Recent research on algebraic models of _quasi-Nelson logic_ has brought new attention to a number of classes of algebras which result from enriching (subreducts of) Heyting algebras with a special modal operator, known in the literature as a _nucleus_. Among these various algebraic structures, for which we employ the umbrella term _intuitionistic modal algebras_, some have been studied since at least the 1970s, usually within the framework of topology and sheaf theory. Others may seem more exotic, for their primitive operations (...) arise from algebraic terms of the intuitionistic modal language which have not been previously considered. We shall for instance investigate the variety of _weak implicative semilattices_, whose members are (non-necessarily distributive) meet semilattices endowed with a nucleus and an implication operation which is not a relative pseudo-complement but satisfies the postulates of Celani and Jansana’s strict implication. For each of these new classes of algebras we establish a representation and a topological duality which generalize the known ones for Heyting algebras enriched with a nucleus. (shrink)

In the present paper we study systematically several consequence relations on the usual language of propositional intuitionistic logic that can be defined semantically by using Kripke frames and the same defining truth conditions for the connectives as in intuitionistic logic but without imposing some of the conditions on the Kripke frames that are required in the intuitionistic case. The logics so obtained are called subintuitionistic logics in the literature. We depart from the perspective of considering a logic just as a (...) set of theorems and also depart from the perspective taken by Restall in that we consider standard Kripke models instead of models with a base point. We study the relations between subintuitionistic logics and modal logics given by the translation considered by Došen. Moreover, we classify the logics obtained according to the hierarchy considered inAlgebraic Logic. (shrink)

We show the first examples of recursively enumerable (even decidable) two-dimensional products of finitely axiomatisable modal logics that are not finitely axiomatisable. In particular, we show that any axiomatisation of some bimodal logics that are determined by classes of product frames with linearly ordered first components must be infinite in two senses: It should contain infinitely many propositional variables, and formulas of arbitrarily large modal nesting-depth.

The present paper introduces and studies the variety WH of weakly Heyting algebras. It corresponds to the strict implication fragment of the normal modal logic K which is also known as the subintuitionistic local consequence of the class of all Kripke models. The tools developed in the paper can be applied to the study of the subvarieties of WH; among them are the varieties determined by the strict implication fragments of normal modal logics as well as varieties that do not (...) arise in this way as the variety of Basic algebras or the variety of Heyting algebras. Apart from WH itself the paper studies the subvarieties of WH that naturally correspond to subintuitionistic logics, namely the variety of R-weakly Heyting algebras, the variety of T-weakly Heyting algebras and the varieties of Basic algebras and subresiduated lattices. (shrink)

En el presente artículo se analiza el relato sobre la supuesta correspondencia mantenida por Jesús y el rey Abgar V de Edesa, presente en la obra Historia Eclesiástica de Eusebio de Cesarea. Desde sus inicios, la leyenda gozó de mucha fama debido a la consideración de los fieles de que se trataba de uno de los pocos testimonios existentes sobre un texto escrito por el mismísimo Jesús. Este hecho provocó que esta tradición se tradujese a numerosas lenguas y recibiera varias (...) influencias distintas, lo que sin duda favoreció su desarrollo y su pervivencia en el tiempo. A pesar de los numerosos estudios sobre su popularidad y sobre las distintas versiones existentes, el origen de esta leyenda sigue sin estar claro y está lejos de llegar a un consenso académico. Por tanto, en este trabajo se estudian las distintas perspectivas sobre el inicio de esta tradición, analizando aquellas teorías que se centran en sugerir que la obra se trata de una invención del autor, pero también buscando algún matiz histórico que pudo servir como fuente de inspiración para Eusebio de Cesarea. (shrink)

