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A travers cet ouvrage nous produisons un lien spécifique entre l'épistémologie et la logique épistémique.Si de nombreuses tentatives de conciliation entre logique épistémique et épistémologie se sont avérées fructueuses, c'est la possibilité d'une étude argumentative de la logique épistémique qui est ici explorée.Étudier la logique épistémique à partir d'une approche argumentative de la logique, c'est-àdire au sein de dialogues, nous permet à la fois de bénéfi cier d'un cadre d'étude dynamique pour explorer le dynamisme et la signifi cation du langage de la logique épistémique mais aussi d'ouvrir de nouvelles pistes de recherches à la confl uence de la logique et du droit.Les considérations juridico-logiques que nous développons portent en premier lieu sur la notion de condition suspensive dans le droit, puis plus généralement sur la forme conditionnelle des normes juridiques.

Le calcul scientifique est devenu essentiel dans de nombreux domaines tels que la mécanique des fluides et des solides, la météo, l'évolution du climat, la biologie ou les semi-conducteurs. Elle permet de comprendre, de prévoir, d'accéder là où les instruments de mesures s'arrêtent.Ce livre présente des méthodes performantes du calcul scientifique : matrices creuses, résolution efficace des grands systegrave;mes linéaires, ainsi que de nombreuses applications à la résolution par éléments finis et différences finies des équations aux dérivées partielles. Alternant algorithmes et applications, les programmes sont directement présentés en langage C++. Ils sont écrits sous forme concise et claire, et utilisent largement les notions de classe et de généricité du langage C++. La diversité des sujets abordés, l'efficacité des algorithmes présentés et leur écriture directe en langage C++ font de cet ouvrage un recueil fort utile dans la vie professionnelle d'un ingénieur.Le livre est complété par de nombreux exercices, dont le corrigé est reporté en annexe, et qui en constituent autant de développements du cours. Des notes bibliographiques retracent l'historique des travaux et fournissent des références sur des logiciels et librairies récents, implémentant ou étendant les algorithmes présentés. Les codes C++ présentés au long de ce livre ainsi que dans les corrigés des exercices sont disponibles librement à l'adresse http://www-ljk.imag.fr/membres/Pierre.Saramito/books sous la licence GNU public licence.

The research programme Semantics and Syntax: A Legacy of Alan Turing, held at the Isaac Newton Institute for the Mathematical Sciences in Cambridge, UK, 9 January - 6 July 2012, was one of the central activities of the Alan Turing Year 2012, the world-wide celebration of the life and work of the exceptional scientist Alan Mathison Turing (1912-1954). It had almost 200 visitingfellows and programme participants, as well as several hundred additional workshop participants, and was organised by Arnold Beckmann (Swansea),S. Barry Cooper (Leeds), Benedikt Löwe (Amsterdam & Hamburg), Elvira Mayordomo(Zaragoza), and Nigel Smart (Bristol).This volume documents the presentations that were given as part of the programme, which include the abstracts of the teaser talks given in the Seminar at the Isaac Newton Institute, and abstracts of the talks given at five of the seven workshops, as well as written versions of two open problem sessions.

Une question fondamentale pour la logique et l'anthropologie sous-tend la thèse défendue ici par M. Gildas Nzokou. Elle s'énonce comme suit : Peuton aborder la notion d'inférence avec la même rigueur théorique dans les civilisations de l'oralité que dans les cultures ayant des systèmes d'écriture ? Cette question est pertinente. En effet, une longue chaîne de raisonnements exige le support de l'écrit. C'est pour cette raison que la pratique argumentative dans les civilisations de l'oralité repose sur l'usage de proverbes, qui par nature sont toujours courts.Pour évaluer le niveau de rationalité du proverbe, il ne faut pas le mesurer à l'aune de l'inférence déductive qui joue un si grand rôle en mathématique, il faut, au contraire, le comparer aux raisonnements de sens commun dont la théorie a été faite aux cours des trente dernières années par les chercheurs en intelligence artificielle. Ceux-ci ont montré que le raisonnement de sens commun se conformait à d'autres canons que ceux de la logique déductive, à savoir les canons de la logique non monotone, ceux du raisonnement par défaut ou encore les principes qui gouvernent la révision des connaissances. Ils ont traité les raisonnements de sens commun avec autant de rigueur que les théoriciens du raisonnement déductif traitent les raisonnements du mathématicien. La leçon que l'auteur tire de sa comparaison entre les argumentations de sens commun formalisées par les chercheurs en intelligence artificielle et les argumentations fondées sur des proverbes peut se résumer ainsi : " la logique est plurielle, mais la raison est une et universelle. C'est une même exigence de rationalité qui habite le raisonnement déductif du mathématicien, la logique non monotone, le raisonnement par défaut et l'argumentation reposant sur des proverbes. Cette rationalité se manifeste par la soumission à des normes ". On peut traiter avec autant de rigueur l'argumentation reposant sur des proverbes et la déduction opérée par le mathématicien.Paul GOCHET (1932-2011), Ancien Membre de l'Académie Royale de Belgique et de l'Académie Internationale de Philosophie des Sciences, Liège, Octobre 2010.

