In this work we propose a labelled tableau method for Łukasiewicz infinite-valued logic Lω. The method is based on the Kripke semantics of this logic developed by Urquhart [25] and Scott [24]. On the one hand, our method falls under the general paradigm of labelled deduction [8] and it is rather close to the tableau systems for sub-structural logics proposed in [4]. On the other hand, it provides a CoNP decision procedure for Lω validity by reducing the check of branch (...) closure to linear programming. (shrink)

In this work we propose a labelled tableau method for ukasiewicz infinite-valued logic L . The method is based on the Kripke semantics of this logic developed by Urquhart [25] and Scott [24]. On the one hand, our method falls under the general paradigm of labelled deduction [8] and it is rather close to the tableau systems for sub-structural logics proposed in [4]. On the other hand, it provides a CoNP decision procedure for L validity by reducing the check of (...) branch closure to linear programming. (shrink)

Fuzzy logics are many-valued logics that are well suited to reasoning in the context of vagueness. They provide the basis for the wider field of Fuzzy Logic, encompassing diverse areas such as fuzzy control, fuzzy databases, and fuzzy mathematics. This book provides an accessible and up-to-date introduction to this fast-growing and increasingly popular area. It focuses in particular on the development and applications of "proof-theoretic" presentations of fuzzy logics; the result of more than ten years of intensive work by researchers (...) in the area, including the authors. In addition to providing alternative elegant presentations of fuzzy logics, proof-theoretic methods are useful for addressing theoretical problems and developing efficient deduction and decision algorithms. Proof-theoretic presentations also place fuzzy logics in the broader landscape of non-classical logics, revealing deep relations with other logics studied in Computer Science, Mathematics, and Philosophy. The book builds methodically from the semantic origins of fuzzy logics to proof-theoretic presentations such as Hilbert and Gentzen systems, introducing both theoretical and practical applications of these presentations. (shrink)

We define a family of intuitionistic non-normal modal logics; they can be seen as intuitionistic counterparts of classical ones. We first consider monomodal logics, which contain only Necessity or Possibility. We then consider the more important case of bimodal logics, which contain both modal operators. In this case we define several interactions between Necessity and Possibility of increasing strength, although weaker than duality. We thereby obtain a lattice of 24 distinct bimodal logics. For all logics we provide both a Hilbert (...) axiomatisation and a cut-free sequent calculus, on its basis we also prove their decidability. We then define a semantic characterisation of our logics in terms of neighbourhood models containing two distinct neighbourhood functions corresponding to the two modalities. Our semantic framework captures modularly not only our systems but also already known intuitionistic non-normal modal logics such as Constructive K and the propositional fragment of Wijesekera’s Constructive Concurrent Dynamic Logic. (shrink)

The aim of this work is to develop a declarative semantics for N-Prolog with negation as failure. N-Prolog is an extension of Prolog proposed by Gabbay and Reyle, which allows for occurrences of nested implications in both goals and clauses. Our starting point is an operational semantics of the language defined by means of top-down derivation trees. Negation as finite failure can be naturally introduced in this context. A goal-G may be inferred from a database if every top-down derivation of (...) G from the database finitely fails, i.e., contains a failure node at finite height.Our purpose is to give a logical interpretation of the underlying operational semantics. In the present work we take into consideration only the basic problems of determining such an interpretation, so that our analysis will concentrate on the propositional case. Nevertheless we give an intuitive account of how to extend our results to a first order language. A full treatment of N-Prolog with quantifiers will be deferred to the second part of this work. (shrink)

In this paper we focus on theorem proving for conditional logics. First, we give a detailed description of CondLean, a theorem prover for some standard conditional logics. CondLean is a SICStus Prolog implementation of some labeled sequent calculi for conditional logics recently introduced. It is inspired to the so called “lean” methodology, even if it does not fit this style in a rigorous manner. CondLean also comprises a graphical interface written in Java. Furthermore, we introduce a goal-directed proof search mechanism, (...) derived from the above mentioned sequent calculi based on the notion of uniform proofs. Finally, we describe GOALDUCK, a simple SICStus Prolog implementation of the goal-directed calculus mentioned here above. Both the programs CondLean and GOALDUCK, together with their source code, are available for free download at. (shrink)

Product logic Π is an important t-norm based fuzzy logic with conjunction interpreted as multiplication on the real unit interval [0,1], while Cancellative hoop logic CHL is a related logic with connectives interpreted as for Π but on the real unit interval with 0 removed (0,1]. Here we present several analytic proof systems for Π and CHL, including hypersequent calculi, co-NP labelled calculi and sequent calculi.

