Localization of semi-Heyting algebras

In this note, we introduce the notion of ideal on semi-Heyting algebras which allows us to consider a topology on them. Besides, we define the concept of F−multiplier, where F is a topology on a semi-Heyting algebra L, which is used to construct the localization semi-Heyting algebra LF. Furthermore, we prove that the semi-Heyting algebra of fractions LS associated with an ∧−closed system S of L is a semi-Heyting of localization. Finally, in the finite case we prove that LS is isomorphic to a special subalgebra of L. Since Heyting algebras are a particular case of semi-Heyting algebras, all these results generalize those obtained in [11].Fil: Figallo, Aldo Victorio. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Instituto de Ciencias Básicas; ArgentinaFil: Pelaitay, Gustavo Andrés. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Instituto de Ciencias Básicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentina. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Departamento de Matemática; Argentin

Remarks on Heyting algebras with tense operators

The concept of tense operators on Heyting algebras was introduced in [3]. The aim of this paper is to prove, that the set of axioms proposed by I. Chajda in [3, Definition 1], is a dependent axioms system and show that tense operators F and P can not be regarded as existential quantifiers.Fil: Figallo, Aldo Victorio. Universidad Nacional de San Juan; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Pelaitay, Gustavo Andrés. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

A topological duality for tense θ -valued Łukasiewicz–Moisil algebras

In 2011, tense θ-valued Łukasiewicz–Moisil algebras (or tense LM θ -algebras) were introduced by Chiriţă as an algebraic counterpart of the tense θ-valued Moisil propositional logic. In this paper we develop a topological duality for these algebras. In order to achieve this we extend the topological duality given in Figallo et al. (J Mult Valued Logic Soft Comput 16(3–5):303–322, 2010), for θ-valued Łukasiewicz–Moisil algebras. This new topological duality enables us to describe the tense LM θ -congruences and the tense θLM θ -congruences on a tense LM θ -algebra and also to determine some properties of these algebras.Fil: Figallo, Aldo Victorio. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Instituto de Ciencias Básicas; ArgentinaFil: Pascual, Inés. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Instituto de Ciencias Básicas; Argentina. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Departamento de Matemática; ArgentinaFil: Pelaitay, Gustavo Andrés. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Instituto de Ciencias Básicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentin

Discrete duality for 3-valued Lukasiewicz-Moisil algebras

In 2011, Düntsch and Orlowska obtained a discrete duality for regular double Stone algebras. On the other hand, it is well known that regular double Stone algebras are polinominally equivalent to 3-valued Lukasiewicz-Moisil algebras (or LM3-algebras). In [R. Cignoli, Injective De Morgan and Kleene algebra, Proc. Amer. Math. Soc. 47 (1975) 269-278], LM3-algebras are considered as a Kleene algebras (L,∨,∧,∼, 0, 1) endowed with a unary operation : L → L, satisfying the properties: a∨ ∼ a = 1, ∼ a ∧ a = a∧ ∼ a and a∨b ≤(a ∨ b). Motivated by this result, in this paper, we determine another discrete duality for LM3-algebras, extending the discrete duality to De Morgan algebras described in [W. Dzik, E. Orlowska and C. van Alten, Relational representation theorems for general lattices with negations, in Relations and Kleene Algebra in Computer Science, Lecture Notes in Computer Science, Vol. 4136 (Springer, Berlin, 2006), pp. 162-176].Fil: Pelaitay, Gustavo Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentina. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes; Argentin

Tense operators on De Morgan algebras

The purpose of this article is to investigate the variety of algebras, which we call tense De Morgan algebras, as a natural generalization of tense algebras developed in Burges (1984, Handbook of Philosophical Logic, vol. II, pp. 89–139) (see also, Kowalski (1998, Rep. Math. Logic, 32, 53–95)). It is worth mentioning that the latter is a proper subvariety of the first one, as it is shown in a simple example. Our main interest is the representation theory for these classes of algebras.Fil: Figallo, Aldo Victorio. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Instituto de Ciencias Básicas; ArgentinaFil: Pelaitay, Gustavo Andrés. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Instituto de Ciencias Básicas; Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentin

