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].

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.

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)

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 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)

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 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 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.

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 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.

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.

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)

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)

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 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.

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.

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)

This paper starts with one of Chalmers’ basic points: first-hand experience is an irreducible field of phenomena. I claim there is no ‘theoretical fix’ or ‘extra ingredient’ in nature that can possibly bridge this gap. Instead, the field of conscious phenomena requires a rigorous method and an explicit pragmatics for its exploration and analysis. My proposed approach, inspired by the style of inquiry of phenomenology, I have called neurophenomenology. It seeks articulations by mutual constraints between phenomena present in experience and (...) the correlative field of phenomena established by the cognitive sciences. It needs to expand into a widening research community in which the method is cultivated further. (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)

A discussão sobre a existência ou não da Filosofia Africana, associada à negação do direito à Filosofia caracterizou seis décadas: 1940-2000. A necessidade de apagar o espectro que as representações ocidentais (europeias) atribuem à África foi, de certa forma, respondida com várias publicações. O presente artigo pretende mostrar que existiram, também, pensadores individuais, preciamente no antigo Kôngo.

An important question in the debate regarding the nature of politically significant human kinds, such as gender, race, and sexual orientations, is concerned with the question of whether these human kinds are socially constructed (Stein 1999; Root 2000; Haslanger 2012; and Ásta 2013). In order to settle this debate, a more fundamental question needs to be answered: what does it mean to say that a category is socially constructed? -/- Recently, many philosophers have become interested in this issue (Hacking 1999; (...) Stein 1999; Haslanger 2003; Mallon 2007; Diaz-Leon 2015; Ásta 2015). They all seem to agree that there is not a single notion of social construction, but rather, there are different notions of social construction for different purposes. The important question in order to formulate a useful notion of social construction, then, is which project is at issue, and which notion of social construction is more useful for the purposes of that project. In this chapter I will focus on two projects that social constructivists are often interested in, namely, (i) the project of arguing against the inevitability of a trait, that is, to show that those features are not determined by human nature; and (ii) the project of arguing against the universality of a trait, that is, to show that a certain human category or kind is not a universal, transcultural, culture-independent property and that it cannot be applied to other cultures, places, and times; and I will discuss which notion of social construction is more useful with respect to each project. -/- My main questions, then, will be the following: (a) Is there any notion of social construction that entails that if X is socially constructed, then X is not inevitable, that is, X is not determined by human nature? (b) Is there any notion of social construction that entails that if X is socially constructed, then X is not transcultural or universal? (shrink)

Are feelings an essential part or aspect of emotion? Cases of unconscious emotion suggest that this is not the case. However, it has been claimed that unconscious emotions are better understood as either (a) emotions that are phenomenally conscious but not reflectively conscious, or (b) dispositions to have emotions rather than emotions proper. Here, I argue that these ways of accounting for unconscious emotions are inadequate, and propose a view of emotions as non-phenomenal attitudes that regard their contents as relevant (...) to one's motivations. (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)

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)

In this paper, I focus on an influential account of phenomenal concepts, the recognitional account, and defend it from some recent challenges. According to this account, phenomenal concepts are recognitional concepts that we use when we recognize experiences as “another one of those.” Michael Tye has argued that this account is viciously circular because the relevant recognitional abilities involve descriptions of the form “another experience of the same type,” which is also a phenomenal concept. Tye argues that we avoid the (...) circularity worry if we explain the reference-fixing of phenomenal concepts in terms of dispositions to re-identify tokens of the same type without appealing to any further phenomenal concepts. However, he argues, this account is incompatible with the intuitive claim that phenomenal concepts seem to involve rich modes of presentation of their referents. Philip Goff and others have similarly argued that a recognitional account of phenomenal concepts would make phenomenal concepts opaque, that is, unable to reveal anything about their referents, which seems problematic. In this paper, I present a new version of the recognitional account that avoids the circularity worry without entailing that phenomenal concepts are opaque. (shrink)

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)

Critico la teoría hermenéutica de Landgrebe sobre el cartesianismo de Husserl mostrando la estructura argumentativa en la que se inserta, lo que pretende y lo que está forzada a pretender. Su núcleo duro radica en los conceptos de crítica inmanente y lógica interna y tiene como meta final promover una idea de trascendental no-entitativa voluntarista y correlacional opuesta a la de un yo absoluto. Para probar esto, analizo tres niveles del cartesianismo de Landgrebe: primero, la síntesis contradictoria entre apodicticidad y (...) experiencia; segundo, su interpretación de Filosofía Primera, y, tercero, el objetivismo de Husserl. Concluyo de la función que juega el cartesianismo en este esquema y del fracaso de documentar con ejemplos la idea que el concepto no describe una noción en la filosofía de Husserl, sino que es una herramienta hermenéutica para controlar el sentido de trascendental en esta filosofía.I criticize Landgrebe’s hermeneutical theory about Husserl’s Cartesianism describing the structure of the argument where this concept is rooted, what it claims and what it is forced to claim. The theory’s hard core is based on the concepts of immanent critique and internal logic and it’s final goal consists in advancing a non-entitative voluntaristic and correlational definition of transcendental opposite to that of an absolute I. To prove this, I analyze three levels inside Landgrebe’s concept of Cartesianism: first, the contradictory synthesis of experience and apodicticity; second, his interpretation of First Philosophy, and, third, Husserl’s objectivism. I conclude from the goal that Cartesianism plays in this argument and the failure in documenting this idea with examples that Landgrebe’s Cartesianism is rather an hermeneutical tool made to control the definition of transcendental in Husserl’s philosophy than a concept describing Husserl’s thought. (shrink)