In this work we provide a new topological representation for implication algebras in such a way that its one-point compactification is the topological space given in [1]. Some applications are given thereof.

An algebraically expandable (AE) class is a class of algebraic structures axiomatizable by sentences of the form $\forall \exists! \mathop{\boldsymbol {\bigwedge }}\limits p = q$. For a logic L algebraized by a quasivariety $\mathcal {Q}$ we show that the AE-subclasses of $\mathcal {Q}$ correspond to certain natural expansions of L, which we call algebraic expansions. These turn out to be a special case of the expansions by implicit connectives studied by X. Caicedo. We proceed to characterize all the AE-subclasses of (...) abelian $\ell $ -groups and perfect MV-algebras, thus fully describing the algebraic expansions of their associated logics. (shrink)

In this paper we study the subdirectly irreducible algebras in the variety of pseudocomplemented De Morgan algebras by means of their De Morgan p‐spaces. We introduce the notion of the body of an algebra and determine when is subdirectly irreducible. As a consequence of this, in the case of pseudocomplemented Kleene algebras, two special subvarieties arise naturally, for which we give explicit identities that characterise them. We also introduce a subvariety of, namely the variety of bundle pseudocomplemented Kleene algebras, fully (...) describe its subvariety lattice and find explicit equational bases for each subvariety. In addition, we study the subvariety of generated by the simple members of, determine the structure of the free algebra over a finite set in this variety and their finite weakly projective algebras. (shrink)

In this paper we extend Mundici’s functor Γ to the category of monadic MV-algebras. More precisely, we define monadic ℓ -groups and we establish a natural equivalence between the category of monadic MV-algebras and the category of monadic ℓ -groups with strong unit. Some applications are given thereof.

There is a constructive method to define a structure of simple k -cyclic Post algebra of order p , L p , k , on a given finite field F ( p k ), and conversely. There exists an interpretation Φ 1 of the variety $${\mathcal{V}(L_{p,k})}$$ generated by L p , k into the variety $${\mathcal{V}(F(p^k))}$$ generated by F ( p k ) and an interpretation Φ 2 of $${\mathcal{V}(F(p^k))}$$ into $${\mathcal{V}(L_{p,k})}$$ such that Φ 2 Φ 1 ( B ) (...) = B for every $${B \in \mathcal{V}(L_{p,k})}$$ and Φ 1 Φ 2 ( R ) = R for every $${R \in \mathcal{V}(F(p^k))}$$. In this paper we show how we can solve an algebraic system of equations over an arbitrary cyclic Post algebra of order p, p prime, using the above interpretation, Gröbner bases and algorithms programmed in Maple. (shrink)

This paper is devoted to the study of some subvarieties of the variety Qof Q-Heyting algebras, that is, Heyting algebras with a quantifier. In particular, a deeper investigation is carried out in the variety Q 3 of three-valued Q-Heyting algebras to show that the structure of the lattice of subvarieties of Qis far more complicated that the lattice of subvarieties of Heyting algebras. We determine the simple and subdirectly irreducible algebras in Q 3 and we construct the lattice of subvarieties (...) (Q 3 ) of the variety Q 3. (shrink)

This paper is devoted to the study of some subvarieties of the variety Q of Q-Heyting algebras, that is, Heyting algebras with a quantifier. In particular, a deeper investigation is carried out in the variety Q subscript 3 of three-valued Q-Heyting algebras to show that the structure of the lattice of subvarieties of Q is far more complicated that the lattice of subvarieties of Heyting algebras. We determine the simple and subdirectly irreducible algebras in Q subscript 3 and we construct (...) the lattice of subvarieties lambda (Q subscript 3) of the variety Q subscript 3. (shrink)

In this paper we prove that the free pseudocomplemented residuated lattices are decomposable if and only if they are Stone, i.e., if and only if they satisfy the identity ¬ x ∨ ¬¬ x = 1. Some applications are given.

In this paper we study some questions concerning Łukasiewicz implication algebras. In particular, we show that every subquasivariety of Łukasiewicz implication algebras is, in fact, a variety. We also derive some characterizations of congruence permutable algebras. The starting point for these results is a representation of finite Łukasiewicz implication algebras as upwardly-closed subsets in direct products of MV-chains.