Localization of tetravalent modal algebras

The main aim of this paper is to define the localization of a tetravalent modal algebra (Formula presented.) with respect to a topology (Formula presented.) on (Formula presented.). In Sec. 5, we prove that the tetravalent modal algebra of fractions relative to a ∧-closed system (defined in Definition 3.1) is a tetravalent modal algebra of localization.Fil: Figallo, Aldo Victorio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentina. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Instituto de Ciencias Básicas; ArgentinaFil: Pelaitay, Gustavo Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentina. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Instituto de Ciencias Básicas; Argentina. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Departamento de Matemática; Argentin

A Topological Duality for k x j-rough Heyting Algebras

k-rough Heyting algebras were introduced by Eric San Juan as an algebraic formalism for reasoning on finite increasing sequences over Boolean algebras in general and on generalizations of rough set concepts in particular. In this paper, k × j-rough Heyting algebras are defined and investigated. These algebras constitute an extension of Heyting algebras and in j = 2 case they coincide with k-rough Heyting algebras. The aim of this paper is to give a topological study for these new class of algebras.Fil: Almiñana Reinoso, Federico Gabriel. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Instituto de Ciencias Básicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; ArgentinaFil: Pelaitay, Gustavo Andrés. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Instituto de Ciencias Básicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentin

Monadic k x j-rough Heyting algebras

In this paper, we introduce the variety of algebras, which we call monadic kxj-rough Heyting algebras. These algebras constitute an extension of monadic Heyting algebras and in 3x2 case they coincide with monadic 3-valued Lukasiewicz--Moisil algebras. Our main interest is the characterization of simple and subdirectly irreducible monadic kxj-rough Heyting algebras. In order to this, an Esakia-style duality for these algebras is developed.Fil: Almiñana Reinoso, Federico Gabriel. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Instituto de Ciencias Básicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; ArgentinaFil: Pelaitay, Gustavo Andrés. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Instituto de Ciencias Básicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentin

Discrete duality for TSH-algebras

In this article, we continue the study of tense symmetric Heyting algebras (or TSH-algebras). These algebras constitute a generalization of tense algebras. In particular, we describe a discrete duality for TSH-algebras bearing in mind the results indicated by Or lowska and Rewitzky in [E. Orlowska and I. Rewitzky, Discrete Dualities for Heyting Algebras with Operators, Fund. Inform. 81 (2007), no. 1-3, 275-295] for Heyting algebras. In addition, we introduce a propositional calculus and prove this calculus has TSH-algebras as algebraic counterpart. Finally, the duality mentioned above allowed us to show the completeness theorem for this calculus.Fil: Figallo, Aldo Victorio. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Instituto de Ciencias Básicas; ArgentinaFil: Pelaitay, Gustavo Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Instituto de Ciencias Básicas; ArgentinaFil: Sanza, Claudia. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Instituto de Ciencias Básicas; Argentin

Principal and boolean congruences on IKt-Algebras

The IKt-algebras were introduced in the paper An algebraic axiomatization of the Ewald’s intuitionistic tense logic by the first and third author. In this paper, our main interest is to investigate the principal and Boolean congruences on IKt-algebras. In order to do this we take into account a topological duality for these algebras obtained in Figallo et al. (Stud Log 105(4):673–701, 2017). Furthermore, we characterize Boolean and principal IKt-congruences and we show that Boolean IKt-congruence are principal IKt-congruences. Also, bearing in mind the above results, we obtain that Boolean IKtcongruences are commutative, regular and uniform. Finally, we characterize the principal IKt-congruences in the case that the IKt-algebra is linear and complete whose prime filters are complete and also the case that it is linear and finite. This allowed us to establish that the intersection of two principal IKt-congruences on these algebras is a principal one and also to determine necessary and sufficient conditions so that a principal IKt-congruence is a Boolean one on theses algebrasFil: Figallo, Aldo Victorio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentina. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Instituto de Ciencias Básicas; ArgentinaFil: Pascual, Inés Inés. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Departamento de Matemática; Argentina. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Instituto de Ciencias Básicas; ArgentinaFil: Pelaitay, Gustavo Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentina. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Instituto de Ciencias Básicas; Argentin