La negación es un fenómeno linguístico, lógico y filosófico que nodeja de asombrarnos con nuevos enigmas. A nuestro juicio, el estudiodel uso de las partículas negativas en las primeras lenguas escritas,tales como el ugarítico, abre nuevas perspectivas para la comprensióndel multifacético no . El tema fundamental de este trabajo, necesariamenteinterdisciplinario, consiste en la propuesta y la defensa de una formulaciónde la negación l¿/ ¿al ugarítica como una negación intensional epistémica.La formulación intensional de dicha negación debe entenderse, de acuerdoa la autora, dentro del marco de un paradigma evidencial de la lenguacuya sémantica formal es desarrollada mediante una lógica dinámicaepistémica. Este libro contiene un análisis pormenorizado de las partículasl¿/ ¿al en ugarítico a partir de sus ocurrencias en las cartas ugaríticasy una discusión de las teorías actuales sobre las partículas l + vocal/vocal+ l (lV/Vl) en varias lenguas semíticas: acadio, hebreo, canaano-acadioy las hipótesis sobre el proto-semítico. Junto con los análisis precedentes,se proveen una visión general de la categoría de modalidad y de lanegación desde una perspectiva de la tipología lingüística contemporánea.El núcleo del trabajo concierne dos partes principales; 1) Un estudiosistemático de los vínculos entre los evidenciales y la modalidadepistémica (o no) y el desarrollo de una nueva semántica formal paralos evidenciales basada en la lógica epistémica dinámica. Tal semánticaofrece la posibilidad de especificar formalmente la diferencia entreevidenciales directos e indirectos 2) La aplicación del estudio generalde la formalización de la evidencialidad a la negación ugarítica,así como su relación con la modalidad ugarítica sentencial y subsentencialmediante el alcance de diferentes operadores.

This volume is dedicated to Robin Cooper on the occasion of his 65th birthday.The honoree's contributions to formal linguistics and language technology range from quantifier storage techniques and generalised quantifiers to the development of foundations and applications of a type-theoretical framework for formal semantics and pragmatics of natural language, with a focus on linguistic interaction in conversation.In this book the reader will find brilliant contributions of prominent linguists, computer scientists and philosophers which ranges over a broad repertoire of topics related to the outstanding work of Robin Cooper.

Throughout his career, Stephen Read has been at the forefront of research in the history and philosophy of logic. Distinctive of his work is his effort both to bring ideas from the history of logic into contemporary debates, and to apply formal logic in his historical analyses. He has made decisive contributions to the study of medieval logic, paradoxes, proof-theoretic semantics, relevant logic, logical consequence, and many other topics.On the occasion of his retirement, friends and colleagues join forces to honor him with a collection of papers reflecting his wide range of interests. Topics covered are: modern treatments of medieval solutions to the Liar paradox, reflections on logical consequence, proof-theoretic semantics, logical pluralism, studies in the history of logic (Latin and Arabic medieval logic in particular), among others.The collection reflects both the breadth and the depth of Read's unique approach to the history and philosophy of logic, containing papers by prominent researchers in these areas. As a whole, it strives to live up to the quality of Stephen's own work.

"The binomial theorem is usually quite rightly considered as one of the mostimportant theorems in the whole of analysis." Thus wrote Bernard Bolzanoin 1816 in introducing the first correct proof of Newton's generalisation of acentury and a half earlier of a result familiar to us all from elementary algebra. Bolzano's appraisal may surprise the modern reader familiar only with the finite algebraic version of the Binomial Theorem involving positive integralexponents, and may also appear incongruous to one familiar with Newton'sseries for rational exponents. Yet his statement was a sound judgment back inthe day. Here the story of the Binomial Theorem is presented in all its glory,from the early days in India, the Moslem world, and China as an essentialtool for root extraction, through Newton's generalisation and its central rolein infinite series expansions in the 17th and 18th centuries, and to its rigorous foundation in the 19th.The exposition is well-organised and fairly complete with all the necessarydetails, yet still readable and understandable for those with a limited mathematical background, say at the Calculus level or just below that.The present book, with its many citations from the literature, will be ofinterest to anyone concerned with the history or foundations of mathematics.

