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

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

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 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.

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 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 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].

The aim of this paper is to investigate the variety of symmetric closure algebras, that is, closure algebras endowed with a De Morgan operator. Some general properties are derived. Particularly, the lattice of subvarieties of the subvariety of monadic symmetric algebras is described and an equational basis for each subvariety is given.

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

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.

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.

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)

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)

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)

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)

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)

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)

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)

The achievements of the textile industry in Roman Britain are often underestimated as a result of the meagreness of our available evidence. The Edict on maximum prices issued by Diocletian in A.D. 301 shows that British capes commanded high prices on the markets of the Empire, and that in the late third century A.D. British rugs were the best in the world. In view of the competition from the traditional centres of rug manufacture in the East, this is an astonishing (...) achievement. (shrink)

The received translation and interpretation of many of the technical terms current in the textile industry of the Roman Empire are inaccurate, because lexicographers have either fought shy of being precise, or have thought that they recognized in the ancient world technical processes which originated at a much later date. The evidence is often equivocal or insufficient, but may still yield details that have been overlooked. The textile expression scutulatus, to take an example, deserves more attention than Blümner has devoted (...) to it. When it refers to the appearance of a garment, Lewis and Short, s.v. scutulatus, translate ‘diamond or lozenge-shaped, checkered’. It seems worth while to attempt a more precise translation, and, if possible, to estimate the significance in context of the goods so designated. (shrink)

El desarrollo de la ciencia y la tecnología y de las competencias técnicas ha impulsado el desarrollo de las sociedad haciéndolas más complejas, causando que las aptitudes emocionales se conviertan en factores de éxito, ya que afectan el desempeño humano en todos los escenarios donde se desenvuelve, no obstante a pesar de las investigaciones en este área, actualmente no se cuenta con modelos que relacionen dichas aptitudes con el rendimiento organizacional, lo cual dio origen a esta investigación que busca determinar (...) el impacto de dichas competencias en la ejecución de proyectos en la empresa ENGISERV VENEZUELA C.A. Para realizar el estudio la metodología usada considero que se trata de una investigación de campo, no experimental y transversal. La población fue de 35 expertos en proyectos y la muestra se seleccionó por el método probabilístico aleatorio simple, Concluyéndose que las competencias emocionales afectan el rendimiento de los proyectos cerca 83,4%. Palabras Clave: Inteligencia emocional, competencias emocionales, rendimiento de proyectos. Referencias [1]J. García. «Caminos de la reflexión La teoría Orteguiana de las ideas y las creencias en el contexto de la escuela de Madrid».Edición 8, España: Biblioteca Nueva 2009. [2]D. McClelland. «Testing for Competencies rather than intelligence». American Psychologist. Edicion 1, NewYork, Harvard University 1973. [3]Levy-Leboyer, Claude. «Gestión de las Competencias».Edición 1, Ediciones Gestión 2000. Barcelona, España 1997. [4]R. Bisquerra. “Educación emocional y competencias básicas para la vida”. RIE, vol 21, pp. 1, 7-43. Junio 2003. [5]R. Fragoso "Inteligencia emocional y competencias emocionales en educación superior, ¿un mismo concepto?” RIES, vol. VI, no. 16, pp.110-125. Marzo 2015. [6]J. Sánchez “La competencia emocional en la escuela: una propuesta de organización dimensional y criterial”, RFEA. vol. 25, pp. 79-96, Abril 2010”. [7]Goleman, D. «Working with emotional intelligence». Bantam. 1998. [8]M. Vivas "La educación emocional: conceptos fundamentales." RUI, vol. 4, no. 2, pp.1-21. Agosto.2003. [9]W. Pinkerton. «Project management achieving project bottom-line success», Edicion 1, Pennsylvania Mc-Graw-Hill, 2003. [10]D. Goleman. «Inteligencia emocional en la empresa» Barcelona, España. Editorial Kairós, 2018. [11]C. Michelena. «Estrategias para la elaboración de un proyecto de investigación». Caracas: Insertos Médicos de Venezuela, 2004. [12]R. Sierra. «Técnicas de Investigación Social». Buenos Aires: Editorial Paraninfo.1992. [13]P. Baptista. C. Fernández y R Hernández. “Metodología de la investigación”. México DF: McGraw–Hill.2010. [14]M. Carbonero. “Formación inicial docente y competencias emocionales”: Educ. Pesqui. vol.45. pp.3-20 Abril, 2019. [15]American Management Association. «Leading with emotional intelligence», Nueva York, AMA 2012. (shrink)

A la lectura de La escritura del duelo de Victoria Eugenia Díaz Facio Lince -psicóloga, magíster en Ciencias Sociales y doctora en Humanidades; profesora e investigadora de la Universidad de Antioquia-, se nos introduce con un epígrafe del escritor español Francisco Umbral.

Doctors’ strikes are legally permissible in the UK, with the situation differing in other countries. But are they morally permissible? Doug McConnell and Darren Mann have systematically attempted to dismiss the arguments for the moral impermissibility of doctors’ strikes and creatively attempted to provide further moral justification for them. Unfortunately for striking doctors, they fail to achieve this. Meanwhile, junior doctors’ strikes have continued in the UK through 2023 and have now extended into 2024. In this response, which focuses on (...) the UK situation and specifically junior doctors’ strikes in the National Health Service (NHS) in England, I will demonstrate a central problem with their arguments—namely that they underplay the harms caused by prolonged doctors’ strikes by ignoring the harms to patients with cancer. This weakens their conclusion that strikes are morally permissible in terms of the conditions and thresholds they set. I then provide a psychological critique of their justification for strikes in terms of the interests of the public. It follows that invoking the controversial concept of supererogatory action is ungrounded but also absurd when you consider time-critical cancer care. If those representing striking doctors wish to maintain a modicum of moral respectability, they should mitigate for patients with cancer and negotiate reasonably and with urgency. (shrink)

