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.

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.

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.

Science is popularly understood as being an ideal of impartial algorithmic objectivity that provides us with a realistic description of the world down to the last detail. The essays collected in this book—written by some of the leading experts in the field—challenge this popular image right at its heart, taking as their starting point that science trades not only in truth, but in fiction, too. With case studies that range from physics to economics and to biology, _Fictions in Science_ reveals (...) that fictions are as ubiquitous in scientific narratives and practice as they are in any other human endeavor, including literature and art. Of course scientific activity, most prominently in the formal sciences, employs logically precise algorithmic thinking. However, the key to the predictive and technological success of the empirical sciences might well lie elsewhere—perhaps even in scientists’ extraordinary creative imagination instead. As these essays demonstrate, within the bounds of what is empirically possible, a scientist’s capacity for invention and creative thinking matches that of any writer or artist. (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)

The title of this volume A Man of Many Interests: Plutarch on Religion, Myth, and Magic. Essays in honour of Aurelio Pérez Jiménez is first and foremost a coalescing homage to Plutarch and to Aurelio, and to the way they have been inspiring (as master and indirect disciple) a multitude of readers in their path to knowledge, here metonymically represented by the scholars who offer their tribute to them. The analysis developed throughout the several contributions favors a philological approach of (...) wide spectrum, i.e., stemming from literary and linguistic aspects, it projects them into their cultural, religious, philosophical, and historical framework. The works were organized into two broad sections, respectively devoted to the Lives and to the Moralia. Contributors are: Frances Titchener, Carlos Alcalde Martín, José Luis Calvo, Delfim Leão, Judith Mossman, Anastasios G. Nikolaidis, Christopher Pelling, Philip Stadter, Paola Volpe, Francesco Becchi, Israel Muñoz Gallarte, Lautaro Roig Lanzillotta, Geert Roskam, Vicente M. Ramón Palerm, Frederick Brenk, John Dillon, Franco Ferrari, Aristoula Georgiadou, Luc van der Stockt, Luisa Lesage Gárriga. (shrink)

This is the Editorial Introduction to “S.I.: Strong and Weak Kleene Logics”.

We investigate the class of strongly distributive pregroups, a common abstraction of MV-algebras and Abelian l-groups which was introduced by E.Casari. The main result of the paper is a representation theorem which yields both Chang's representation of MV-algebras and Clifford's representation of Abelian l-groups as immediate corollaries.

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)

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)

In his milestone textbook Lattice Theory, Garrett Birkhoff challenged his readers to develop a "common abstraction" that includes Boolean algebras and lattice-ordered groups as special cases. In this paper, after reviewing the past attempts to solve the problem, we provide our own answer by selecting as common generalization of ������������ and ������������ their join ������������∨������������ in the lattice of subvarieties of ������ℒ (the variety of FL-algebras); we argue that such a solution is optimal under several respects and we give an (...) explicit equational basis for ������������∨������������ relative to ������ℒ. Finally, we prove a Holland-type representation theorem for a variety of FL-algebras containing ������������∨������������. (shrink)

[1]. Liber V, De varietate legum humanarum et praesertim de odiosis --- [2]. Liber VI, de interpretatione, cessatione et mutatione legis humanae.

L'état de crise générale qui règne aujourd'hui dans la société française, comme l'a révélé, entre autres, l'ampleur sans précédent de la "manif pour tous", menace aujourd'hui l'universalité même de notre modèle sociopolitique national. Depuis que les trois notions qui fondent nos "valeurs républicaines" - liberté, égalité, fraternité - ont été détournées de leur sens véritable. La "liberté", devenue illimitée, consacre un sujet dominé par son seul ego, l'"égalité" est désormais synonyme d'une abolition de toute différence, fût-elle biologique, et la "fraternité" (...) se réduit à des promiscuités imposées. D'une promesse d'élévation citoyenne passant par l'accession de tous à l'autonomie, les principes des Lumières semblent bien conduire aujourd'hui à la négation même de ce qui définit notre humanité. Comment pareille grandeur humaniste a-t-elle pu dégénérer, en moins de trois siècles, en humanitarisme hygiénique de base? Ne faut-il pas chercher dans l'échec métapolitique du libéralisme mondialisé la réponse à cette question, qui dépasse de loin la banale scission gauche/droite? Paul-François Paoli passe au crible les mensonges et les contradictions criantes de la "religion laïque" en convoquant tour à tour dans le débat saint Augustin, Nietzsche, Raymond Boudon ou encore Pierre Manent. (shrink)

This work provides an original account of Francis Bacon's conception of natural inquiry. P'erez-Ramos sets Bacon in an epistemological tradition that postulates an intimate relation between objects of cognition and objects of construction, and regards the human knower as, fundamentally, a maker. By exploring the background to this tradition, and contrasting the responses of major philosophers of the 17th century with Bacon's own, the book charts Bacon's contribution to the modern philosophy of science.

