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)

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 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.

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)

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)

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 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.

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 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.

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 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.

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)

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.

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)

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.

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 ..

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.

The public University is an actor capable of energizing local ecosystems to transform the territory, and open innovation is its instrument of connection with the environment. University open innovation was studied through factor analysis by the principal components’ method in Mexico and Colombia. Data were collected in 54 research groups of two public universities. The analysis showed that the first six components explain 82.479% of the variance of the university open innovation model. The coincidences were evidenced in the factors that (...) affect the general process of open innovation in Universities of Mexico and in Colombia. It was concluded that open innovation is a relevant mechanism for linking the University with its environment. (shrink)

Some recently articulated American Christian liberation theolo­gies maintain that they seek justice for the oppressed. But such “justice” fails to encompass the respecting of certain rights of the oppressed to compensation from their oppressors. The right of the oppressed to holistic (including compensatory) reparations from their oppressors is explored in terms of why liberation theologies ought to, among other things, respect and embrace such a right. For economic issues, both distributive and compensatory, are inseparable from oppression-based poverty and hence inseparable (...) from the will of God insofar as it is the will of God to liberate the oppressed. By pressing the importance of reparations for oppressed groups, we seek to liberate liberation theologies from the shackles of a view that fails to recognize in a robust sense the law as a vehicle of rectification of oppression. (shrink)

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)

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

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 lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 40.1 (2006) 35-53 [Access article in PDF] "Truth Is What Works": Francisco J. Varela on Cognitive Science, Buddhism, the Inseparability of Subject and Object, and the Exaggerations of Constructivism—A Conversation Francisco J. Varela Bernhard Poerksen Institut für Journalistik und Kommunikationswissenschaft Universität Hamburg Francisco J. Varela (1946-2001) studied biology in Santiago de Chile, obtained his doctorate 1970 at Harvard University with a (...) dissertation on the insect eye, and worked there for some time in the laboratory of Torsten Wiesel, the later Nobel Laureate for medicine. From his scientific beginnings as a researcher in biology, he not only studied and practiced biology but, resisting the dominating mainstream, pursued a research program that ignored and broke down traditional disciplinary boundaries. This research program is best characterized as experimental epistemology, a concept introduced by the neuropsychiatrist and cybernetician Warren S. McCulloch. Francisco J. Varela's great aspiration was to examine and answer the philosophical ur-question of cognition with scientific precision and with the help of the best possible theoretical framework. [End Page 35]Having obtained his doctorate, he went back to Chile to work as a professor of biology together with Humberto R. Maturana. He contributed to the writing of the theory of autopoiesis, which was to cause a furor in the world of science as a universally applicable explanatory model. After the overthrow of Allende and the installation of the dictatorship by the putsch general Pinochet, Francisco J. Varela first escaped to Costa Rica, then became a professor at the American University of Colorado and University of New York, and finally returned in 1980 to the University of Chile in Santiago for five years. Temporary positions as guest professor for neurobiology, philosophy, and cognitive science in Germany, Switzerland, and France led him to Paris in the end, where he worked as research director of the Centre National de Recherche Scientifique until his death on May 28, 2001.In his research work embracing cognitive science, evolutionary theory, and immunology, Francisco J. Varela, constantly inspired by his fundamental interest in the key questions of epistemology, gave the epistemological debate a new orientation. In his thinking he refuses to accept the strict separation of subject and object, of knower and known, which as a rule unites realists and constructivists alike. Francisco J. Varela rejects the fundamental dualism dividing mind and world, which had shaped Western philosophy from its earliest beginnings. He does not subscribe to the idea that human individuals can invent their own realities—blindly and arbitrarily, and without experiencing any resistance from the external world and all other things given. He equally distances himself, however, from the diametrically opposite position that overstates the eigenpower of the world of objects. The external world and all other things given cannot determine what happens in an organism. Varela's claim is that individual and world create each other. The Computational Model of the Mind Poerksen: The ancient key questions of philosophy are at the center of modern cognitive science. What is the essence of the mind? Do our conceptions represent a given world, which is independent from our minds? What is the formative power of external objects over our perceptions? How does cognition function? The search for an adequate answer and an improved understanding of the human mind has led many cognitive scientists to entertain the assumption that the brain is actually a kind of computer. Memory is taken to be a store. Thinking and perceiving are understood as data processing in the sense that an independent external world is computationally transformed into symbols and represented in the organism in this manner. You are very critical of this view. Why?Varela: If the brain is considered as a kind of computer, then cognitive research is limited to discovering certain self-sufficient shapes—the symbols—together with the rules [End Page 36] governing them—the programs. But this search for symbols and programs will never be profitable because it... (shrink)

