Super-\L ukasiewicz logics expanded by Δ\Delta

Baaz's operator $\Delta$ was introduced (by Baaz) in order to extend G\"odel logics, after that this operator was used to expand fuzzy logics by H\'ajek in his celebrated book. These logics were called $\Delta$-fuzzy logics. On the other hand, possibility operators were studied in the setting of \L ukasiewicz-Moisil algebras; curiously, one of these operators coincide with the Baaz's one. In this paper, we study the $\Delta$ operator in the context of ($n$-valued) Super-\L ukasiewicz logics. An algebraic study of these logics is presented and the cardinality of Lindembaun-Tarski algebra with a finite number of variables is given. Finally, as a by-product, we present an alternative axiomatization of H\'ajek's \L ukasiwicz logic expanded with $\Delta$

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

Tense distributive lattices: algebra, logic and topology

Tense logic was introduced by Arthur Prior in the late 1950s as a result of his interest in the relationship between tense and modality. Prior's idea was to add four primitive modal-like unary connectives to the base language today widely known as Prior's tense operators. Since then, Prior's operators have been considered in many contexts by different authors, in particular, in the context of algebraic logic. Here, we consider the category tdlat of bounded distributive lattices equipped with Prior's tense operators. We establish categorical dualities for tdlat in terms of certain categories of Kripke frames and Priestley spaces, respectively. As an application, we characterize the congruence lattice of any tense distributive lattice as well as the subdirectly irreducible members of this category. Finally, we define the logic that preserves degrees of truth with respect to tdlat-algebras and precise the relation between particular sub-classes of tdlat and know tense logics found in the literature

Liberal, masón y socialista : El exilio de Jiménez de Asúa en la Argentina, 1939-1970

Estudiar el exilio de Luis Jiménez de Asúa en la Argentina comporta una tarea historiográfica compleja. Se trata de una intensa personalidad que atraviesa con parejo protagonismo cincuenta años de la historia española y argentina y que implica, a la vez, desandar diferentes circuitos de relacionamiento exiliar, el de su adscripción al republicanismo liberal, al socialismo y a la masonería, permitiendo un estudio transnacional que, producto de su desempeño académico y profesional, se derrama también sobre América Latina. Significa también recorrer los distintos momentos que atravesó el exilio antifranquista, desde la lucha y la denuncia a una languideciente resistencia testimonial no exenta de persecuciones. Pero además, historiar su derrotero vital constituye tanto una oportunidad como un desafío pues la documentación disponible sobre Jiménez de Asúa es inmensa: desde la organizada disponibilidad de sus papeles que ofrecen en Alcalá de Henares el Archivo de la Fundación Pablo Iglesias y el Centro Documental de la Memoria Histórica de Salamanca, el Archivo de Asuntos Exteriores de España en Madrid, el rastro que ha dejado su paso por universidades argentinas, hasta su casi millar de libros, artículos, prólogos, notas, conferencias y contribuciones en la prensa periódica, producto de una capacidad creadora enorme, donde las referencias al exilio español son numerosas. Así, reconstruir la rica experiencia exiliar de Jiménez de Asúa en la Argentina exige navegar por un mar de testimonios y por ello esta ponencia constituye un anticipo de una investigación en larga ejecución.Instituto de Investigaciones en Humanidades y Ciencias Sociales (IdIHCS

Non-deterministic algebraization of logics by swap structures1

Multialgebras have been much studied in mathematics and in computer science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic framework for dealing with several Logics of Formal Inconsistency that cannot be semantically characterized by a single finite matrix. In particular, these LFIs are not algebraizable by the standard tools of abstract algebraic logic. In this paper, the first steps towards a theory of non-deterministic algebraization of logics by swap structures are given. Specifically, a formal study of swap structures for LFIs is developed, by adapting concepts of universal algebra to multialgebras in a suitable way. A decomposition theorem similar to Birkhoff’s representation theorem is obtained for each class of swap structures. Moreover, when applied to the 3-valued algebraizable logics J3 and Ciore, their classes of algebraic models are retrieved, and the swap structures semantics become twist structures semantics. This fact, together with the existence of a functor from the category of Boolean algebras to the category of swap structures for each LFI, suggests that swap structures can be seen as non-deterministic twist structures. This opens new avenues for dealing with non-algebraizable logics by the more general methodology of multialgebraic semantics