In this work we develop goal-directed deduction methods for the implicational fragment of several modal logics. We give sound and complete procedures for strict implication of K, T, K4, S4, K5, K45, KB, KTB, S5, G and for some intuitionistic variants. In order to achieve a uniform and concise presentation, we first develop our methods in the framework of Labelled Deductive Systems [Gabbay 96]. The proof systems we present are strongly analytical and satisfy a basic property of cut admissibility. We (...) then show that for most of the systems under consideration the labelling mechanism can be avoided by choosing an appropriate way of structuring theories. One peculiar feature of our proof systems is the use of restart rules which allow to re-ask the original goal of a deduction. In case of K, K4, S4 and G, we can eliminate such a rule, without loosing completeness. In all the other cases, by dropping such a rule, we get an intuitionistic variant of each system. The present results are part of a larger project of a goal directed proof theory for non-classical logics; the purpose of this project is to show that most implicational logics stem from slight variations of a unique deduction method, and from different ways of structuring theories. Moreover, the proof systems we present follow the logic programming style of deduction and seem promising for proof search [Gabbay and Reyle 84, Miller et al. 91]. (shrink)

The logic of Conditional Beliefs has been introduced by Board, Baltag, and Smets to reason about knowledge and revisable beliefs in a multi-agent setting. In this article both the semantics and the proof theory for this logic are studied. First, a natural semantics forCDLis defined in terms of neighbourhood models, a multi-agent generalisation of Lewis’ spheres models, and it is shown that the axiomatization ofCDLis sound and complete with respect to this semantics. Second, it is shown that the neighbourhood semantics (...) is equivalent to the original one defined in terms of plausibility models, by means of a direct correspondence between the two types of models. On the basis of neighbourhood semantics, a labelled sequent calculus forCDLis obtained. The calculus has strong proof-theoretic properties, in particular admissibility of contraction and cut, and it provides a decision procedure for the logic. Furthermore, its semantic completeness is used to obtain a constructive proof of the finite model property of the logic. Finally, it is shown that other doxastic operators can be easily captured within neighbourhood semantics. This fact provides further evidence of the naturalness of neighbourhood semantics for the analysis of epistemic/doxastic notions. (shrink)

We present logic programming style “goal-directed” proof methods for Łukasiewicz logic Ł that both have a logical interpretation, and provide a suitable basis for implementation. We introduce a basic version, similar to goal-directed calculi for other logics, and make refinements to improve efficiency and obtain termination. We then provide an algorithm for fuzzy logic programming in Rational Pavelka logic RPL, an extension of Ł with rational constants.

In this paper we propose a conditional logic called IBC to represent iterated belief revision systems. We propose a set of postulates for iterated revision which are a small variant of Darwiche and Pearl''s ones. The conditional logic IBC has a standard semantics in terms of selection function models and provides a natural representation of epistemic states. We establish a correspondence between iterated belief revision systems and IBC-models. Our representation theorem does not entail Gärdenfors'' Triviality Result.

