The following is an attempt to read Anselm’s treatise De veritate in accordance with its immanent intention by considering the question: to what extent and in which sense does it, in unfolding the concept of truth, more concretely determine the concept of God—and accordingly also the concept of man and his relationship to God? The question of whether and to what extent Anselm argues sola ratione will not be raised, but instead in what way his ratio is capable of developing (...) out of the data of belief a conceptuality that is binding for the intellectus credens. (shrink)

This work, The Rational-Architectonic of Modernity, understands itself to be part of a whole, which was begun with the same author’s Topologie der Metaphysik. The Topologie presented the history of metaphysics as a whole in the sense of something completed, which was taken there in the full significance of that which consists not only of beginning, middle, and end—contrary to the usual talk of the end of metaphysics as a failed undertaking—but also which had a concretely determined task to fulfill (...) and did so—contrary to the notion of that history as a continuum of philosophically relevant questions, which may be arbitrarily taken up and furthered. This task was shown in the Topologie to be a threefold one, in each instance prescribed by a different configuration of an originary knowledge of the determination of man. Each configurations of wisdom, having already come into the world, called forth a reason that, loving this wisdom itself, was thus philosophic in the strict sense—a reason which corresponded to this wisdom and conceived it in a logic appropriate to it alone. This reason called forth by these configurations of wisdom formed a series of rationes, which in each instance constituted a figure, an entire epoch of metaphysics. Taken abstractly, the terms out of which the rationes were made up were ‘the determination of the topic’, ‘the topic of thinking’, and ‘thinking itself’—it is no accident that these terms stem from the province of the Heideggerian sense-explication. (shrink)

We group the existing variants of the familiar set-theoretical and truth-theoretical paradoxes into two classes: connective paradoxes, which can in principle be ascribed to the presence of a contracting connective of some sort, and structural paradoxes, where at most the faulty use of a structural inference rule can possibly be blamed. We impute the former to an equivocation over the meaning of logical constants, and the latter to an equivocation over the notion of consequence. Both equivocation sources are tightly related, (...) and can be cleared up by adopting a particular substructural logic in place of classical logic. We then argue that our perspective can be justified via an informational semantics of contraction-free substructural logics. (shrink)

This paper focuses on the role of punishment as a critical social mechanism for cheating prevention in MMORPGs. The role of punishment is empirically investigated in a case study of the MMORPG Tibia and by focusing on the use of bots to cheat. We describe the failure of punishment in Tibia, which is perceived by players as one of the elements facilitating the proliferation of bots. In this process some players act as a moral enterprising group contributing to the reform (...) of the game rules and in particular to the reform of the Tibia punishment system by the game company. In the conclusion we consider the ethical issues raised by our findings and we propose some general reflections on the role of punishment and social mechanisms for the governance of online worlds more generally. (shrink)

ISSN:1909-9711 (En línea) Misión La Revista Acta Colombiana de Psicología publica hallazgos originales de las investigaciones en Psicología y de esta disciplina en diálogo con otras, con el propósito de divulgarlas a la comunidad universitaria y a todas las personas interesadas en conocer sus nuevos avances y aplicaciones a distintos campos y necesidades de la sociedad contemporánea.

Es innegable que la noción de epoché fue crucial para el surgimiento y el posterior desarrollo de la tradición fenomenológica. Si bien la resignificación que Husserl hace de ésta es sumamente original, él mismo se detiene a reconocer en la filosofía antigua el mérito de haber encontrado el camino idóneo para acceder a la subjetividad trascendental. En el siguiente trabajo buscaré, por un lado, definir la epoché tal como se origina en el pensamiento de los sofistas para luego pasar a (...) analizar el modo en el que Husserl logra reversionar dicha noción hasta convertirla en el método predilecto que nos permite arribar a la esfera trascendental. Por otro lado, continuaré rastreando la evolución de la epoché para llegar a su abandono en la filosofía de Sartre. En relación con esto último, me interesa preguntarme si el existencialismo reniega de la suspensión del juicio por considerarla inapropiada o si, más bien, se trata de una supresión parcial del método fenomenológico. Me propongo defender esta segunda tesis, alegando que, en realidad, la epoché no es una noción que esté totalmente ausente en la filosofía de Sartre sino que se mantiene vigente en términos de angustia existencial. (shrink)

Portuguese translation of Aristotle’s _Prophecy in Sleep_, preceded by a short presentation of the text and accompanied by explanatory notes.