Łukasiewicz implication algebras are {→,1}-subreducts of Wajsberg algebras (MV-algebras). They are the algebraic counterpart of Super-Łukasiewicz Implicational logics investigated in Komori, Nogoya Math J 72:127–133, 1978. The aim of this paper is to study the direct decomposability of free Łukasiewicz implication algebras. We show that freely generated algebras are directly indecomposable. We also study the direct decomposability in free algebras of all its proper subvarieties and show that infinitely freely generated algebras are indecomposable, while finitely free generated algebras can be (...) only decomposed into a direct product of two factors, one of which is the two-element implication algebra. (shrink)

Łukasiewicz implication algebras are the {→,1}-subreducts of MV- algebras. They are the algebraic counterpart of Super-Łukasiewicz Implicational Logics investigated in Komori (Nogoya Math J 72:127–133, 1978). In this paper we give a description of free Łukasiewicz implication algebras in the context of McNaughton functions. More precisely, we show that the |X|-free Łukasiewicz implication algebra is isomorphic to ${\bigcup_{x\in X} [x_\theta)}$ for a certain congruence θ over the |X|-free MV-algebra. As corollary we describe the free algebras in all subvarieties of Łukasiewicz (...) implication algebras. (shrink)

In this paper we continue the study of the variety \ of monadic Gödel algebras. These algebras are the equivalent algebraic semantics of the S5-modal expansion of Gödel logic, which is equivalent to the one-variable monadic fragment of first-order Gödel logic. We show three families of locally finite subvarieties of \ and give their equational bases. We also introduce a topological duality for monadic Gödel algebras and, as an application of this representation theorem, we characterize congruences and give characterizations of (...) the locally finite subvarieties mentioned above by means of their dual spaces. Finally, we study some further properties of the subvariety generated by monadic Gödel chains: we present a characteristic chain for this variety, we prove that a Glivenko-type theorem holds for these algebras and we characterize free algebras over n generators. (shrink)

AbstractŁukasiewicz implication algebras are {→,1}-subreducts of Wajsberg algebras (MV-algebras). They are the algebraic counterpart of Super-Łukasiewicz Implicational logics investigated in Komori, Nogoya Math J 72:127–133, 1978. The aim of this paper is to study the direct decomposability of free Łukasiewicz implication algebras. We show that freely generated algebras are directly indecomposable. We also study the direct decomposability in free algebras of all its proper subvarieties and show that infinitely freely generated algebras are indecomposable, while finitely free generated algebras can be (...) only decomposed into a direct product of two factors, one of which is the two-element implication algebra. (shrink)

AbstractŁukasiewicz implication algebras are the {→,1}-subreducts of MV- algebras. They are the algebraic counterpart of Super-Łukasiewicz Implicational Logics investigated in Komori (Nogoya Math J 72:127–133, 1978). In this paper we give a description of free Łukasiewicz implication algebras in the context of McNaughton functions. More precisely, we show that the |X|-free Łukasiewicz implication algebra is isomorphic to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bigcup_{x\in X} [x_\theta)}$$\end{document} for a certain congruence θ over the |X|-free MV-algebra. As corollary we (...) describe the free algebras in all subvarieties of Łukasiewicz implication algebras. (shrink)

This study details the methodological process for creating a tool for the identification of COVID-19 potential contagion situations in sports and physical education before, during, and after practice and competition. It is a tool that implies an educational and methodological process with all the agents of the sports system. This tool identifies the large number of interactions occurring through sports action and everything that surrounds it in training, competition, and organization. The aim is to prepare contingency protocols based on an (...) exhaustive analysis, risk detection, and proposal of contingency measures trying to reduce the residual risk to a minimum. In the second part, the results of the implementation of this tool in the sports system of Galicia (Spain) are shown. The technicians have changed their perceptions about the coronavirus transmission in sports. They highlight the problem for returning to sports participation for athletes under 18 years in the pandemic context. (shrink)

There is a constructive method to define a structure of simple k-cyclic Post algebra of order p, L p,κ, on a given finite field F, and conversely. There exists an interpretation Ф₁ of the variety V generated by L p,κ into the variety V) generated by F and an interpretation Ф₂ of V) into V such that Ф₂Ф₁ = B for every B ϵ V and Ф₁₂ = R for every R ϵ V). In this paper we show how we (...) can solve an algebraic system of equations over an arbitrary cyclic Post algebra of order p, p prime, using the above interpretation, Gröbner bases and algorithms programmed in Maple. (shrink)

Proyecto: REFERENCIA: RTI2018-093498-B-I00 I.P. 1: JOSE LUIS TASSET CARMONA TÍTULO: ESIS Y EFINICION DE LA MATRIZ CONCEPTUAL DEL ARADIGMA TILITARISTA DE ACIONALIDAD. ACRÓNIMO: GEN-RED-PUR.