In this paper we propoee a logic programming language which supports hypothetical updates together with integrity constraints. The language makes use of a revision mechanism, which is needed to restore consistency when an update violates some integrity constraint. The revision policy adopted is based on the simple idea that more recent information is preferred to earlier one. We show how this language can be used to represent and perform several types of defeasible reasoning. We develop a logical characterization of the (...) language in a three-valued conditional logic, by introducing a completion construction. We show that the operational semantics is sound and complete with respect to the completion construction. (shrink)

Sometimes physicians lie to third-party payers in order to grant their patients treatment they would otherwise not receive. This strategy, commonly known as gaming the system, is generally condemned for three reasons. First, it may hurt the patient for the sake of whom gaming was intended. Second, it may hurt other patients. Third, it offends contractual and distributive justice. Hence, gaming is considered to be immoral behavior. This article is an attempt to show that, on the contrary, gaming may sometimes (...) be a physician's duty. Under specific circumstances, gaming may be necessary from the viewpoint of the internal morality of medicine. Moreover, the objections against gaming are examples of what we call the idealistic fallacy, that is, the fallacy of passing judgments in a nonideal world according to ideal standards. Hence, the objections are inconclusive. Gaming is sometimes justified, and may even be required in the name of beneficence. (shrink)

In Plato's Sophist, a mysterious Eleatic Stranger, the main character of the dialogue, undertakes a systematic definition of the philosopher's fiercest rival, the sophist. His hunt for a definition of the sophist, however, is interrupted by an attempt to refute the ontology of Parmenides. The philosophical significance of this refutation and its exact relationship to the sought-after definition remains a matter of great scholarly dispute. This book, by means of a running commentary on the dialogue, argues that the oft-neglected distinction (...) between dialectic and appearances is not only the key to solving this and other exegetical conundrums, but also reveals the unity and originality of Plato's argument in the Sophist. (shrink)

Trente et un penseurs, parmi lesquels Jacques Derrida, Françoise Héritier, Edgar Morin, Jean-Luc Nancy, Michel Onfray ou encore Jacques Rancière, pour comprendre les errements et les raisons d'espérer d'une planète convulsée. Dix-neuf entretiens et débats avec les intellectuels les plus engagés dans la réflexion sur le temps présent dressent un état des lieux des questions qui taraudent notre modernité. Issu du Théâtre des idées, cycle de rencontres intellectuelles du Festival d'Avignon (2004-2012), ces dialogues singuliers s'attachent à faire vivre l'esprit critique, (...) cette faculté de juger, de soumettre la réalité sociale, artistique ou politique au tamis du jugement argumenté, qu'il soit sérieux ou ironique, virulent ou tempéré. De très actuelles "résistances intellectuelles" qui esquissent ce que pourrait être un service public des idées, c'est-à-dire un accès direct, libre et partagé à l'intellectualité. (shrink)

Cet article est consacré au problème du rapport entre l’entrelacement des genres (συμπλοκὴ τῶν εἰδῶν) et le logos dans le Sophiste. Après avoir brièvement présenté le problème, je discute, dans la première partie, différentes solutions proposées par les commentateurs. Je cherche à montrer qu’aucune de ces solutions n’est pleinement satisfaisante. Dans la deuxième partie, je propose une nouvelle solution au problème de la συμπλοκὴ τῶν εἰδῶν fondée sur une distinction entre deux types de logos, le logos dialectique et le logos (...) doxique. Dans la troisième partie, je cherche à justifier textuellement cette solution en recourant à la fois au texte du Sophiste lui-même et à la dernière partie du Théétète. Dans ma conclusion, je suggère que la distinction entre logos dialectique et logos doxique correspond à une différence qui traverse toute l’œuvre de Platon, à savoir la différence entre connaissance et opinion. / This paper deals with the problem of the συμπλοκὴ τῶν εἰδῶν in the Sophist. In the first part, after a brief presentation of this problem, I discuss different solutions which have been proposed in the recent literature. I try to show that none of them is entirely satisfying. In the second part, I propose and explain a new solution based on a distinction between two types of logos : dialectical logos and doxastic logos. In the third part, I try to justify this solution on the basis of some passages of the Sophist and of the final part of the Theaetetus. To conclude, I suggest that the distinction between dialectical logos and doxasticlogos matches the difference between knowledge and belief made by Plato in his dialogues. (shrink)

Jacques Derridas Verständnis von Freundschaft wird, so zeigt Nicola Tams, nicht nur in seinen veröffentlichten Texten, sondern vor allem in seinen Briefen deutlich. Ihre Studie untersucht eine Auswahl des Briefverkehrs Derridas (etwa mit Blanchot, Nancy, Bauchau, Ukai und Granel), verwebt die Ergebnisse mit Derridas Theorien der Freundschaft und zeigt, dass die vornehmlich in Briefen entwickelten Gedanken traditionellen Konzepten der Freundschaft in der Philosophiegeschichte nicht so fern sind.