We consider a 2-valued non-deterministic connective \({\wedge \!\!\!\!\!\vee }\) defined by the table resulting from the entry-wise union of the tables of conjunction and disjunction. Being half conjunction and half disjunction we named it _platypus_. The value of \({\wedge \!\!\!\!\!\vee }\) is not completely determined by the input, contrasting with usual notion of Boolean connective. We call non-deterministic Boolean connective any connective based on multi-functions over the Boolean set. In this way, non-determinism allows for an extended notion of truth-functional connective. (...) Unexpectedly, this very simple connective and the logic it defines, illustrate various key advantages in working with generalized notions of semantics (by incorporating non-determinism), calculi (by allowing multiple-conclusion rules) and even of logic (moving from Tarskian to Scottian consequence relations). We show that the associated logic cannot be characterized by any finite set of finite matrices, whereas with non-determinism two values suffice. Furthermore, this logic is not finitely axiomatizable using single-conclusion rules, however we provide a very simple analytic multiple-conclusion axiomatization using only two rules. Finally, deciding the associated multiple-conclusion logic is \(\mathbf {coNP}\) -complete, but deciding its single-conclusion fragment is in \({\mathbf {P}}\). (shrink)

The Mexican cult around the image of the Virgin of Tepeyac is commonly addressed in relation with creole nationalism, but that emphasis ignores the survival of its cult until today. Given that construction of identity through ‘miraculous’ images persists through technologies of iconic deployment, it is necessary to examine the original functions of its technologies. I investigate these problems by considering the construction of a newexhibition site for the Virgin of Tepeyac, and the modalities of reproducing the image until today. (...) The historical comparison of these contemporary techniques with those of the seventeenth century enables to appreciate the coherence of this visual tradition and its importance to the construction of social processes in Mexico. (shrink)

O que se pretende com este artigo é mostrar, seguindo o itinerário da sucessão das categorias, que é o mesmo das atitudes nas quais o homem se compreende, a relação entre as duas últimas categorias da Lógica da filosofia - Sentido e Sabedoria - e a ideia de cidada­nia. Com efeito, a tese de fundo deste texto consiste em dizer que uma das originalidades do pensamento de Eric Weil reside justamente no conceito de retomada, que é um conceito de compreensão, (...) e dizer, ao mesmo tempo, que ele é decisivo para a problematização da relação entre Sentido, Sabedoria e cidadania. (shrink)

This paper discusses historical-critical thought to address the problems of restoration and preservation of tape music, proposing viable solutions to the matter of digitizing the historically valuable data that exists on and is represented by magnetic tapes. A detailed program of research and restoration and some software for helping in creation of critical editions of the musical works are proposed. We also present some of the issues and controversies that must be considered and approaches we have applied in the preservation (...) of tape music, highlighting how these interpretations can impact later performances of these tape documents. Fundamentally, we argue that the act of tape music restoration has a parallel with the interpretation of the “Urtext score” in the performance of music from the Common Practice Era. (shrink)

This paper deals with the proposal of a person‐affecting version of the principle of Procreative Beneficence. Such a principle has been stated by Savulescu & Kahane in an impersonal form and balanced with a person‐affecting principle of harm to address the moral problem of the selection of future children. The paper aims to show some differences between Person‐affecting Procreative Beneficence and Savulescu & Kahane’s hybrid position, and to distinguish the former from other pro‐selection perspectives. Moreover, it explores the extension of (...) such a principle beyond selection to other issues of reproductive ethics. (shrink)