Partiendo de la comprensión de Heidegger en torno a los pensadores del inicio desplegada en los cuatros cursos de principios de los años cuarenta del siglo XX, querríamos mostrar la lectura de Heidegger de los pensadores del inicio en contraste con la de Gadamer en torno a los «presocráticos» mostrada en El inicio de la Filosofía occidental. Estudiaremos para ello la palabra Anfang en uno y otro autor contextualizando sus aproximaciones hermenéuticas a los textos griegos. Finalmente prestaremos atención a la (...) interpretación del poema de Parménides de Elea en El Inicio de la Filosofía occidental. Además de una diversa comprensión del final de la filosofía y la tarea del pensar, se nos irá revelando cómo Heidegger despliega indicaciones en torno a la articulación del pensar y la palabra en los pensadores del inicio, mientras Gadamer hace referencias al «valor poético» del poema de Parménides. Tras recorrer los diversos fragmentos transmitidos del poema, concluiremos señalando cómo la cuestión del ser y la verdad interpretada por Gadamer en Parménides remite a la pregunta por el carácter unitario —o al problema del continuo— de la presencia o aparecer que dice «ser», henologicamiente incomprensible sin atender a los cruces ἀλήθεια y φύσις. (shrink)

The objective of this paper is to make a rhetorical analysis of the op-ed entitled «Finding Design in Nature» by Cardinal Christoph Schönborn, Archbishop of Vienna, published by The New York Times in 2005, three months after the death of John Paul II. In this essay, the Cardinal states that it is an error to affirm that Catholic doctrine is compatible with the «neo-Darwinist» theory of evolution and that the Roman Catholic Church accepts that theory. For the Archbishop, the origin (...) of this error lies in the abuses committed in the interpretation of John Paul’s 1996 speech in which the Pope affirmed that evolution was more than a hypothesis and showed himself more favourable towards evolutionary theory than his predecessors. In his article the Cardinal described that papal message as «vague and unimportant». In this paper, the rhetorical techniques used by Schönborn in his article are analysed: the lexical choices to make a negative assessment of «neo Darwinist» evolutionary theory; the argumentative definition to make a polemical description of that theory; and the polyphonic proceedures designed to decontextualise the papal discourse and present Catholic beliefs as the truth. We interpret Cardinal Schönborn’s position as a rhetorical change with respect to John Paul II’s 1996 speech. From our point of view, the Archbishop directed his criticism against evolutionary theory not only because of its scientific theories (not rejected by Church teaching) but also for being potentially dangerous in its use by certain authors as a scientific argument in defence of their atheism. (shrink)

El artículo tiene por objetivo cuestionar la institucionalidad educativa y los nuevos actores que van transformando la relación enseñanza/aprendizaje, su potencialidad democrática y los saberes adecuados para la actualidad y el futuro próximo. Esto se realiza, a través de una discusión con el Transhumanismo y el Capitalismo Cognitivo, analizando los riesgos y las posibilidades pedagógicas y normativas que abren estas transformaciones. Además, por el examen de las perspectivas epistemológicas-educativas decoloniales y transmodernas, que buscan movilizar contenidos y formas de reflexión democráticas, (...) emancipadoras y alternativas para la construcción de otros futuros de la educación, que denominamos transeducación. (shrink)

La política de desarrollo regional constituye una de las principales herramientas con las que cuenta la Administración pública para impulsar un modelo de desarrollo económico regional descentralizado en razón a las potencialidades endógenas de las diferentes regiones. Por tanto, la concreción de un modelo de política indicativa destinada a ser implementada en los territorios regionales españoles, como es el caso de Galicia, pretende ejercer de motor de arrastre para incentivar el desarrollo económico del territorio en base a sus potencialidades internas. (...) Galicia, durante mucho tiempo de su historia, ha estado padeciendo el enclavamiento territorial. (shrink)

El conocimiento del medio urbano de La Coruña constituye una temática básica para el estudio de la realidad territorial regional de Galicia. Así, el análisis del modelo de ciudad, su evolución histórica, su red urbana y sus características territoriales, nos facilitan la interpretación de la conformación evolutiva de la red urbana. Para ello, al estudiar mediante el manejo de las diferentes cartografías históricas de la ciudad podremos disponer de una relevante información sobre sus características físicas y territoriales; su articulación en (...) el sistema urbano español, etc. (shrink)

