The variety O2 of double Ockham algebras consists of the algebras (A ∨, ∧, f,g 0,1) of type (2,2,1,1,0,0) where (A; ∨, ∧,f, 0,1) and (A; ∨, ∧,g 0,1) are Ockham algebras. In [16], M. Sequeira introduced several subvarieties of O2. In this paper we give a construction of free double Ockham algebras on a partially ordered set. We also describe free objects for the subvarieties of O2 considered in [16].

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 prove that the free algebras in a subvariety equation image of the variety equation image of semi-Heyting algebras are directly decomposable if and only if equation image satisfies the Stone identity.

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 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)

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.

This article is about reductionism; as a tendency of thought, reductionism tells us that the hole can be explained as the sum of its parts. From this principle, one can deduce that the properties and laws of complex systems can be explained by the laws and properties of simple systems. On the other ..

To analyze the concept about scientific fact was the purpose of this work. This concept is a principal element to scientific hypothesis formulation. The properties and characteristics of this must observance were enumerated. Moreover, the concept studied of this work was compared with another.

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.

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)

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)

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.

ObjectiveCOVID-19 caused a complete stop in non-professional sports. The use of face masks for team sports is not a widely used measure in non-professional sports. The study aimed to evaluate the perception about using the mask and the adaptation difficulties related to training and competition in team sports following the FISICOVID-DXTGALEGO protocol.MethodsSeven hundred eighty-seven handball players from the Galician Handball Federation were followed during their return to participation after months of confinement through an electronic questionnaire of perception and experience on (...) the use of a mask.ResultsThere is an excellent adaptation to the mask in training and competition with medium and high correlations. The 86,41% of players reported an adaptation to the mask in 3 weeks with a three times a week training frequency. The negative opinion on the mask was drastically reduced after use. The 80,44% of players considered the use of a mask as an essential measure to resume competitions.ConclusionsIt is very feasible to adapt to training and compete with a mask in a short period. The use of a mask following these protocols changed previous opinions on the disadvantages of the mask during training and competition. (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.

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)

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)

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.

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)

Transition experienced by trans people shakes Social Sciences conven-tional understanding of time and space as static analytical units based on tradi-tional biological and physical axioms. Overcoming sexual binarism entails also questioning time and space as isolated elements to become, instead, entangled realities. Departing from trans studies and Halberstam´s concepts of queer temporalities and space as theoretical framework, this papers lines up the indi-vidual story of a trans man with physical disability and ASD with social “trans-formations”, by linking the exposition of (...) the body with the transgression of heteronormative cis time, to be replaced, gradually by trans temporality and new ways of cohabitating spaces. (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)

Pourquoi s'interroger sur la possibilité de l'existence d'une philosophie au Chili? Voici la question traitée ici, en prenant comme axe le travail intellectuel du philosophe chilien Jorge Eduardo Rivera, décédé en janvier 2017, après l'écriture de cet ouvrage. Jorge Eduardo Rivera représente parfaitement le travail philosophique et universitaire. Celui qui se réalise dans le plus grand silence, hors de toute stridence ou de toute mode. Etranger au raffut des bavardages qui nous inonde. Une méditation sobre, loin de toute bouffonnerie. Peut-être (...) est-ce cela qui amena Rivera à décrire simplement et profondément des zones inconnues, éclairées par une parole qui, sans être poétique, nous renvoie à l'être en tant que tel et sous toutes ses formes. Ce livre présente l'exercice philosophique de Jorge Eduardo Rivera sous un horizon de réflexion à la fois propre et inspiré de la tradition européenne. Il expose sa biographie et son histoire intellectuelle, les différents espaces dans lesquels sa pensée s'est formée, depuis son noviciat et son scolasticat chez les Pères Français, jusqu'à ses études philosophiques et théologiques en Allemagne et ses rencontres avec Heidegger, Gadamer, Fink, Welte, Von Herrmann et Xavier Zubiri. (shrink)

Resumen Este escrito es fruto de una investigación documental y bibliográfica realizada en el Archivo General del Consejo Episcopal Latinoamericano. Busca presentar una síntesis del impulso que ha realizado el CELAM en orden al diálogo interreligioso. Este no ha sido un camino fácil y aún hay mucho por hacer. No obstante, en el ámbito de la Iglesia Católica, el CELAM ha sido un permanente animador de las orientaciones de los obispos en esta temática, plasmadas en el Concilio Vaticano II y (...) las Conferencias Generales del Episcopado Latinoamericano.This paper is the product of documentary and bibliographic research in the General Archives of the Latin American Bishops’ Council and it endeavors to provide a synthesis of the efforts that CELAM has made in regard to interreligious dialogue. This has not been an easy path to follow and there is still much more yet to be done. However, in the context of the Catholic Church, CELAM has been a persistent dynamic force, encouraging bishops on this topic, according to the guidelines found in the documents of Vatican II and the General Conferences of Latin American Bishops. (shrink)