The influence of age and formal education on the development of moral reasoning in a Spanish sample of students was assessed by using a Spanish translation of Rest's Defining Issues Test. Our results support the hypothesis that moral development is highly related to both variables in our cultural context, although more so with formal education than with age.

This paper addresses some relations between the spatial politics of queer assemblies in spaces of protest and the constitution of collective political subjects. It does so by exploring the spatial politics of queer activism within the global Occupy movements, in the light of Judith Butler’s work on the performative power of assembly and the ambivalences of the Foucauldian concept of heterotopia. Specific challenges faced by queer activists in various encampments will be addressed in order to expose some tensions between the (...) constitutive exclusions inherent to the constitution of spaces of protest and the processes of coalition building needed to effectively overcome those very constitutive exclusions. (shrink)

Figurative communication (the use of metaphor, metonymy, hyperbole and irony) provides economy of expression, clarity, persuasiveness, politeness, evaluation, and communication of emotions. However, it also increases the potential for misunderstanding in situations when people lack shared background knowledge. This book combines theoretical frameworks with empirical studies that measure the effectiveness of different approaches to the use of figurative language in advertisements, to show how to maximise the benefits of creative metaphor and metonymy in global advertising. It highlights how subtle differences (...) in colour, layout, and combinations of different kinds of figurative language affect the reception and appreciation of creative advertising, shedding new light on the nature of figurative communication itself. With a balance between theory, experiments and practical case studies, this book is accessible for academics in linguistics and communication studies, as well as advertising and marketing professionals. (shrink)

Here, we discuss historical, philosophical and technical problems associated with relating logic and relating semantics. To do so, we proceed in three steps. First, Section 1 is devoted to providing an introduction to both relating logic and relating semantics. Second, we address the history of relating semantics and some of the main research directions and their philosophical applications. Third, we discuss some technical problems related to relating semantics, particularly whether the direct incorporation of the relation into the language of relating (...) logic is needed. The starting point for our considerations presented here is the 1st Workshop On Relating Logic and the selected papers for this issue. (shrink)

In this paper I consider recent discussions within the representationalist theories of phenomenal consciousness, in particular, the discussions between first order representationalism (FOR) and higher order representationalism (HOR). I aim to show that either there is only a terminological dispute between them or, if the discussion is not simply terminological, then HOR is based on a misunderstanding of the phenomena that a theory of phenomenal consciousness should explain. First, I argue that we can defend first order representationalism from Carruthers' attacks (...) and ignore higher order thoughts in our account of phenomenal consciousness. Then I offer a diagnostic of Carruthers' misunderstanding. In the last section I consider further reasons to include mindreading abilities in an explanation of phenomenal consciousness. (shrink)

The aim of the present book is to give a comprehensive account of the ‘state of the art’ of substructural logics, focusing both on their proof theory and on their semantics (both algebraic and relational. It is for graduate students in either philosophy, mathematics, theoretical computer science or theoretical linguistics as well as specialists and researchers.

(2014). Cross-world luck at the time of decision is a problem for compatibilists as well. Philosophical Explorations: Vol. 17, No. 2, pp. 112-125. doi: 10.1080/13869795.2014.912673.

In this paper we introduce a new natural deduction system for the logic of lattices, and a number of extensions of lattice logic with different negation connectives. We provide the class of natural deduction proofs with both a standard inductive definition and a global graph-theoretical criterion for correctness, and we show how normalisation in this system corresponds to cut elimination in the sequent calculus for lattice logic. This natural deduction system is inspired both by Shoesmith and Smiley's multiple conclusion systems (...) for classical logic and Girard's proofnets for linear logic. (shrink)

In this work we argue that there is no strong demarcation between pure and applied mathematics. We show this first by stressing non-deductive components within pure mathematics, like axiomatization and theory-building in general. We also stress the “purer” components of applied mathematics, like the theory of the models that are concerned with practical purposes. We further show that some mathematical theories can be viewed through either a pure or applied lens. These different lenses are tied to different communities, which endorse (...) different evaluative standards for theories. We evaluate the distinction between pure and applied mathematics from a late Wittgensteinian perspective. We note that the classical exegesis of the later Wittgenstein’s philosophy of mathematics, due to Maddy, leads to a clear-cut but misguided demarcation. We then turn our attention to a more niche interpretation of Wittgenstein by Dawson, which captures aspects of the aforementioned distinction more accurately. Building on this newer, maverick interpretation of the later Wittgenstein’s philosophy of mathematics, and endorsing an extended notion of meaning as use which includes social, mundane uses, we elaborate a fuzzy, but more realistic, demarcation. This demarcation, relying on family resemblance, is based on how direct and intended technical applications are, the kind of evaluative standards featured, and the range of rhetorical purposes at stake. (shrink)

Paraconsistent Weak Kleene Logic is the 3-valued propositional logic defined on the weak Kleene tables and with two designated values. Most of the existing proof systems for PWK are characterised by the presence of linguistic restrictions on some of their rules. This feature can be seen as a shortcoming. We provide a cut-free calculus for PWK that is devoid of such provisos. Moreover, we introduce a Priest-style tableaux calculus for PWK.