Background: Chronic Pain (CP) has serious medical and social consequences, and leads to economic burden that threatens the sustainability of healthcare services. Thus, optimized management of pain tools to support CP patients in adjusting to their condition and improving quality of life is timely. Although Acceptance and Commitment Therapy (ACT) is considered an evidence-based psychological approach for CP, evidence for the efficacy of online-delivered ACT for CP is still scarce. At the same time, studies suggest that self-compassion mediates the change (...) in disability and psychopathological symptoms in ACT interventions for CP, although self-compassion is not a specific target in ACT. Thus, an explicit focus on self-compassion might increase the efficacy of ACT interventions for CP, although this hypothesis has not been tested. This study aims to develop an eHealth ACT and compassion-based self-management intervention for CP, the iACTwithPain, and to compare its efficacy in improving health outcomes to a similar ACT-only intervention and a waiting list group. Methods: The eHealth platform that will host the interventions will be developed using a flat design identity and will be interactive. The iACTwithPain intervention will comprise 8 weekly self-management sessions, and will be developed taking into consideration the psychological flexibility model applied to CP, with the addition of explicit compassion-based components. To analyse whether the iACTwithPain intervention will present superiority in improving CP’s impact and related health markers over the two other conditions, this study will follow a RCT design with three arms. CP patients will be recruited through direct contact with patient associations and healthcare services and a national press release in Portugal. Outcome measurement will be conducted at baseline, post-intervention and at 3- and 6-months follow-ups. The interventions’ acceptability will also be assessed. Discussion: The iACTwithPain intervention is expected to improve CP patients’ psychosocial functioning, quality of life, and empowerment, by promoting adaptive disease management and regulation of pain-related internal experiences. Results will contribute to a better understanding on the pertinence of adding compassion elements to ACT for CP and to reach an optimized intervention for CP. (shrink)

In recent years, there have been several high-profile recalls of hybrid products. If consumers perceive a global firm to be responsible for the recall, then it will reduce their brand equity. Therefore, global firms may respond in ethically questionable ways to justify themselves to important stakeholders and avoid blame. Understanding how stakeholders attribute blame for crises involving hybrid products is important to shed light on the unethical manner in which global firms might avoid blame in such situations. The research reported (...) here shows that in a hybrid product crisis, consumers show a bias in favor of the brand company and against the manufacturing company. This bias is more pronounced when the country of manufacture has an unfavorable image or when consumers lack familiarity with the recalled brand. Ambiguous recall announcements by companies that fail to provide a specific and clear reason for the product defect prompt consumers to assume that a manufacturing flaw caused the product defect. As a result, consumers reduce their attribution of blame for the brand company, and thus its brand equity is maintained. (shrink)

This study explores the impact of B Corp certification and its associated impact assessment on four case studies of small and medium-sized Brazilian companies certified as B Corps. The results reveal that although all companies had achieved high scores in the certification assessment, awarded on the basis of existing performance, they did not subsequently develop road maps for the future to improve their scores in the way which the B Corp Impact Assessment process endorses as one of the benefits of (...) certification. Their incremental changes are discussed in the light of the main motivations and expectations of these companies’ founders with regard to the certification. A central role of the B Corp certification for this group of companies was to improve their external reputation with investors, clients and consumers. They were not strongly driven to reshape internal processes in ways which would advance their scores in the impact assessment and which would tackle complex problems of corporate governance. Our findings contribute to enriching the discussion of stakeholder engagement and corporate governance in hybrid organizations and contribute to the emerging agenda on studying change over time in B Corps. (shrink)

This study explores the impact of B Corp certification and its associated impact assessment on four case studies of small and medium-sized Brazilian companies certified as B Corps. The results reveal that although all companies had achieved high scores in the certification assessment, awarded on the basis of existing performance, they did not subsequently develop road maps for the future to improve their scores in the way which the B Corp Impact Assessment process endorses as one of the benefits of (...) certification. Their incremental changes are discussed in the light of the main motivations and expectations of these companies’ founders with regard to the certification. A central role of the B Corp certification for this group of companies was to improve their external reputation with investors, clients and consumers. They were not strongly driven to reshape internal processes in ways which would advance their scores in the impact assessment and which would tackle complex problems of corporate governance. Our findings contribute to enriching the discussion of stakeholder engagement and corporate governance in hybrid organizations and contribute to the emerging agenda on studying change over time in B Corps. (shrink)

Tarski algebras, also known as implication algebras or semi-boolean algebras, are the \-subreducts of Boolean algebras. In this paper we shall introduce and study the complete and atomic Tarski algebras. We shall prove a duality between the complete and atomic Tarski algebras and the class of covering Tarski sets, i.e., structures \, where X is a non-empty set and \ is non-empty family of subsets of X such that \. This duality is a generalization of the known duality between sets (...) and complete and atomic Boolean algebras. We shall also analize the case of complete and atomic Tarski algebras endowed with a complete modal operator, and we will prove a duality for these algebras. (shrink)