O carte de cugetări, în care se întâlnește tradiția ortodoxă a Răsăritului creștin cu gândirea filosofică occidentală. „Simulez viața, ca să par la fel cu cei ce trăiesc. Îi ascult ce discută, pentru a ști cum discută oamenii. Dar de fiecare dată rămân mut de uimire. De când am început să cred în Dumnezeu am uitat atât de multe încât sunt mai aproape de extratereștri decât de oamenii fără zei, «oamenii naturali», «bunii sălbatici».”.

This work proposes a philosophical analysis of the ideal of authenticity, first by presenting and discussing the works of Charles Taylor and Charles Larmore, then by developing some more personal analysis of conformism and what the author calls experiences of authenticity.

Connecting Reconceptualist Thinking with Early Childhood Education Practices highlights the relationships between reconceptualist theory and classroom practice, and makes those theories relateable through the lens of practitioners' experiences. Each chapter in this edited collection considers a contemporary issue and explores its potential to be meaningful in the lives of young children. The book pairs reconceptualist academics and practitioners to discuss how theories can be relevant in everyday educational contexts, working with children who are from a wide range of cultural, ethnic, (...) gender, language and social orientations. (shrink)

An examination of the ways human movement can be represented as a formal language and how this language can be mediated technologically. In Motion and Representation, Nicolás Salazar Sutil considers the representation of human motion through languages of movement and technological mediation. He argues that technology transforms the representation of movement and that representation in turn transforms the way we move and what we understand to be movement. Humans communicate through movement, physically and mentally. To record and capture integrated movement (...) (both bodily and mental), by means of formal language and technological media, produces a material record and cultural expression of our evolving kinetic minds and identities. Salazar Sutil considers three forms of movement inscription: a written record (notation), a visual record (animation), and a computational record (motion capture). He focuses on what he calls kinetic formalism—formalized movement in such pursuits as dance, sports, live animation, and kinetic art, as well as abstract definitions of movement in mathematics and computer science. He explores the representation of kinetic space and spatiotemporality; the representation of mental plans of movement; movement notation, including stave notation (Labanotation) and such contemporary forms of notation as Choreographic Language Agent; and the impact of digital technology on contemporary representations of movement—in particular motion capture technology and Internet transfer protocols. Motion and Representation offers a unique cultural theory of movement and of the ever-changing ways of representing movement. (shrink)

De réchauffement climatique en scandale sanitaire et d’OGM en catastrophe nucléaire, la science et la technique sont devenues des questions pleinement politiques, tandis que la « technoscience » vient interroger les concepts moraux les mieux ancrés. Pourtant, ce qui devrait susciter un intérêt soutenu ne génère souvent que la résignation de « n’y rien comprendre » - ce qui laisse le champ libre aux lobbies de la technologie et aux bluffs scientifiques les plus éhontés. Qu’y puis-je, direz-vous, si la science (...) m’a toujours été présentée comme rébarbative et « chiantifique », et si la parole des experts, même de mauvaise foi, couvre la mienne quand je tente de m’exprimer à ce sujet? Et puis, cela me concerne-t-il vraiment? Un seul remède : se plonger dans ce dictionnaire, qui vise moins à « faire passer » de l’information qu’à donner les outils nécessaires pour dégonfler les prétentions excessives de la technoscience. De « abeille » à « zz » en passant par « sérendipité » et « post-humanisme », c’est tout le domaine de la science et de la technologie qui se révèle non seulement comme digne d’être exploré mais aussi comme susceptible d’être squatté efficacement : les théories les plus décoiffantes, les idées les moins convenues et les personnages les plus inattendus font de ce domaine un incomparable tremplin pour l’imagination, et incitent à pénétrer sans crainte dans ce que tant d’autres aimeraient continuer à considérer comme une chasse gardée. (shrink)