I develop a non-representationalist account of mathematical thought, on which the point of mathematical theorizing is to provide us with the conceptual capacity to structure and articulate information about the physical world in an epistemically useful way. On my view, accepting a mathematical theory is not a matter of having a belief about some subject matter; it is rather a matter of structuring logical space, in a sense to be made precise. This provides an elegant account of the cognitive utility (...) of mathematics. Further, it makes explicit how the brand of non-representationalism I develop is compatible with there being substantive rationality constraints on our mathematical theorizing. (shrink)

This book is a unique exploration of the idea of the "second person" in human interaction, the idea that face-to-face interactions involve a distinctive form of reciprocal mental state attributions that mediates their dynamical unfolding. Challenging the view of mental attribution as a sort of "theory of mind", Pérez and Gomila argue that the second person perspective of mental understanding is the conceptually, ontogenetically, and phylogenetically basic way of understanding mentality. Second person interaction provides the opportunity for the acquisition of (...) concepts of mental states of increasing complexity. The book reviews the growing interest in a variety of second person phenomena, both in development and in adulthood, presenting research that shows how participants in human interaction attribute psychological states of a referentially transparent kind to each other. This review documents the spontaneous preference for face-to-face interaction, from eye contact to joint attention, from forms of vitality to communicative intentions, from interaction detection to joint action, and from synchrony to interpersonal coordination. Also looking at the implications and applications of the second person perspective within fields as diverse as art and morality, this book is fascinating reading for students and academics in social and cognitive psychology, cognitive science, neuroscience, and philosophy. (shrink)

Pérez Carballo adopts an epistemic utility theory picture of epistemic norms where epistemic utility functions measure the value of degrees of belief, and rationality consists in maximizing expected epistemic utility. Within this framework he seeks to show that we can make sense of the intuitive idea that some true beliefs—say true beliefs about botany—are more valuable than other true beliefs—say true beliefs about the precise number of plants in North Dakota. To do so, however, Pérez Carballo argues that we must (...) think of the value of epistemic states as consisting in more than simply accuracy. This sheds light on which questions it is most epistemically valuable to pursue. (shrink)

This research analyses the influence of the perception of Corporate Social Responsibility (CSR image) on consumer–company identification (C–C identification). This analysis involves an examination of the influence of CSR image on brand identity characteristics which provide consumers with an instrument to satisfy their self-definitional needs, thereby perceiving the brand as more attractive. Also, the direct and mediated influences (through their effect on brand attitude), of CSR-based C–C identification on purchase intention are analysed. The results offer empirical evidence that CSR generates (...) more C–C identification because it improves brand prestige and distinctiveness; brand coherence is also a powerful antecedent of brand attractiveness in the context of CSR communication. Finally, CSR-based C–C identification is able to generate directly better attitude towards the brand and greater purchase intention. (shrink)

Proof-theoretic semantics is an alternative to model-theoretic semantics. It aims at explaining the meaning of the logical constants in terms of the inference rules that govern their behaviour in proofs. We argue that this must be construed as the task of explaining these meanings relative to a logic, i.e., to a consequence relation. Alas, there is no agreed set of properties that a relation must have in order to qualify as a consequence relation. Moreover, the association of a consequence relation (...) to a logical calculus is not as straightforward as it may seem. We show that these facts are problematic for the proof-theoretic project but the problems can be solved. Our thesis is that the consequence relation relevant for proof-theoretic semantics is the one given by the sequent-to-sequent derivability relation in Gentzen systems. (shrink)