Este artículo tiene como objetivo dilucidar la función que cumple el temor reverencial en el Leviatán de Thomas Hobbes y en la Ciencia Nueva de Giambattista Vico como principio del mundo civil. Se centra la atención en la imaginación y en la religión como elementos fundantes de las instituciones humanas, analizando sus implicaciones.Palabras clave: Vico, Hobbes, política, temor, “terror”.This article aims to elucidate the role of ‘awe’ in Thomas Hobbes’s Leviathan and in Giambattista Vico’s Scienza Nuova as a principle of (...) civilian world. The focus is on imagination and religion as foundational elements of human institutions, analyzing its implications.Keywords: Vico, Hobbes, politics, fear, “awe”. (shrink)

Philosophy & Social Criticism, Volume 48, Issue 6, Page 882-903, July 2022. Indigenous conservation through patrimonialization is the product of political and legal decisions made by a non-indigenous agent: the liberal state, using the law to retain a form of bios. We propose that patrimonialization is the device by which liberal states have processed and integrated indigenous claims into a form of bios ultimately designed to safeguard state legal structures. We argue that, to uphold the rule of law in contexts (...) of struggle and resistance that challenge the very understanding of the law, states respond by wielding the law in the form of the rule by law, that is, pushing the law to the limit to give normative content to the criteria by which the state conducts its affairs, without straying from the individual rights framework. We hold that the rule by law is an operation that defines the patrimonialization of indigenous peoples. It increases their visibility while imposing limits on political action to keep them from becoming sui juris subjects capable of breaching the distinction between zoe and bios. In this article, we try to understand the political–ideological intent of these decisions, the intentions beyond the letter of the law of patrimonialized peoples. (shrink)

The aim of this paper is to show that Thomas Hobbes suggests an original understanding of the doctrine of the discernment of spirits in the Leviathan. I claim that, from a radical reading of the concepts of spirit and prophecy in the Bible, the philosopher of Malmesbury proposes a discernment of allegiances as a way to control prophecy inside the State.

A widespread need to explain the behavior and outcomes of AI-based systems has emerged, due to their ubiquitous presence. Thus, providing renewed momentum to the relatively new research area of eXplainable AI (XAI). Nowadays, the importance of XAI lies in the fact that the increasing control transference to this kind of system for decision making -or, at least, its use for assisting executive stakeholders- already affects many sensitive realms (as in Politics, Social Sciences, or Law). The decision-making power handover to (...) opaque AI systems makes mandatory explaining those, primarily in application scenarios where the stakeholders are unaware of both the high technology applied and the basic principles governing the technological solutions. The issue should not be reduced to a merely technical problem; the explainer would be compelled to transmit richer knowledge about the system (including its role within the informational ecosystem where he/she works). To achieve such an aim, the explainer could exploit, if necessary, practices from other scientific and humanistic areas. The first aim of the paper is to emphasize and justify the need for a multidisciplinary approach that is beneficiated from part of the scientific and philosophical corpus on Explaining, underscoring the particular nuances of the issue within the field of Data Science. The second objective is to develop some arguments justifying the authors’ bet by a more relevant role of ideas inspired by, on the one hand, formal techniques from Knowledge Representation and Reasoning, and on the other hand, the modeling of human reasoning when facing the explanation. This way, explaining modeling practices would seek a sound balance between the pure technical justification and the explainer-explainee agreement. (shrink)

La concepción de _disciplina_ y la reflexión sobre las disciplinas liberales en la filosofía temprana de Agustín se encuentran mayormente en su obra _De ordine_. Allí, el Hiponense describe la sabiduría de las artes liberales como modesta y sucinta, de modo más prescriptivo que descriptivo. Por otra parte, en _Retractationes_, el autor reseña su proyecto de volver a pensar las disciplinas liberales dedicando una obra a cada una de ellas. Esta empresa inconclusa dio lugar a una obra sobre la gramática, (...) perdida en tiempos de Agustín, y otra sobre la música. En _De musica_, Agustín describe el funcionamiento de la sensibilidad y su articulación con la racionalidad que culmina en el reconocimiento de Dios en el alma. Intentaremos mostrar cómo la dimensión psicológica del funcionamiento de la sensibilidad permite volver sobre el concepto de disciplina y comprender las disciplinas liberales mediante el desarrollo de una de ellas en particular tomando como eje el acercamiento a lo divino por la vía racional. (shrink)

El concepto de igualdad articula el análisis de Agustín de Hipona en su diálogo De musica. Agustín comienza por el estudio técnico del ritmo de los versos latinos con la función de organizar los pies métricos de acuerdo con su cercanía a la igualdad. La cercanía a la igualdad es el criterio de la delectación, entendida como respuesta de los sentidos ante las proporciones simples. El análisis racional de la experiencia estética da lugar al ascenso del alma hacia Dios, identificado (...) como fundamento de la belleza y de la delectación por las cosas proporcionadas y bellas. Este pasaje de la teoría musical a la filosofía de la música con alcances teológicos articula una teoría estética que aborda la experiencia estética y la reflexión sobre esta experiencia. Sostendremos que los tres momentos del diálogo permiten comprender el concepto de aequalitas de acuerdo con tres perspectivas: aritmética, estética y teológica. La igualdad aritmética es la relación entre dos cantidades iguales. La igualdad estética refiere a las relaciones entre las cantidades de la realidad temporal en tanto que son percibidas y respecto de su belleza. Por último, la igualdad teológica es una igualdad suprema, divina y ajena a la multiplicidad. (shrink)

