Tense like equality algebras
Authors
Abstract:
In this paper, first we define the notion of involutive operator on bounded involutive equality algebras and by using it, we introduce a new class of equality algebras that we called it a tense like equality algebra. Then we investigate some properties of tense like equality algebra. For two involutive bounded equality algebras and an equality homomorphism between them, we prove that the tense like equality algebra structure can be transfer by this equality homomorphism. Specially, by using a bounded involutive equality algebra and quotient structure of it, we construct a quotient tense like equality algebra. Finally, we investigate the relation between tense like equality algebras and tense MV-algebras.
similar resources
TENSE OPERATORS ON SHn-ALGEBRAS
In 1982, L. Iturrioz introduced symmetrical Heyting algebras of order n (or SHnalgebras). In this paper, we define and study tense SHn-algebras namely, SHnalgebras endowed with two tense operators. These algebras constitute a generalization of tense Łukasiewicz-Moisil algebras. Our main interest is the duality theory for tense SHn-algebras. In order to do this, we requiere Esakia’s duality for ...
full textState Pseudo Equality Algebras
Pseudo equality algebras were initially introduced by Jenei and Kóródi as a possible algebraic semantic for fuzzy type theory, and they have been revised by Dvurečenskij and Zahiri under the name of JK-algebras. The aim of this paper is to investigate the internal states and the state-morphisms on pseudo equality algebras. We define and study new classes of pseudo equality algebras, such as com...
full textCommutative pseudo-equality algebras
Pseudo equality algebras were initially introduced by Jenei and Kóródi as a possible algebraic semantic for fuzzy type theory, and they have been revised by Dvurečenskij and Zahiri under the name of JK-algebras. In this paper we define and study the commutative pseudo equality algebras. We give a characterization of commutative pseudo equality algebras and we prove that an invariant pseudo equa...
full textTense Operators on MV-Algebras and Lukasiewicz-Moisil Algebras
We introduce the tense LMn-algebras and the tense MV algebras as algebraic structures for some tense many-valued logics. A representation theorem for tense LMn-algebras is proved and the polynomially equivalence between tense LM3-algebras (resp. tense LM4-algebras) and tense MV3-algebras (resp. tense MV4-algebras) is established. We study the pairs of dually-conjugated operations on MV -algebra...
full textTense Operators on m–Symmetric Algebras
Here we initiate an investigation of the equational classes of m– symmetric algebras endowed with two tense operators. These varieties is a generalization of tense algebras. Our main interest is the duality theory for these classes of algebras. In order to do this, we require Urquart’s duality for Ockham algebras and Goldblatt’s duality for bounded distributive lattice with operations. The dual...
full textAlgebraic Logic Iv. Equality in Polyadic Algebras
Introduction. A standard way to begin the study of symbolic logic is to describe one after another the propositional calculus, the monadic functional calculus, the pure first-order functional calculus, and the functional calculus with equality. The algebraic aspects of these logical calculi belong to the theories of Boolean algebras, monadic algebras, polyadic algebras, and cylindric algebras r...
full textMy Resources
Journal title
volume 13 issue 1
pages 143- 166
publication date 2020-07-01
By following a journal you will be notified via email when a new issue of this journal is published.
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023