Dave Ripley has recently argued against the plausibility of multiset consequence relations and of contraction-free approaches to paradox. For Ripley, who endorses a nontransitive theory, the best arguments that buttress transitivity also push for contraction—whence it is wiser for the substructural logician to go nontransitive from the start. One of Ripley’s allegations is especially insidious, since it assumes the form of a trivialisation result: it is shown that if a multiset consequence relation can be associated to a closure operator in (...) the expected way, then it necessarily contracts. We counter Ripley’s objection by presenting an approach to multiset consequence that escapes this trap. This approach is multiple-conclusioned in a heterodox way, for multiple succedents are given a conjunctive, rather than a disjunctive reading. Finally, we address a further objection by French and Ripley to the effect that the informational interpretation of sequents in linear logic does not motivate cut. (shrink)

The strict-tolerant approach to paradox promises to erect theories of naïve truth and tolerant vagueness on the firm bedrock of classical logic. We assess the extent to which this claim is founded. Building on some results by Girard we show that the usual proof-theoretic formulation of propositional ST in terms of the classical sequent calculus without primitive Cut is incomplete with respect to ST-valid metainferences, and exhibit a complete calculus for the same class of metainferences. We also argue that the (...) latter calculus, far from coinciding with classical logic, is a close kin of Priest’s LP. (shrink)

The logic DAI of demodalised analytic implication has been introduced by J.M. Dunn as a variation on a time-honoured logical system by C.I. Lewis’ student W.T. Parry. The main tenet underlying this logic is that no implication can be valid unless its consequent is “analytically contained” in its antecedent. DAI has been investigated both proof-theoretically and model-theoretically, but no study so far has focussed on DAI from the viewpoint of abstract algebraic logic. We provide several different algebraic semantics for DAI, (...) showing their equivalence with the known semantics by Dunn and Epstein. We also show that DAI is algebraisable and we identify its equivalent quasivariety semantics. This class turns out to be a linguistic and axiomatic expansion of involutive bisemilattices, a subquasivariety of which forms the algebraic counterpart of Paraconsistent Weak Kleene logic. This fact sheds further light on the relationship between containment logics and logics of nonsense. (shrink)

The aim of this article is to discuss pure variable inclusion logics, that is, logical systems where valid entailments require that the propositional variables occurring in the conclusion are included among those appearing in the premises, or vice versa. We study the subsystems of Classical Logic satisfying these requirements and assess the extent to which it is possible to characterise them by means of a single logical matrix. In addition, we semantically describe both of these companions to Classical Logic in (...) terms of appropriate matrix bundles and as semilattice-based logics, showing that the notion of consequence in these logics can be interpreted in terms of truth (or non-falsity) and meaningfulness (or meaninglessness) preservation. Finally, we use Płonka sums of matrices to investigate the pure variable inclusion companions of an arbitrary finitary logic. -/- . (shrink)

Meeting 5G high bandwidth rates, ultra-low latencies, and high reliabilities requires of network infrastructures that automatically increase/decrease the resources based on their customers’ demand. An autonomous and dynamic management of a 5G network infrastructure represents a challenge, as any solution must account for the radio access network, data plane traffic, wavelength allocation, network slicing, and network functions’ orchestration. Furthermore, federation among administrative domains (ADs) must be considered in the network management. Given the increased dynamicity of 5G networks, artificial intelligence/machine learning (...) (AI/ML) solutions are strong candidates able to learn, and take quick provisioning decisions upon fast changes in network conditions. Therefore, this chapter presents an analysis of the state-of-the-art solutions for 5G networks’ management, where AI/ML solutions are discussed and compared with traditional methods. Additionally, the chapter provides a technology overview of both standards, and existing solutions regarding the 5G network management, and directions toward the integration of AI/ML in 5G networks. (shrink)

"Tough, smart, superbly engaging, The Material Ghost is a terrific book." -- Edward W. Said In The Material Ghost , Gilberto Perez draws on his lifelong love of the movies as well as his work as a film scholar to write a lively, wide-ranging, penetrating study of films and filmmakers and the nature of the art form. For Perez, film is complex and richly contradictory, lifelike and dreamlike at once, a peculiar mix of reality and imagination. "The images on the (...) screen," he writes, "carry in them something of the world itself, something material, and yet something transposed, transformed into another world: the material ghost." "Dazzling... The sheer intelligence at work in these lucid pages is exhilarating." -- Alfred Guzzetti, Boston Book Review "A pleasure. Gilberto Perez is one of the smartest film critics writing anywhere." -- Jonathan Rosenbaum "Strikes an ideal balance between insightful analysis and graceful writing... A model of thoughtful criticism." -- David Sterritt, Christian Science Monitor "Brilliantly polemical in his critique of cynical reason ('the official philosophy of late capitalism'), no less passionate in defending the truth-value of cinema, Perez seems to be the clearest heir to the great humanist critic André Bazin." -- Sight & amp Sound "The chapters on Keaton and Renoir are stunning, full of perceptive remarks the chapter on Godard is a persuasive rehabilitation none of the chapters is without memorable insights." -- Michael Wood, London Review of Books "Gilberto Perez's ambitious, abundant, and cultivated book--the fruit of decades of thinking and teaching -- accompanies readers on a journey of discovery into the wonder of film." -- Stanley Cavell "Few books of film criticism in the past twenty-five years have been so enjoyable or instructive... [Perez] has excellent things to say about authorship, about documentaries, about popular genres, about cinematic point of view and narrative technique, about actors, and above all about camera style... He makes us want to look once more at the remarkable pictures he discusses." -- James Naremore, Cineaste. (shrink)