Faced with an Alexandrian (Arian) anthropology of Neoplatonic inspiration, Eustathius adopts a strong position in several statements that is similar to astoic Aristotelianism of the 4th century. Nevertheless, Eustathius's reflection is more genuinely theological, than it is reflective of any particular philosophical trend. For him, the human body is a dynamic concept which finds its full meaning in light of the history of salvation, wherein the incarnate and glorified Logos, the second Adam, brings to completion the perfection and incorruptibility of (...) the humble body formed from clay in the first Adam, the protoplast. (shrink)

La objeción que Simmias formula en el Fedón (85e-86d) responde al tercer argumento presentado por Sócrates acerca de la inmortalidad del alma, a saber, el argumento de la afinidad (78b-84b). Allí Simmias sugiere que el alma es una especie de armonía. Como la armonía desaparece tras la destrucción de la lira, entonces hay que afirmar que el alma desaparece tras la destrucción del cuerpo. O bien, habría que afirmar que la armonía sobrevive a la destrucción de la lira, lo cual (...) es absurdo. Ante la objeción, Sócrates formula tres refutaciones que se dirigen específicamente contra la tesis del alma como armonía. Proponemos que ἁρμονία debe entenderse como afinación para comprender el sentido de la objeción de Simmias y de las refutaciones de Sócrates. Esta tesis del alma como ἁρμονία fue atribuida mayormente al pitagorismo, especialmente a Filolao. No obstante, si se entiende el término ἁρμονία como afinación, se presentan problemas teóricos para aceptar la atribución. (shrink)

Pedro Alvares Cabral's ships left Portugal on 9 March 1500 en route for the territory that he first named Terra de Vera Cruz and that later came to be known as Brazil. On the 22 March they called at the island of São Nicolau [Caminha, 1500], one of the northernmost islands of the Cape Verde group; this was about forty years after the discovery of the archipelago in 1460-62 [Albuquerque, 1991]. It is known that Vasco da Gama had stopped at (...) the island of Santiago in 1498 on his voyage to India, and also in 1499 on the return journey. Straight after the discovery of Brazil Cabral sailed for India and on the way back also dropped anchor at Santiago. Indeed, our archipelago, which is situated off Cape Verde in Senegal (the place from which it appears to take its name), was to become an important stopover point for maritime traffic between Europe, Asia and the Americas in the fifteenth and sixteenth centuries, both to allow crews to rest and to take on water, wood and some food supplies. It also became important as a holding point for slaves (a large number of whom came from around thirty Guinean ethnic groups and subgroups). They were dispatched from Santiago, known then as Cape Verde island, to territories such as Brazil from the early sixteenth century onwards, since these territories, which had only recently been discovered and were little known, needed people to work and populate them. (shrink)

Resumen En este artículo analizaremos, a través de una serie de actividades diseñadas para implementar en el aula, el modo en el que un grupo de jóvenes gallegos co-construyen el conocimiento metalingüístico y metapragmático acerca de las diferentes variedades locales del español y gallego. La exposición de su trayectoria biográfica permite que afloren diversos saberes y conocimientos metalingüísticos que los estudiantes han ido adquiriendo a lo largo de su escolarización y, además, surgen diversas categorizaciones sobre lenguas y variedades que ponen (...) de manifiesto sus ideologías lingüísticas, pp. 157–174). A través del análisis de las prácticas metalingüísticas y metapragmáticas comprobaremos cómo se reproducen las ideologías lingüísticas de estos jóvenes; por una parte, las ideologías de la institución académica y escolar; y por otra, las ideologías lingüísticas de los jóvenes presentes en el aula, en donde etiquetan, clasifican y establecen jerarquizaciones y valoraciones de su repertorio comunicativo. Finalmente, se comprueba cómo las diferentes variedades del español y del gallego actúan como índices de identidad social diferente de la reconocida en el ámbito institucional y académico, con distintos valores en el mercado lingüístico. (shrink)

Este artigo tem como objetivo fazer uma reflexão sobre uma metodologia para analisar a relação entre pós-modernidade e comunicação. Com isso, busca fortalecer um método que pode auxiliar na compreensão da organização da sociedade pós-moderna, relacionada ao uso de dois meios de comunicação. Para atender a esses objetivos, pretendemos partir das visões de Marshall Mcluhan, estudamos dois meios de comunicação; Michael Foucault, sua Arqueologia do Saber constitui dois paradigmas de uma época; e por Giorgio Agamben e seu método baseado na (...) relação entre paradigma, arqueologia e matéria. Este debate torna-se relevante para que seja possível desenvolver um método científico das Ciências da Comunicação que questione o contexto contemporâneo de dois saberes académicos. (shrink)

The Embodied Mind provides a unique, sophisticated treatment of the spontaneous and reflective dimension of human experience.