An equivalence between the category of MV-algebras and the category $${{\rm MV^{\bullet}}}$$ MV ∙ is given in Castiglioni et al. :67–92, 2014). An integral residuated lattice with bottom is an MV-algebra if and only if it satisfies the equations $${a = \neg \neg a, \vee = 1}$$ a = ¬ ¬ a, ∨ = 1 and $${a \odot = a \wedge b}$$ a ⊙ = a ∧ b. An object of $${{\rm MV^{\bullet}}}$$ MV ∙ is a residuated lattice which in (...) particular satisfies some equations which correspond to the previous equations. In this paper we extend the equivalence to the category whose objects are pairs, where A is an MV-algebra and I is an ideal of A. (shrink)

This paper deals about dualities for bounded prelinear Hilbert algebras. In particular, we give an Esakia-style duality between the algebraic category of bounded prelinear Hilbert algebras and a category of H-spaces whose morphisms are certain continuous p-morphisms.

In this paper we shall introduce the variety FWHA of frontal weak Heyting algebras as a generalization of the frontal Heyting algebras introduced by Leo Esakia in [ 10 ]. A frontal operator in a weak Heyting algebra A is an expansive operator τ preserving finite meets which also satisfies the equation $${\tau(a) \leq b \vee (b \rightarrow a)}$$, for all $${a, b \in A}$$. These operators were studied from an algebraic, logical and topological point of view by Leo Esakia (...) in [ 10 ]. We will study frontal operators in weak Heyting algebras and we will consider two examples of them. We will give a Priestley duality for the category of frontal weak Heyting algebras in terms of relational spaces $${\langle X, \leq, T, R \rangle}$$ where $${\langle X, \leq, T \rangle}$$ is a WH -space [ 6 ], and R is an additional binary relation used to interpret the modal operator. We will also study the WH -algebras with successor and the WH -algebras with gamma. For these varieties we will give two topological dualities. The first one is based on the representation given for the frontal weak Heyting algebras. The second one is based on certain particular classes of WH -spaces. (shrink)

A subresiduated lattice is a pair, where A is a bounded distributive lattice, D is a bounded sublattice of A and for every there exists the maximum of the set, which is denoted by. This pair can be regarded as an algebra of type (2, 2, 2, 0, 0), where. The class of subresiduated lattices is a variety which properly contains the variety of Heyting algebras. In this paper we study the subvariety of subresiduated lattices, denoted by, whose members satisfy (...) the equation. Inspired by the fact that in any subresiduated lattice whose order is total the previous equation and the condition for every are satisfied, we also study the subvariety of generated by the class whose members satisfy that for every. (shrink)

This work extend to residuated lattices the results of [ 7 ]. It also provides a possible generalization to this context of frontal operators in the sense of [ 9 ]. Let L be a residuated lattice, and f : L k → L a function. We give a necessary and sufficient condition for f to be compatible with respect to every congruence on L . We use this characterization of compatible functions in order to prove that the variety of (...) residuated lattices is locally affine complete. We study some compatible functions on residuated lattices which are a generalization of frontal operators. We also give conditions for two operations P ( x , y ) and Q ( x , y ) on a residuated lattice L which imply that the function $${x \mapsto min\{y \in L : P(x, y) \leq Q(x, y)\}}$$ when defined, is equational and compatible. Finally we discuss the affine completeness of residuated lattices equipped with some additional operators. (shrink)

Let |$\textbf{A}$| be a |$BCK$|-algebra and |$f:A^{k}\rightarrow A$| a function. The main goal of this article is to give a necessary and sufficient condition for |$f$| to be compatible with respect to every relative congruence of |$\textbf{A}$|⁠. We extend this result in some related algebras, as e.g. in pocrims.