I discuss paradoxes of implication in the setting of a proof-conditional theory of meaning for logical constants. I argue that a proper logic of implication should be not only relevant, but also constructive and nonmonotonic. This leads me to select as a plausible candidate LL, a fragment of linear logic that differs from R in that it rejects both contraction and distribution.

Educar implica, en gran medida, transgredir la flecha del tiempo y actuar a modo de contratiempo. Los profesores saben bien que, en numerosas ocasiones, para asegurar el éxito de su acción, deben a menudo "perder tiempo" dejándose paradójicamente llevar por él. El conocimiento del tiempo educativo nos introduce en el estudio de este peculiar contratiempo que, a diferencia del tiempo objetivo, predecible y cronométrico que sirve para racionalizar las actividades pedagógicas, permite a los educadores impedir que en educación el tiempo (...) pase, se consuma sin más, fluya o simplemente suceda. De ahí que la autora plantee las relaciones tiempo y educación desde una perspectiva más integradora, incorporando para ello los múltiples tiempos que confluyen en la realidad educativa junto aquéllos que confieren legitimidad al proyecto educativo. La escuela ha venido recreando un modelo no normativo tiempo -básicamente predictivo y probabilístico- y ha aplicado una racionalidad ahistórica que dificulta la emergencia del sujeto al que se dirige y el modelo de sociedad hacia la que se proyecta. En la actualidad se plantea la necesidad de educar desde una nueva perspectiva ética que integre el tiempo como categoría normativa de acción. Educar hoy para mañana exigirá, en este sentido, atender a dos lógicas temporales: impregnar de historicidad la dimensión de sentido de todo proyecto educativo y planificar las acciones pedagógicas de acuerdo con una nueva tecnología temporal que incorpore la incertidumbre, la complejidad, la interdependencia y la sostenibilidad temporal. (shrink)

In a famous and controversial paper, B. H. Slater has argued against the possibility of paraconsistent logics. Our reply is centred on the distinction between two aspects of the meaning of a logical constant *c* in a given logic: its operational meaning, given by the operational rules for *c* in a cut-free sequent calculus for the logic at issue, and its global meaning, specified by the sequents containing *c* which can be proved in the same calculus. Subsequently, we use the (...) same strategy to counter Quine's meaning variance argument against deviant logics. In a nutshell, we claim that genuine rivalry between (similar) logics *L* and *L'* is possible whenever each constant in *L* has the same operational meaning as its counterpart in *L'* although differences in global meaning arise in at least one case. (shrink)

We introduce a generalization of MV algebras motivated by the investigations into the structure of quantum logical gates. After laying down the foundations of the structure theory for such quasi-MV algebras, we show that every quasi-MV algebra is embeddable into the direct product of an MV algebra and a “flat” quasi-MV algebra, and prove a completeness result w.r.t. a standard quasi-MV algebra over the complex numbers.

Proof-theoretic semantics is an alternative to model-theoretic semantics. It aims at explaining the meaning of the logical constants in terms of the inference rules that govern their behaviour in proofs. We argue that this must be construed as the task of explaining these meanings relative to a logic, i.e., to a consequence relation. Alas, there is no agreed set of properties that a relation must have in order to qualify as a consequence relation. Moreover, the association of a consequence relation (...) to a logical calculus is not as straightforward as it may seem. We show that these facts are problematic for the proof-theoretic project but the problems can be solved. Our thesis is that the consequence relation relevant for proof-theoretic semantics is the one given by the sequent-to-sequent derivability relation in Gentzen systems. (shrink)