How can science be brought to connect with experience? This book addresses two of the most challenging problems facing contemporary neurobiology and cognitive science. Firstly, understanding how we unconsciously execute habitual actions as a result of neurological and cognitive processes that are not formal actions of conscious judgment but part of a habitual nexus of systematic self-organization. Secondly, attempting to create an ethics adequate to our present awareness that there is no such thing as a transcendental self, a stable subject (...) or soul. The author combines researches in cognitive science and phenomenology with two representatives of what he calls the 'wisdom traditions': Confucianism and Buddhist epistemology. (shrink)

Response to the Commentary on ‘The View from Within’ The numerous commentators to this Special Issue have greatly enhanced its focus and usefulness. We thank them all very sincerely for their efforts. Within the restricted space of this rejoinder we cannot respond in detail to all the issues raised. Instead, we shall concentrate first on some fundamental criticisms.The remaining additions and complementary ideas will only be touched on briefly, merely to see them in perspective. We shall start with our two (...) main critics of the global enterprise, Baars and Nixon. They both offer arguments that our enterprise is misguided, but their arguments fall on two opposite extremes: empirical and hermeneutical. (shrink)

Most theories of slurs fall into one of two families: those which understand slurring terms to involve special descriptive/informational content (however conveyed), and those which understand them to encode special emotive/expressive content. Our view is that both offer essential insights, but that part of what sets slurs apart is use-theoretic content. In particular, we urge that slurring words belong at the intersection of a number of categories in a sociolinguistic register taxonomy, one that usually includes [+slang] and [+vulgar] and always (...) includes [-polite] and [+derogatory]. Thus, e.g., what distinguishes ‘Chinese’ from ‘chink’ is neither a peculiar sort of descriptive nor emotional content, but rather the fact that ‘chink’ is lexically marked as belonging to different registers than ‘Chinese’. It is, moreover, partly such facts which makes slurring ethically unacceptable. (shrink)

This paper analyses the details that characterized the negotiation and collection of the servicio de los naturales from the year 1603 onwards, the last time of those three in which moriscos of Granada paid to the Hispanic Monarchy after the Alpujarras War, when they were settled in Castile. The author has analysed documents coming from the Archivo General de Simancas, but also those included in notary’s protocols and in local archives. Its main contributions are three: to publish the content of (...) the actual contract signed by the moriscos and the Crown; to contribute to set up a precise spatial distribution of the communities that paid the tax and, finally, to show the amounts delivered by them. Irregularities, problems, and conflicts lived while the precedent servicios were being paid, are analysed too. There are aspects that we know thanks to other previous works. Nevertheless, if they are considered in relation with the situation of the year 1603, they allow observing that all those difficulties were used in order to improve the servicio itself and the agreement between the minority and the King. (shrink)

Some major leftist thinkers, including Alain Badiou, Slavoj Žižek and Terry Eagleton, have lately offered readings that claim the relevance of alternative interpretations of the Christian tradition in the face both of the conservative turn in the Catholic Church and of the contemporary secular oblivion of anything that has to do with religion. Furthermore, post-colonial studies have tended to blame the West en bloc for the disasters of past and present colonization, and have attacked the western endeavour to extend universal (...) truths as an ethnocentric device to facilitate and justify exploitation. In Holy Terror, Terry Eagleton both condemns western politics and questions its appeal to universals; but he also hears in this tradition a demand for a relationship with the other which offers an alternative to that established by current politics and capitalist exploitation. The other is the excluded, the oppressed, the exploited; the true material, rather than ideal, universal produced by global capitalist exploitation. As a consequence, anything that happens in any part of the planet belongs in our world and indicts us, though we tend to build barriers around an ideally safe and stable identity that ignores part of its own reality and that is therefore haunted by it. Texts like the Bacchae or the New Testament open the gates of the city and of the heart to the excluded. Terrorists — saints for their own communities and satanic for the rest — offer an example of the other that is impossible to comprehend within our conventional ways of life. Nevertheless, only if we hear in their violence a demand for justice can an exit be found from the vicious circle of violence and revenge. (shrink)

Mujerista Theology, the name given to the groundbreaking work of Ada María Isasi-Díaz, can be understood as a constellation, with each star symbolizing its various concepts, themes, and theories, all forming a pattern that can be perceived from a distance. This pattern — the legacy of mujerista theology — changes as these stars shift against the celestial backdrop over time. This essay explores the implications of Mujerista Theology for social change by exploring three ‘stars’ of the Mujerista Theology constellation (...) — mestizaje-mulatez, lo cotidiano, and subversive narratives — and examining some of the underlying presuppositions operative in Mujerista Theology. It contends that Mujerista Theology significantly contributes to the social change strategies of liberationist, feminist, and Hispanic theologies. (shrink)

My purpose in this article is to propose an explicitly naturalized account of the experience of present nowness on the basis of two complementary sources: phenomenological analysis and cognitive neuroscience. What I mean by naturalization, and the role cognitive neuroscience plays will become clear as the paper unfolds, but the main intention is to use the consciousness of present time as a study case for the phenomenological framework presented by Depraz in this Special Issue.

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)