiewicz propositional calculus. Recently, the algebraic theory of MV-algebras is intensively studied, see 2–5 . The notion of derivation, introduced from the analytic theory, is helpful to the research of structure and property in algebraic...

Imai and Iséki [1] introduced the concept of BCK-algebra as a generalization of notions of set difference operation and propositional calculus. The notion of pseudo-BCK algebra was introduced by Georgescu and Iorgulescu [2] as generalization of BCK-algebras not assuming commutativity. Hájek [3] introduced the concept of BL-algebras as the general semantics of basic fuzzy logic (BL-logic). Iorgu...

This paper presents an algebraic approach of some many-valued generalizations of modal logic. The starting point is the de nition of the [0, 1]-valued Kripke models, where [0, 1] denotes the well known MV-algebra. Two types of structures are used to de ne validity of formulas: the class of frames and the class of Šn-valued frames. The latter structures are frames in which we specify in each wor...

Characterizations of fuzzy ideals of a pseudo-BCK algebra are established. Conditions for a fuzzy set to be a fuzzy ideal are given. Given a fuzzy set μ, the least fuzzy ideal containing μ is constructed. The homomorphic properties of fuzzy ideals of a pseudoBCK algebra are provided. Finally, characterizations of Noetherian pseudo-BCK algebras and Artinian pseudo-BCK algebras via fuzzy ideals a...