In this note we introduce the variety $${{\mathcal C}{\mathcal D}{\mathcal M}_\square}$$ of classical modal De Morgan algebras as a generalization of the variety $${{{\mathcal T}{\mathcal M}{\mathcal A}}}$$ of Tetravalent Modal algebras studied in [ 11 ]. We show that the variety $${{\mathcal V}_0}$$ defined by H. P. Sankappanavar in [ 13 ], and the variety S of Involutive Stone algebras introduced by R. Cignoli and M. S de Gallego in [ 5 ], are examples of classical modal De Morgan algebras. (...) We give a representation theory, and we study the regular filters, i.e., lattice filters closed under an implication operation. Finally we prove that the variety $${{{\mathcal T}{\mathcal M}{\mathcal A}}}$$ has the Amalgamation Property and the Superamalgamation Property. (shrink)

In this research, we evaluate the response of Brazilian consumers to corporate social responsibility (CSR) initiatives accompanied by a price increase. We demonstrate that the extent to which Brazilian consumers perceive a company to be socially responsible (i.e., their CSR perceptions) is related to both the basic transactional outcome of purchase intentions as well as two relational outcomes: the likelihood to switch to a competitor and to complain about the CSR-based price increase. More interestingly, we find that these relationships are (...) jointly mediated by the consumers’ perceptions of price fairness and feelings of personal satisfaction. Perhaps most interesting, we find that these mediating effects vary with consumer purchasing power; the mediating effect of price fairness on purchase intention is stronger for lower income than for higher income consumers, whereas the mediating effects of personal satisfaction on switching and complaining intentions are stronger for higher income than for lower income consumers. (shrink)

About 35 years ago Wheeler introduced the motto “law without law” to highlight the possibility that Physics may be understood only following regularity principles and few relevant facts, rather than relying on a treatment in terms of fundamental theories. Such a proposal can be seen as part of a more general attempt summarized by the slogan “it from bit”, which privileges the information as the basic ingredient. Apparently it seems that it is possible to obtain, without the use of physical (...) laws, some important results in an easy way, for instance, the probability distribution of the canonical ensemble. In this paper we will present a general discussion on those ideas of Wheeler’s that originated the motto “law without law”. In particular we will show how the claimed simplicity is only apparent and it is rather easy to produce wrong results. We will show that it is possible to obtain some of the results treated by Wheeler in the realm of the statistical mechanics, using precise assumptions and nontrivial results of probability theory, mainly concerning ergodicity and limit theorems. (shrink)

Like Einstein's general theory of relativity is concerned with explaining the basics of an observable experience – i.e., gravity – most people take for granted that Chomsky's theory of generative grammar (GG) is concerned with the basic nature of language. This chapter highlights a mere subset of central constructs in GG, showing how they have featured prominently and thus shaped formal linguistic studies in multilingualism. Because multilingualism includes a wide range of nonmonolingual populations, the constructs are divided across child bilingualism (...) and adult third language for greater coverage. In the case of the former, the chapter examines how poverty of the stimulus has been investigated. Using the nascent field of L3/Ln acquisition as the backdrop, it discusses how the GG constructs of I‐language versus E‐language sit at the core of debates regarding the very notion of what linguistic transfer and mental representations should be taken to be. (shrink)

In this note we introduce and study algebras of type such that is a bounded distributive lattice and ⌝ is an operator that satisfies the condition ⌝ = a ⌝ b and ⌝ 0 = 1. We develop the topological duality between these algebras and Priestley spaces with a relation. In addition, we characterize the congruences and the subalgebras of such an algebra. As an application, we will determine the Priestley spaces of quasi-Stone algebras.