This article presents the stance taken by José Ortega y Gasset in the debate that took place in early-twentieth-century Spain regarding the convenience of reading Don Quixote in schools. To this end, we start by describing, albeit briefly, the state of Ortega y Gasset’s thought in 1920, when he writes Biología y pedagogía, the essay with which we shall concern ourselves. According to Ortega y Gasset, Don Quixote must not be read in the classroom because it does not contribute (...) to the development of the students’ spontaneous life, or natura naturans. In order to foster this development, Ortega y Gasset suggests leaving Don Quixote aside and resort to myths such as Odysseus or Heracles because their exploits would excite the students’ vital pulse. However, we suggest several reasons why the aim stated by Ortega y Gasset —and several other highly valuable educational benefits— could be reached resorting to the reading of selected passages of Don Quixote instead of the feats of Odysseus and Heracles. (shrink)

El presente artículo invita a considerar la dimensión política de la obra de Lorenzo Hervás y Panduro como una pieza crítica que desde el universalismo de la filosofía cristiana replantea la reelaboración moderna de los ideales cosmopolitas antiguos (de raíz cínica uno, estoica el otro). Con este fin, en primer lugar, se descubrirán al lector los debates literarios, políticos y científicos que explican la aparición de los volúmenes del Viaggio estatico dentro de la Idea dell’Universo. A continuación, al subrayar la (...) peculiaridad literaria del Viaggio dentro de la Idea, la calificación de su interlocutor como Cosmopolita, se analizará cómo Hervás respondió con ella a la ideologización del término por obra del Cosmopolite (1751) de Fougeret de Monbron. Finalmente, se contrasta la reacción del Hervás posterior a la Revolución francesa con el giro estoico del cosmopolitismo que representa la obra del Kant del período crítico, desarrollada entre 1781 y 1795. (shrink)

El presente artículo pretende invitar al estudio del impacto que tuvo _El Evangelio en Triumpho_ de Olavide sobre el pensamiento decimonónico. Con ese fin propone, en primer lugar, leerlo captando en sus rasgos esenciales el valor alegórico de sus personajes en sus relaciones. A continuación, señala qué aspectos de esa lectura habrían influido de manera más marcada en las obras de Maistre y Saint-Simon, con las que abarca las dos tendencias post-revolucionarias de entender la historia, catecóntica y quiliástica. Finalmente, presenta (...) la unidad milenarista de la obra de Olavide, ajena a aquellas interpretaciones precisamente por su ortodoxia, apuntando, como lectura alternativa a la francesa, la que sugiere Dostoyevski en _El Gran Inquisidor_. (shrink)

El presente artículo tiene como fin principal publicar la traducción de la lección de fray Luis de León del título, recientemente publicada y, como homenaje a este hecho, presentar la misma ofreciendo al lector el camino que la cuestión original planteada en la lección —con una trayectoria previa en Italia- recorre en el pensamiento español del XVII. Un camino que tiene dos grandes hitos: Cervantes y Spinoza. Cervantes, como se tratará de mostrar, desde una lectura directa del texto de fray (...) Luis, reflejada en su novela quijotesca _El curioso impertinente_. Spinoza, en cambio, más bien como filósofo impregnado de la cultura española y su pensamiento moral, del que se despega, como permite mostrar precisamente la reflexión anterior, al acoger el marco cartesiano de pensamiento ya en sus inicios, en el_ Tractatus de Intellectus Emendatione_. (shrink)

El artículo propone una contribución al debate contemporáneo sobre el futuro de la educación, enmarcado en las discusiones entre la escuela crítica de J. Habermas y el transhumanismo de S. Sorgner. Se somete a crítica, desde una perspectiva crítica y decolonial, los olvidos y omisiones de las condiciones materiales en las cuales se realizan las relaciones de enseñanza/aprendizaje. En términos metodológicos optamos por una hermenéutica crítica y democrática que nos permitió diseñar un cuadro propositivo de ‘Dimensiones de transformación’. Estas pueden (...) contribuir en la democratización y universalización de las educaciones futuras, a través de la definición de cuatro dimensiones claves: ‘Relaciones con la comunidad y la otredad’, ‘Saberes y sentires éticos y políticos’, ‘Inclusión de agentes invisibilizados’ y ‘Herramientas de transformación social’. (shrink)

El objetivo de la investigación es demostrar que la aplicación del Flipped Classroom mejora el nivel de logro del aprendizaje significativo en estudiantes universitarios. Para la recolección de datos en los grupos control y experimental se aplicaron dos instrumentos: el pre-test y el post-test. Concluido con la aplicación de los talleres basados en la metodología FC, en el postest se observó que en el grupo control, 26 estudiantes obtuvieron una calificación aprobatoria y 11 reprobatoria, mientras que en el grupo experimental, (...) 38 estudiantes, de acuerdo a los criterios de evaluación, todos lograron una calificación aprobatoria. (shrink)