The Lambda Calculus, treated in this book mainly in its untyped version, consists of a collection of expressions, called lambda terms, together with ways how to rewrite and identify these. In the parts conversion, reduction, theories, and models the view is respectively 'algebraic', computational, with more ('coinductive') identifications, and finally set-theoretic.The lambda terms are built up from variables, using application and abstraction. Applying a term F to M has as intention that F is a function, M its argument, and FM the result of the application. This is only the intention: to actually obtain the result one has to rewrite the expression FM according tothe reduction rules. Abstraction provides a way to create functions according to the effect when applying them.The power of the theory comes from the fact that computations, both terminating and infinite, can be expressed by lambda terms at a 'comfortable' level of abstraction.

This book comprises a collection of 12 research articlespertaining to the infl uence of phenomenological analysison current issues of epistemology, this one meantas a philosophy of science. Ten of these articles havealready appeared in various research journals of thefi eld at large and have been to a considerable extentre-edited, updated and in certain respects reworked. Theremaining two are published originally for this book and naturallycomplement and invigorate the argumentation and the scope ofthe published articles. Overall, the content of the book can bedescribed as an original attempt to demonstrate the relevanceof Husserlian phenomenology with regard to theoreticalquestions arising from the contemporary evolution of suchdiverse scientifi c fi elds as the foundations of mathematics andthe interpretation of quantum mechanics."Stathis Livadas has pushed the investigation of the foundationsof mathematics and of present day physical theories out of astrictly analytic point of view, by considering a phenomenologicalapproach on these matters. According to him mathematicsand science present various ambiguous notions which cannotbe, in principle, resolved by analytical means only. Therefore, amore general approach is pursued. This book contains severalof his already published articles, and now they are put togetherfor a more general audience in the form of a book. I think thatthis line of investigation, facing current epistemological issuesunder a phenomenological point of view, is fruitful and relevant,and ought to be considered by a wide range of philosophers."Décio Krause. Universidad Federal de Santa Catarina, Brazil."Stathis Livadas' book embodies a masterly analysis of someimportant questions in the philosophy of mathematics andin Husserl's phenomenology. According to Livadas, non-Cantorian theories and intuitionistic ones are "trapped" in theimpredicativity of the continuum when they shift the boundariesbeyond naturally intuited countability in our witnesseduniverse. In this perspective, from a theoretical point of view,mathematical intuition is not eliminable. Hence the challengeto point out to the intuition of continuum in accordancewith a phenomenological point of view, i.e., making essentialreference to the existence of a categorial intuition based onthe intentionality of primary experience which is geneticallyconstituted in the unity of the fl ux of consciousness."Arturo Carsetti. University of Rome "Tor Vergata"

El razonamiento abductivo ha recibido una gran atención en los últimos años gracias a sus aplicaciones en diversas disciplinas, desde la epistemología hasta la lingüística o la inteligencia artificial. Este libro presentaalgunas de las aproximaciones a la abducción más populares dentro de la lógica clásica, tanto proposicional como de predicados.Dado el interés de la abducción dentro de la programación logica, el libro incluye un capítulo dedicado a las aplicaciones de la abducción en el razonamiento automático. Igualmente, se ofrece un razonador abductivo escritoen Prolog. En los apéndices se encuentra el código fuente, así como una pequeñaintroducción a la programación lógica.A lo largo del libro se incluyen numerosos ejemplos de problemas abductivos resueltos con cada uno de los sistemas que se presentan.

On 17-18 February 2011 the third installment of PhDs in Logic took place at the Academy Palace in Brussels, Belgium. Some forty European logicians gathered to discuss a diverse range of topics in mathematical and philosophical logic. PhDs in Logic is an annual series of graduate conferences/winter schools, run for and by PhD students. The winter school consists of tutorials taught by well established researchers; the graduate conference provides young logicians withan excellent opportunity to share their results with a large audience of peersand established logicians. This volume bundles thirteen of the papers presented at the graduate conference of PhDs in Logic III. These papers deal with a wide variety of topics, coming from subfields such as algebraic logic, set theory, and philosophical logic. All papers share the common goal of advancing the boundaries of research in logic and its applications, thus turning this volume into a unique overview of what's hot and upcoming in the field of logic.

Modal logic is a subject with ancient roots in the western logical tradition. Up until the last few generations, it was pursued mainly as a branch ofphilosophy. But in recent years, the subject has taken new directions with connections to topics in computer science and mathematics.This volume is the proceedings of the conference of record in its fi eld, Advances in Modal Logic. Its contributions are state-of-the-art papers. Thetopics include decidability and complexity results for specifi c modal logics, proof theory of modal logic, logics for reasoning about time and space,provability logic, dynamic epistemic logic, and the logic of evidence.