In the philosophy of science, abstraction has usually been analyzed in terms of the interface between our experience and the design of our concepts. The often implicit assumption here is that such interface has a definite identifiable and universalizable structure, determining the epistemic correctness of any abstraction. Our claim is that, on the contrary, the epistemic grounding of abstraction should not be reduced to the structural norms of such interface but is also related to the constraints on the cognitive processes (...) of specific abstractions. This suggests that we should understand abstraction as embodied in different kinds of abstraction practices. (shrink)

A Hilbert algebra with supremum is a Hilbert algebra where the associated order is a join-semilattice. This class of algebras is a variety and was studied in Celani and Montangie . In this paper we shall introduce and study the variety of $${H_{\Diamond}^{\vee}}$$ H ◊ ∨ -algebras, which are Hilbert algebras with supremum endowed with a modal operator $${\Diamond}$$ ◊ . We give a topological representation for these algebras using the topological spectral-like representation for Hilbert algebras with supremum given in (...) Celani and Montangie . We will consider some particular varieties of $${H_{\Diamond}^{\vee}}$$ H ◊ ∨ -algebras. These varieties are the algebraic counterpart of extensions of the implicative fragment of the intuitionistic modal logic $${\mathbf{IntK}_{\Diamond}}$$ IntK ◊ . We also determine the congruences of $${H_{\Diamond}^{\vee}}$$ H ◊ ∨ -algebras in terms of certain closed subsets of the associated space, and in terms of a particular class of deductive systems. These results enable us to characterize the simple and subdirectly irreducible $${H_{\Diamond}^{\vee }}$$ H ◊ ∨ -algebras. (shrink)

La filosofía de la ciencia se desarrolló durante la primera mitad del siglo xx bajo el supuesto de que la ciencia podía caracterizarse por la estructura lógica tanto del conocimiento articulado en las teorías más exitosas como de sus explicaciones. En la segunda mitad del siglo xx se cuestiona fuertemente esa idea, pero se sigue asumiendo que la filosofía de la ciencia debe hacerse siguiendo los cánones de una epistemología fundamentalista que considera que el avance de la ciencia pasa por (...) una ontología cada vez mas austera guiada por la idea de "mientras menos mejor". Desde esta perspectiva fundamentalista, el que las diferentes ciencias hablen de diferentes tipos de cosas es un obstáculo al entendimiento, producto de la imperfección del conocimiento actual. Este ideal nos invita a pensar que la epistemología debe hacerse reflexionando sobre el conocimiento articulado en nuestras teorías más austeras y nos compromete con propuestas reduccionistas problemáticas que no permiten explicar la diversidad de recursos epistémicos que de hecho utilizan los científicos. En este libro promovemos una epistemología que no sigue el lema de "mientras menos mejor", sino el de "organizar nuestros recursos epistémicos de manera que se genere entendimiento". Así, la misma estructura de las explicaciones y las prácticas (que incluye métodos y normas respecto de lo que se considera plausible y valioso) es lo que nos da la pauta para responder a la pregunta de qué es lo que hay. Esta estrategia epistémica nos obliga a hacer una filosofía de la ciencia muy cercana a la ciencia, reconociendo la pluralidad de sus métodos, objetivos y prácticas, sin reducir la filosofía de la ciencia a la sociología o a cualquier otra ciencia en particular. (shrink)

A dominant theme in the ninth of the Heroides, Deianira's letter to Hercules, is Deianira's indignation that Hercules has been defeated by a woman: first by Iole ; then by Omphale . The theme is exploited so insistently that Vessey, who regards the epistle as spurious, sees in this insistence a sign of the forger's clumsiness. consider the exploitation of the motive of‘victor victus’ in Heroides 9, on the contrary, as a strong sign of Ovidian authorship. From the very beginning (...) of the letter, the reader is reminded that if a woman, Iole, has metaphorically destroyed Hercules, another woman is on the point of destroying Hercules in a much more real and literal way, and this woman is none other than Deianira herself. When Deianira writes the letter, she has just sent to Hercules the garment soaked in Nessus' poison that will provoke Hercules' horrible death : thus Deianira, rather than Iole or Omphale, is the woman who vanquishes the unvanquished hero. But this is not only a matter of dramatic irony based on the general lines of the story. Heroides 9 is an elegiac rewriting of Sophocles' Trachiniae , and at the same time is inserted in the time and the ‘body’ of the tragedy. Ironic prefiguration in Heroides is normally realized through intertextual anticipation: thefuture events that are prefigured are present in the texts of the model epic or tragedy. Deianira blames Hercules for bis defeat: quern numquam Iuno seriesque immensa laborum fregerit, huic Iolen imposuisse iugum quem non mille ferae, quern non Stheneleius hostis, non potuit Iuno vincere, vincit amor. (shrink)