In this paper we shall prove that certain subvarieties of the variety of Salgebras (Heyting algebras with successor) has amalgamation. This result together with an appropriate version of Theorem 1 of [L. L. Maksimova, Craig’s theorem in superintuitionistic logics and amalgamable varieties of pseudo-boolean algebras, Algebra i Logika, 16(6):643-681, 1977] allows us to show interpolation in the calculus IPC S (n), associated with these varieties.We use that every algebra in any of the varieties of S-algebras studied in this work has (...) a canonical extension, to show completeness of the calculus IPC S (n) with respect to appropriate Kripke models. (shrink)

In this paper we study the variety \(\textsf{WL}\) of bounded distributive lattices endowed with an implication, called weak Lewis distributive lattices. This variety corresponds to the algebraic semantics of the \(\{\vee,\wedge,\Rightarrow,\bot,\top \}\) -fragment of the arithmetical base preservativity logic \(\mathsf {iP^{-}}\). The variety \(\textsf{WL}\) properly contains the variety of bounded distributive lattices with strict implication, also known as weak Heyting algebras. We introduce the notion of WL-frame and we prove a representation theorem for WL-lattices by means of WL-frames. We extended (...) this representation to a topological duality by means of Priestley spaces endowed with a special neighbourhood relation between points and closed upsets of the space. These results are applied in order to give a representation and a topological duality for the variety of weak Heyting–Lewis algebras, i.e., for the algebraic semantics of the arithmetical base preservativity logic \(\textsf{iP}^{-}\). (shrink)

In this paper we study the variety of order Hilbert algebras, which is the equivalent algebraic semantics of the order implicational calculus of Bull.

An equivalence between the category of MV-algebras and the category \ is given in Castiglioni et al. :67–92, 2014). An integral residuated lattice with bottom is an MV-algebra if and only if it satisfies the equations \ \vee = 1}\) and \ = a \wedge b}\). An object of \ is a residuated lattice which in particular satisfies some equations which correspond to the previous equations. In this paper we extend the equivalence to the category whose objects are pairs, where (...) A is an MV-algebra and I is an ideal of A. (shrink)

This work extend to residuated lattices the results of [7]. It also provides a possible generalization to this context of frontal operators in the sense of [9].Let L be a residuated lattice, and f : Lk → L a function. We give a necessary and sufficient condition for f to be compatible with respect to every congruence on L. We use this characterization of compatible functions in order to prove that the variety of residuated lattices is locally affine complete.We study (...) some compatible functions on residuated lattices which are a generalization of frontal operators. We also give conditions for two operations P(x, y) and Q(x, y) on a residuated lattice L which imply that the function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${x \mapsto min\{y \in L : P(x, y) \leq Q(x, y)\}}$$\end{document} when defined, is equational and compatible. Finally we discuss the affine completeness of residuated lattices equipped with some additional operators. (shrink)

Book reviewed in this article: Ethical Issues in Social Research. Edited by Tom L. Beauchamp, Ruth R. Faden, R. Jay Wallace, Jr., and LeRoy Walters. Baltimore: The Johns Hopkins University Press, 1982. xii + 436 pp. $25.00 (hardcover); $8.95 (paper). Ethics of Human Subject Research. Edited by Allan J. Kimmel, Jr. San Francisco: Jossey‐Bass, 1981. 106 pp. $6.95 (paper). Social Research Ethics. Edited by Martin Bulmer. New York: Holmes & Meier, 1982. xiv + 284 pp. $39.50 (hardcover); $14.50 (paper). The (...) Ethics of Social Research: Field‐work, Regulation and Publication. Edited by Joan E. Sieber. New York: Springer‐Verlag, 1982. x + 187 pp. $23.50 (hardcover). The Ethics of Social Research: Surveys and Experiments. Edited by Joan E. Sieber. New York: Springer‐Verlag, 1982. xii + 249 pp. $23.50 (hardcover). (shrink)

El artículo analiza el trabajo de apropiación crítica llevado a cabo por Enrique Dussel de la obra de F. W. J. Schelling. Es interesante analizar, desde el marco aportado por la Historia de las Ideas en América Latina, cómo el filósofo de la liberación entiende y resignifica las categorías filosóficas desarrolladas por el filósofo romántico. El artículo se propone identificar los supuestos epistemológicos y metodológicos mediadores en este trabajo de interpretación categorial que le permite al filósofo argentino, entre otros aportes, (...) articular el método analéctico, método a partir del cual es posible proponer una filosofía que se aparta de la dialéctica de lo Uno y puede conceptualmente llegar al otro. (shrink)