Paraconsistent weak Kleene logic is the $3$-valued logic based on the weak Kleene matrices and with two designated values. In this paper, we investigate the poset of prevarieties of generalized involutive bisemilattices, focussing in particular on the order ideal generated by Α$\textrm{lg} $. Applying to this poset a general result by Alexej Pynko, we prove that, exactly like Priest’s logic of paradox, $\textrm{PWK}$ has only one proper nontrivial extension apart from classical logic: $\textrm{PWK}_{\textrm{E}}\textrm{,}$ PWK logic plus explosion. This $6$-valued logic, (...) unlike $\textrm{PWK} $, fails to be paraconsistent. We describe its consequence relation via a variable inclusion criterion and identify its Suszko-reduced models. (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.

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)

Strict-Tolerant Logic ($$\textrm{ST}$$ ST ) underpins naïve theories of truth and vagueness (respectively including a fully disquotational truth predicate and an unrestricted tolerance principle) without jettisoning any classically valid laws. The classical sequent calculus without Cut is sometimes advocated as an appropriate proof-theoretic presentation of $$\textrm{ST}$$ ST. Unfortunately, there is only a partial correspondence between its derivability relation and the relation of local metainferential $$\textrm{ST}$$ ST -validity – these relations coincide only upon the addition of elimination rules and only within (...) the propositional fragment of the calculus, due to the non-invertibility of the quantifier rules. In this paper, we present two calculi for first-order $$\textrm{ST}$$ ST with an eye to recapturing this correspondence in full. The first calculus is close in spirit to the Epsilon calculus. The other calculus includes rules for the discharge of sequent-assumptions; moreover, it is normalisable and admits interpolation. (shrink)

We investigate some properties of two varieties of algebras arising from quantum computation - quasi-MV algebras and $\sqrt{^{\prime }}$ quasi-MV algebras - first introduced in \cite{Ledda et al. 2006}, \cite{Giuntini et al. 200+} and tightly connected with fuzzy logic. We establish the finite model property and the congruence extension property for both varieties; we characterize the quasi-MV reducts and subreducts of $\sqrt{^{\prime }}$ quasi-MV algebras; we give a representation of semisimple $\sqrt{^{\prime }}$ quasi-MV algebras in terms of algebras of functions; (...) finally, we describe the structure of free algebras with one generator in both varieties. (shrink)

This chapter defends a deflationary, or ‘quietist’ account of causation in science. It begins by laying out the elements of four central philosophical theories of causation, namely the regularity, counterfactual, probabilistic and process accounts. It then proceeds to briefly criticise them. While the criticisms are essentially renditions of arguments that are well-known in the literature, the conclusion that is derived from these is new. It is argued that the limitations of each of the theories point to a deflationary or quietist (...) approach to causation in science. The practical focus is on interventionist methods for causal inference in physics and biology, and on the extant debates within the philosophy of each discipline as to how best to approach such methods. It is then argued that none of the four central theories proposed can completely explain or reduce the methods of causal inference that appear in each science. Yet, each theory provides partial insights into some of the grounds of causal inference and causal discovery. It is consequently suggested that we should retain the various methodological lessons without committing expressly to any metaphysics of causation. (shrink)

This is the first time that the Disputations 20-22 have been translated into English. They deal with the divine action of creation, conservation and concurrence.

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)

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)

Phase models for affine linear logic were independently devised by Lafont [10] and Piazza [15], although foreshadowed by Ono [14]. However, the existing semantics either contain no explicit directions for the construction of models in the general case, or else are forced to resort to additional conditions extending Girard's semantics. We dispense with these extra postulates - at least for the subexponential fragment of this logic - considering structures where the set of antiphases is concretely constructed. Moreover, we show the (...) equivalence of our phase models and the algebraic models of affine linear logic by means of a representation theorem. (shrink)

In the initial verses of Seven against Thebes, Eteocles recognizes the need of pronounce the right words as one of his duties as leader and defender of the city of Thebes. The concerns of Eteocles for what ought, or ought not, be said towards an imminent attack comes from a perception of language as a divine form of the world which base itself on the belief among the Greeks that words have a numen in itself and leads, thus, to a (...) prophetic fulfillment. The aim of this paper is, therefore, reveal the contribution of the word to the defense of the city in Seven against Thebes, by Aeschylus. (shrink)

Analizar el pensamiento político de Julián Marías supone reflexionar acerca de la propuesta de un modelo de hombre en relación con la sociedad, el poder, la libertad, la justicia y la democracia como sistema político y como educadora de convivencia. La continuidad histórica y la imaginación aparecen como reflejo de una realidad vital, que se concreta en el estudio de la monarquía, los principios que impregnaron la Transición en España y la elaboración de la Constitución.