This paper defends the claim that pragmatic encroachment—the idea that knowledge is sensitive to the practical stakes of believing—can explain a distinctive kind of epistemic injustice: the injustice that occurs when prejudice causes someone to know less than they otherwise would. This encroachment injustice, as we call it, occurs when the threat of being met with prejudice raises the stakes for someone to rely on her belief when acting, by raising the level of evidential support required for knowledge. We explain (...) this notion of encroachment injustice, connect it to the empirical literature on implicit bias, and defend it against important objections. (shrink)

We consider the class of pointed varieties of algebras having a lattice term reduct and we show that each such variety gives rise in a natural way, and according to a regular pattern, to at least three interesting logics. Although the mentioned class includes several logically and algebraically significant examples (e.g. Boolean algebras, MV algebras, Boolean algebras with operators, residuated lattices and their subvarieties, algebras from quantum logic or from depth relevant logic), we consider here in greater detail Abelian ℓ-groups, (...) where such logics respectively correspond to: i) Meyer and Slaney’s Abelian logic [31]; ii) Galli et al.’s logic of equilibrium [21]; iii) a new logic of “preservation of truth degrees”. (shrink)

According to an influential view, when it comes to representing reality, some words are better suited for the job than others. This is elitism. There is reason to believe that the set of the best, or elite, words should not be redundant or arbitrary. However, we are often forced to choose between these two theoretical vices, especially in cases involving theories that seem to be mere notational variants. This is the riddle of redundancy: both redundancy and arbitrariness are vicious, but (...) there are cases in which one must be picked. Logical realists admit that there are some logical constants among the elite words. This leads to awkward questions, such as which among conjunction and disjunction is elite. In this paper, I show how the riddle of redundancy arises for logical realists, and offer a solution. This approach requires us to change how we represent negation. Instead of using some particular symbol, we represent negation by flipping formulae over the horizontal axis. (shrink)

We investigate certain Brouwer-Zadeh lattices that serve as abstract counterparts of lattices of effects in Hilbert spaces under the spectral ordering. These algebras, called PBZ*-lattices, can also be seen as generalisations of orthomodular lattices and are remarkable for the collapse of three notions of “sharpness” that are distinct in general Brouwer-Zadeh lattices. We investigate the structure theory of PBZ*-lattices and their reducts; in particular, we prove some embedding results for PBZ*-lattices and provide an initial description of the lattice of PBZ*-varieties.

We continue the investigation, initiated in Salibra et al. (Found Sci, 2020), of Boolean-like algebras of dimension n (nBA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\textrm{BA}$$\end{document}s), algebras having n constants e1,⋯,en\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf e_1,\dots,\mathsf e_n$$\end{document}, and an (n+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(n+1)$$\end{document}-ary operation q (a “generalised if-then-else”) that induces a decomposition of the algebra into n factors through the so-called n-central elements. Varieties of nBA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} (...) \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\textrm{BA}$$\end{document}s share many remarkable properties with the variety of Boolean algebras and with primal varieties. Putting to good use the concept of a central element, we extend the Boolean power construction to that of a semiring power and we prove two representation theorems: (i) Any pure nBA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\textrm{BA}$$\end{document} is isomorphic to the algebra of n-central elements of a Boolean vector space; (ii) Any member of a variety of nBAs with one generator is isomorphic to a Boolean power of this generator. This yields a new proof of Foster’s theorem on primal varieties. (shrink)

In the tradition of substructural logics, it has been claimed for a long time that conjunction and inclusive disjunction are ambiguous:we should, in fact, distinguish between ‘lattice’ connectives (also called additive or extensional) and ‘group’ connectives (also called multiplicative or intensional). We argue that an analogous ambiguity affects the quantifiers. Moreover, we show how such a perspective could yield solutions for two well-known logical puzzles: McGee’s counterexample to modus ponens and the lottery paradox.

We show that intuitionistic logic is deductively equivalent to Connexive Heyting Logic ($$\textrm{CHL}$$ CHL ), hereby introduced as an example of a strongly connexive logic with an intuitive semantics. We use the reverse algebraisation paradigm: $$\textrm{CHL}$$ CHL is presented as the assertional logic of a point regular variety (whose structure theory is examined in detail) that turns out to be term equivalent to the variety of Heyting algebras. We provide Hilbert-style and Gentzen-style proof systems for $$\textrm{CHL}$$ CHL ; moreover, we (...) suggest a possible computational interpretation of its connexive conditional, and we revisit Kapsner’s idea of superconnexivity. (shrink)