In this work we will study Tarski algebras endowed with a subordination, called subordination Tarski algebras. We will define the notion of round filters, and we will study the class of irreducible round filters and the maximal round filters, called ends. We will prove that the poset of all round filters is a lattice isomorphic to the lattice of the congruences that are compatible with the subordination. We will prove that every end is an irreducible round filter, and that in (...) a topological subordination Tarski algebra A, every irreducible round filter is an end iff A is a monadic subordination Tarski algebra. As corollary of this result we have that the variety of monadic Tarski algebra can be characterised as the topological Tarski algebras where every irreducible open filter is a maximal open filter. (shrink)

Designers’ intentions are important for determining an artifact’s proper function (i.e., its perceived real function). However, there are disagreements regarding why. In one view, people reason causally about artifacts’ functional outcomes, and designers’ intended functions become important to the extent that they allow inferring outcomes. In another view, people use knowledge of designers’ intentions to determine proper functions, but this is unrelated to causal reasoning, having perhaps to do with intentional or social forms of reasoning (e.g., authority). Regarding these latter (...) social factors, researchers have proposed that designers’ intentions operate through a mechanism akin to social conventions, and that therefore both are determinants of proper function. In the current work, participants learned about an object’s creation, about social conventions for its use and about a specific episode where the artifact was used. The function implemented by the user could be aligned with the designer’s intended function, the social convention, both, or neither (i.e., an opportunistic use). Importantly, the use episode always resulted in an accident. Data show that the accident negatively affected proper function judgments and perceived efficiency for conventional and opportunistic functions, but not for designers’ intended functions. This is inconsistent with the view that designers’ intentions are conceptualized as causes of functional outcomes and with the idea that designers’ intentions and social conventions operate through a common mechanism. (shrink)

The present paper introduces and studies the variety [MATHEMATICAL SCRIPT CAPITAL W]ℋn of n-linear weakly Heyting algebras. It corresponds to the algebraic semantic of the strict implication fragment of the normal modal logic K with a generalization of the axiom that defines the linear intuitionistic logic or Dummett logic. Special attention is given to the variety [MATHEMATICAL SCRIPT CAPITAL W]ℋ2 that generalizes the linear Heyting algebras studied in [10] and [12], and the linear Basic algebras introduced in [2].

Hilbert algebras provide the equivalent algebraic semantics in the sense of Blok and Pigozzi to the implication fragment of intuitionistic logic. They are closely related to implicative semilattices. Porta proved that every Hilbert algebra has a free implicative semilattice extension. In this paper we introduce the notion of an optimal deductive filter of a Hilbert algebra and use it to provide a different proof of the existence of the free implicative semilattice extension of a Hilbert algebra as well as a (...) simplified characterization of it. The optimal deductive filters turn out to be the traces in the Hilbert algebra of the prime filters of the distributive lattice free extension of the free implicative semilattice extension of the Hilbert algebra. To define the concept of optimal deductive filter we need to introduce the concept of a strong Frink ideal for Hilbert algebras which generalizes the concept of a Frink ideal for posets. (shrink)

We critically analyse the point of view for which laws of nature are just a mean to compress data. Discussing some basic notions of dynamical systems and information theory, we show that the idea that the analysis of large amount of data by means of an algorithm of compression is equivalent to the knowledge one can have from scientific laws, is rather naive. In particular we discuss the subtle conceptual topic of the initial conditions of phenomena which are generally incompressible. (...) Starting from this point, we argue that laws of nature represent more than a pure compression of data, and that the availability of large amount of data, in general, is not particularly useful to understand the behaviour of complex phenomena. (shrink)

In the fourth line of her first speech in Book 1, to Ilioneus and the Trojan castaways, Dido quotes the first word of the first line of Lucretius’ De rerum natura, and in the fourth line of her second speech, to Aeneas, she quotes the first words of the second line of the De rerum natura. This is not a coincidence but a signal of the importance of Lucretius and Epicureanism for the characterization of Dido in the Aeneid.