El presente trabajo resume y comenta algunas de las aportaciones que nos han parecido más relevantes realizadas en los últimos años en torno a la obra filosófica de J. Ortega y Gasset. Desde la aparición del libro de P. Cerezo Galán La voluntad de aventura en 1983, el interés por el problema de Ortega ha experimentado un auge muy significativo y creciente en España, del que son muestra los estudios de Javier San Martín, Mª Carmen Paredes, Fco J. (...) class='Hi'>Martín, Máximo Martín Serrano y Jaime de Salas. Nuestro trabajo, tras una exposición resumida de estas interpretaciones, intenta una síntesis conciliadora que creemos sugerida por los propios textos del filósofo. (shrink)

An l-hemi-implicative semilattice is an algebra $$\mathbf {A} = $$ A= such that $$$$ is a semilattice with a greatest element 1 and satisfies: for every $$a,b,c\in A$$ a,b,c∈A, $$a\le b\rightarrow c$$ a≤b→c implies $$a\wedge b \le c$$ a∧b≤c and $$a\rightarrow a = 1$$ a→a=1. An l-hemi-implicative semilattice is commutative if if it satisfies that $$a\rightarrow b = b\rightarrow a$$ a→b=b→a for every $$a,b\in A$$ a,b∈A. It is shown that the class of l-hemi-implicative semilattices is a variety. These algebras provide (...) a general framework for the study of different algebras of interest in algebraic logic. In any l-hemi-implicative semilattice it is possible to define an derived operation by $$a \sim b := \wedge $$ a∼b:=∧. Endowing $$$$ with the binary operation $$\sim $$ ∼ the algebra $$$$ results an l-hemi-implicative semilattice, which also satisfies the identity $$a \sim b = b \sim a$$ a∼b=b∼a. In this article, we characterize the commutative l-hemi-implicative semilattices. We also provide many new examples of l-hemi-implicative semilattice on any semillatice with greatest element. Finally, we characterize congruences on the classes of l-hemi-implicative semilattices introduced earlier and we characterize the principal congruences of l-hemi-implicative semilattices. (shrink)

El ejercicio filosófico de raíz marxista en Chile tiene un capítulo escrito por los intelectuales comunistas de la década del 60 del siglo XX. Uno de ellos, Sergio Vuskovic, se abocó a discutir con las tesis althusserianas que identificaron la teorización de Marx como un antihumanismo teórico. Para oponerse a tal perspectiva, Vuskovic realiza una operación teórica al interior de la obra de Marx con el objetivo de afirmar la categoría de sujeto, así como la interna relación entre ejercicio teórico (...) y praxis socio-histórica. Chilean communist intellectuals of the 1960's wrote a chapter of the history of Marxist philosophy. One of them was Sergio Vuskovic who focused on discussing Marx's theories according to Althusser's thesis of anti-humanism. By affirming the subject category and the internal relationship between "theoretical operation" and socio-historical praxis within Marx's philosophy, Vuskovic opposes Althusser's perspective. (shrink)

The debate about Ortega’s relation to phenomenology has been continuous since the eighties of the last century. Before this date, Ortega’s manifestations that he had abandoned phenomenology at the same moment he came to know it were understood literally, without scrutinising other manifestations of his that he had made on phenomenology, or that his philosophy is similar to that of Husserl’s final works. Both manifestations seek to question the previous ones. The text clarifies first the meaning and importance of this (...) polemic for Spanish philosophy, deeply influenced by that of Ortega’s, and, secondly, I will set out what are the fundamental phenomenological concepts of Ortega’s philosophy. / El debate sobre la relación de Ortega con la fenomenología ha sido continuo desde los años ochenta del siglo pasado. Antes de esta fecha, las manifestaciones de Ortega de que había abandonado la fenomenología en el mismo momento que la conoció, fueron tomadas al pie de la letra, sin examinar otras manifestaciones que había hecho sobre la fenomenología, o la de que su filosofía es similar a la de los últimos trabajos de Husserl. Ambas manifestaciones buscan cuestionar las anteriores. El texto aclara en primer lugar el significado y la importancia de esta polémica en la filosofía española, profundamente influenciada por la de Ortega, y, en segundo lugar, se expondré cuáles son los conceptos fenomenológicos fundamentales de la filosofía de Ortega. (shrink)