This paper defends traditional political philosophy against the challenges Gaus leverages against it in The Open Society and Its Complexities. Granting Gaus that consensus on the principles of political philosophy is not forthcoming and that complexity undermines many of our most ambitious reform efforts, the paper argues that much work remains for political philosophy as it has been practiced for centuries. This is for three reasons. First, Gaus's own defense of the open society requires resources from the very traditions that (...) he tends to dismiss. Secondly, the kinds of reform Gaus encourages us to focus on in light of complexity presuppose answers to philosophical questions, answers that philosophers have long attempted to provide. Thirdly, not all politically salient philosophical questions are aimed at action guidance. Despite the value in Gaus's analysis, I conclude that political philosophy's future will look, at least in part, like its storied past. (shrink)

This chapter discusses author's view a Thomistic‐like dualism. Next, it lays out the details of his position and he argues that it has certain advantages over physicalist treatments of the human person, and, to a lesser degree, over alternate versions of substance dualism. Then, he responds to some objections against his position. He accepts constituent realism regarding properties (and relations), according to which properties (and relations) are universals that, when exemplified (and they need not be to exist), become constituents of (...) the ordinary particulars that have them. Furthermore, with the Thomistic framework in mind, the chapter offers his view of a human person. Finally, there is the argument that attempts to show that the unity of consciousness cannot be explained if one is a brain, because a brain is just an aggregate of different physical (separable) parts. (shrink)

This chapter contains sections titled: Section One: The Backdrop for Locating Consciousness in a Naturalist Ontology Section Two: The AC Section Three: John Searle and Contingent Correlation Section Four: Timothy O'Connor and Emergent Necessitation Section Five: Colin McGinn and Mysterian “Naturalism” Conclusion Further Reading References.

In their thought-provoking article, Sedlakova and Trachsel (2023) defend the view that the status—both epistemic and ethical—of Conversational Artificial Intelligence (CAI) used in psychotherapy is complicated. While therapeutic CAI seems to be more than a mere tool implementing particular therapeutic techniques, it falls short of being a “digital therapist.” One of the main arguments supporting the latter claim is that even though “the interaction with CAI happens in the course of conversation… the conversation is profoundly different from a conversation with (...) a human therapist” (Sedlakova and Trachsel 2023, 8). In particular, unlike a human therapist, CAI cannot help its users gain new insight and self-understanding (Sedlakova and Trachsel 2023). We agree that currently available therapeutic CAI cannot be considered a “digital therapist,” however, we think that the issue surrounding the acquisition of new self-understanding in the interaction with therapeutic CAI is more complicated than Sedlakova and Trachsel suggest. (shrink)

Growing demand for broadly accessible mental health care, together with the rapid development of new technologies, trigger discussions about the feasibility of psychotherapeutic interventions based on interactions with Conversational Artificial Intelligence (CAI). Many authors argue that while currently available CAI can be a useful supplement for human-delivered psychotherapy, it is not yet capable of delivering fully fledged psychotherapy on its own. The goal of this paper is to investigate what are the most important obstacles on our way to developing CAI (...) systems capable of delivering psychotherapy in the future. To this end, we formulate and discuss three challenges central to this quest. Firstly, we might not be able to develop effective AI-based psychotherapy unless we deepen our understanding of what makes human-delivered psychotherapy effective. Secondly, assuming that it requires building a therapeutic relationship, it is not clear whether psychotherapy can be delivered by non-human agents. Thirdly, conducting psychotherapy might be a problem too complicated for narrow AI, i.e., AI proficient in dealing with only relatively simple and well-delineated tasks. If this is the case, we should not expect CAI to be capable of delivering fully-fledged psychotherapy until the so-called “general” or “human-like” AI is developed. While we believe that all these challenges can ultimately be overcome, we think that being mindful of them is crucial to ensure well-balanced and steady progress on our path to AI-based psychotherapy. (shrink)

While my own philosophical views are largely in keeping with my mentor, Dallas Willard, nevertheless, I find his conception of the human person puzzling, hard to specify precisely, and prima facie contradictory in a few places. Dallas's central goal in formulating his anthropology was to develop a model that shed light on, allowed for deeper insight into, and fostered interest in spiritual formation, especially the role of the body in spiritual maturation. I share this goal, and agree with most of (...) his model. But in what follows, I will make more precise what his views were, try to clear up what, prima facie, seem to be contradictions in his theory, and, finally, recommend an alternative that captures the central concerns Dallas had for his own position. Thus, I will lay out a few general points of Dallas's ontology, provide a description of his philosophical/theological anthropology, along with two problems that seem to be present, and offer a slightly adjusted alternative to his position that accomplishes his main goal in a way with which I believe he would be satisfied. (shrink)

The majority of our linguistic exchanges, such as everyday conversations, are divided into turns; one party usually talks at a time, with only relatively rare occurrences of brief overlaps in which there are two simultaneous speakers. Moreover, conversational turn-taking tends to be very fast. We typically start producing our responses before the previous turn has finished, i.e., before we are confronted with the full content of our interlocutor’s utterance. This raises interesting questions about the nature of linguistic understanding. Philosophical theories (...) typically focus on linguistic understanding characterized either as an ability to grasp the contents of utterances in a given language or as outputs of this ability—mental states of one type or another. In this paper, I supplement these theories by developing an account of the process of understanding. I argue that it enables us to capture the dynamic and temporal aspect of understanding and reconcile philosophical investigations with empirical research on language comprehension. (shrink)