In this work, we study the relational representation of the class of Tarski algebras endowed with a subordination, called subordination Tarski algebras. These structures were introduced in a previous paper as a generalisation of subordination Boolean algebras. We define the subordination Tarski spaces as topological spaces with a fixed basis endowed with a closed relation. We prove that there exist categorical dualities between categories whose objects are subordination Tarski algebras and categories whose objects are subordination Tarski spaces. These results extend (...) the known dualities for modal algebras. Finally, we are going to characterise some algebraic conditions written in the quasi-modal language by means of first-order conditions. (shrink)

In this paper we shall discuss properties of saturation in monotonic neighbourhood models and study some applications, like a characterization of compact and modally saturated monotonic models and a characterization of the maximal Hennessy-Milner classes. We shall also show that our notion of modal saturation for monotonic models naturally extends the notion of modal saturation for Kripke models.

We introduce a variety of algebras in the language of Boolean algebras with an extra implication, namely the variety of pseudo-subordination algebras, which is closely related to subordination algebras. We believe it provides a minimal general algebraic framework where to place and systematise the research on classes of algebras related to several kinds of subordination algebras. We also consider the subvariety of pseudo-contact algebras, related to contact algebras, and the subvariety of the strict implication algebras introduced in Bezhanishvili et al. (...) [(2019). A strict implication calculus for compact Hausdorff spaces. Annals of Pure and Applied Logic, 170, 102714]. The variety of pseudo-subordination algebras is term equivalent to the variety of Boolean algebras with a binary modal operator. We exploit this fact in our study. In particular, to obtain a topological duality from which we derive the known topological dualities for subordination algebras and contact algebras. (shrink)

This paper focuses on order-preserving logics defined from varieties of distributive lattices with negation, and in particular on the problem of whether these can be axiomatized by means Hilbert-style calculi that are finite. On the negative side, we provide a syntactic condition on the equational presentation of a variety that entails failure of finite axiomatizability for the corresponding logic. An application of this result is that the logic of all distributive lattices with negation is not finitely axiomatizable; we likewise establish (...) that the order-preserving logic of the variety of all Ockham algebras is also not finitely axiomatizable. On the positive side, we show that an arbitrary subvariety of semi-De Morgan algebras is axiomatized by a finite number of equations if and only if the corresponding order-preserving logic is axiomatized by a finite Hilbert-style calculus. This equivalence also holds for every subvariety of a Berman variety of Ockham algebras. We obtain, as a corollary, a new proof that the implication-free fragment of intuitionistic logic is finitely axiomatizable, as well as a new corresponding Hilbert-style calculus. Our proofs are constructive in that they allow us to effectively convert an equational presentation of a variety of algebras into a Hilbert-style calculus for the corresponding order-preserving logic, and vice versa. We also consider the assertional logics associated to the above-mentioned varieties, showing in particular that the assertional logics of finitely axiomatizable subvarieties of semi-De Morgan algebras are finitely axiomatizable as well. (shrink)

Este texto plantea una lectura de la propuesta estética del joven Nietzsche desde una óptica de la estética de las pasiones en su teoría de la voluntad de poder. Se analiza el desarrollo intelectual desde El nacimiento de la tragedia hasta su conversión psicofisiológica del arte en la etapa de madurez, a la vez que se estudia la repercusión de esta evolución en su planteamiento desde la psicología de los afectos. De esta forma, aunque es cierto que el transcurso intelectual (...) de Nietzsche cambia en el momento que abandona la metafísica del artista, continúa ahondando en una propuesta estética desde las tendencias afectivas de la psicología y el cuerpo. (shrink)

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)