El escrito se propone analizar la discusión metodológica desarrollada por Enrique Dussel en la época en que se formuló la filosofía de la liberación; lo que se afirma es que la filosofía de la liberación, en su versión dusseliana, se configura al modo de un diseño metodológico adecuado a la condición de alteridad latinoamericana. Desde este supuesto se abordan algunos puntos de la discusión dusseliana con la filosofía del concepto y con el pensar ontológico en vistas de la configuración de (...) la analéctica. Finalmente, se afirma que la formulación analéctica de la filosofía de la liberación es uno de los modos en que la filosofía latinoamericana desarrolla una propuesta crítica de la categoría de sujeto. This paper sets out to analyze the methodological discussion developed by Enrique Dussel at the time that the philosophy of liberation was formulated; what is stated is that the philosophy of liberation, in its dusselian version, configures an adequate methodological design to the condition of Latin-American otherness. From this assumption some points of the dusselian discussion are undertaken with the philosophy of the concept and with the ontological thinking in views of the configuration of the analectics. Finally, it is stated that the analectic formulation of the philosophy of liberation is one of the ways in which the Latin American philosophy develops a critical proposal of the category of subject. (shrink)

Prsentación del libro El zigzag husserliano, por Ana Lucas, Editorial Endymion, Madrid, 1991. Libro sobre la filosofía del filósofo burgalés Luis Martín Santos.

A partir de la afirmación en la que Ortega dice que el científico se aloja en el ser humano, el texto pretende, por un lado y desde una perspectiva fenomenológica, abordar el vínculo entre las ciencias naturales y las ciencias humanas y sociales y, por otro lado, analizar las consecuencias de las maneras en las que estos dos grupos de ciencias se han relacionado a fin de imaginar la posición que tanto las ciencias naturales como las humanas y sociales deben (...) ocupar. From a phenomenological perspective and begining with the statement from Ortega saying that a scientist lives inside a human being, this text has a twofold structure. First, the author analyzes the relationship among natural sciences and human and social sciences. Second, the author analyzes the consequences of the different ways in which bothsciences have interrelated, in order to imagine the place that either natural sciences, and social sciences and humanities, should occupy. (shrink)

El presente texto tiene como objetivo exponer el concepto de “cultura básica”, fundamental en la fenomenología de Lester Em-bree. En la primera parte se expondrá el contexto biográfico de ese texto. En la segunda se abordará el primer avance que hace Lester Embree, para en la tercera centrarse en el artículo fundamental sobre el mismo. El núcleo del concepto está en relación con la diferencia que Lester Embree establece entre la experiencia y la posicionalidad de uso, valoración y creencia. Estas (...) son características o determinaciones culturales que constituyen el mundo humano, que por eso es siempre un mundo cultural. Esa cultura básica se da también, al menos, en algunos animales no humanos. Aunque se alude a puntos problemáticos de esa teoría, no se entra de lleno en esos problemas.The present paper aims to expose the concept of "basic culture", fundamental in Lester Embree’s phenomenology. In the first part the biographical context of that text is explained. In the second one, the first advance made by Lester Embree is described, and in the third one the fundamental article about it will be focused on. The core of the concept is in relation to the difference that Lester Embree establishes between experience and the positionality of use, valuation and belief. These are characteristics or cultural determinations that constitute the human world, which therefore is always a cultural world. This basic culture also occurs, at least, in some non-human animals. Although problematic points of that theory are alluded to, these problems are not fully developed. (shrink)

La obra de Julia V. Iribarne se basa, entre otros, en tres conceptos centrales, intersubjetividad trascendental, ética trascendental y antropología trascendental. En este texto de homenaje a su persona y a su trayectoria intelectual, dado que nuestra autora se basa fundamentalmente en los inéditos de Husserl, aclararé, en primer lugar la posición del legado póstumo [Nachlass] husserliano en la obra de este. A continuación dedicaré un apartado a exponer el desarrollo de cada uno de esos conceptos a lo largo de (...) su trayectoria, desde la intersubjetividad, pasando por la ética, hasta antropología trascendental.Julia V. Iribarne’s lifework rests, among others, on three central concepts, transcendental intersubjectivity, transcendental ethics and transcendental anthropology. In this text in tribute to her person and intellectual trajectory, and because Julia V. Iribarne’s writings are founded basically on Husserl’s Nachlass, I shall first clarify my conception about the relation of this Nachlass to his work. Next I will dedicate a section to explain the development of each of the concepts throughout her career, from intersubjectivity,, to ethics and to transcendental anthropology. (shrink)