Mathematics originates with intuition. But intuition alone can only go so far and formalism develops to handle the more difficult problems. Formalism, however, has its inherent dangers. There are three types of formalism. Type Iformalism, exemplified in the work of Euler, is basically heuristic reasoning, the use of familiar reasoning in areas where the reasoning might not or ought not apply. The results include startling successes, and also theorems admitting exceptions. Type II formalism, associated with names like Bolzano, Cauchy, and Weierstrass, attempts to clarify the situation by means of precise definitions of the terms used. Type III formalism, the axiomatic method, leaves the fundamental concepts undefined, but offers precise rules for their use. Such precision deserts intuition and one pays the price. Most dramatically, the formal definitions of Type II formalism allow for the construction of monsters -bizarre counterexamples that exhibit behaviour inconsistent with existing intuition. The initially repellant nature of these "monsters" leads to dissatisfaction that is only dispelled by their growing familiarity and applicability. The present book covers the history of formalism in mathematics from Euclid through the 20th century. It should be of interest to advancedmathematics students, anyone who teaches mathematics, and anyone generally interested in the foundation of mathematics.

Originating as an attempt to provide solid logical foundations for fuzzy set theory, and motivated also by philosophical and computational problems of vagueness and imprecision, Mathematical Fuzzy Logic (MFL) has become a significant subfield of mathematical logic. Research in this area focuseson many-valued logics with linearly ordered truth values and has yielded elegant and deep mathematical theories and challenging problems, thus continuing to attract an ever increasing number of researchers.This two-volume handbook provides an up-to-date systematic presentation of the best-developed areas of MFL. Its intended audience is researchers working on MFL or related fields, who may use the text as a reference book, and anyone looking for a comprehensive introduction to MFL. Despite being located in the realm of pure mathematical logic, this handbook will also be useful for readers interested in logical foundations of fuzzy set theory or in a mathematical apparatus suitable for dealing with some philosophical and linguistic issues related to vagueness.The first volume contains a gentle introduction to MFL, a presentation of an abstract algebraic framework for MFL, chapters on proof theory and algebraic semantics of fuzzy logics, and, finally, an algebraic study of Hájek's logic BL.The second volume is devoted to ¿ukasiewicz logic and MValgebras, Gödel-Dummett logic and its variants, fuzzy logics in expanded propositional languages, studies of functional representations for fuzzy logics and their free algebras,computational complexity of propositional logics, and arithmetical complexity of first-order logics.

Originating as an attempt to provide solid logical foundations for fuzzy set theory, and motivated also by philosophical and computational problems of vagueness and imprecision, Mathematical Fuzzy Logic (MFL) has become a significant subfield of mathematical logic. Research in this area focuses on many-valued logics with linearly ordered truth values and has yielded elegant and deep mathematical theories and challenging problems, thus continuing to attract an ever increasing number of researchers.This two-volume handbook provides an up-to-date systematic presentation of the best-developed areas of MFL. Its intended audience is researchers working on MFL or related fields, who may use the text as a reference book, and anyone looking for a comprehensive introduction to MFL. Despite being located in the realm of pure mathematical logic, this handbook will also be useful for readers interested in logical foundations of fuzzy set theory or in a mathematical apparatus suitable for dealing with some philosophical and linguistic issues related to vagueness.The first volume contains a gentle introduction to MFL, a presentation of an abstract algebraic framework for MFL, chapters on proof theory and algebraic semantics of fuzzy logics, and, fi nally, an algebraic study of Hájek's logic BL. The second volume is devoted to ¿ukasiewicz logic and MValgebras, Gödel-Dummett logic and its variants, fuzzy logics in expanded propositional languages, studies of functional representations for fuzzy logics and their free algebras, computational complexity of propositional logics, and arithmetical complexity of first-order logics.

Philosophy and sociology of science aim at understanding the workings of scientific endeavour. Despite their different emphasis and methodology,they deal with the same subject matter; and yet, they seem to be worlds apart. In the course of the last few decades, steps have been taken towardsa (partial) reconciliation. The conference FotFS VII was part of this process, bringing sociological aspects into philosophy of science and philosophicalaspects into sociology of science. Since the FotFS conference series focusses on the formal sciences, the conference had a certain, but non-exclusive focuson the role of mathematics as one of the sciences covered by philosophy and sociology. FotFS VII was organized by the research network PhiMSAMP Philosophy of Mathematics:Sociological Aspects and Mathematical Practice. A volume documenting the work of this network has already been published in the series Texts in Philosophy and covers specific questions linking philosophical issues in mathematics to mathematical practice. The present volume provides the generalmethodological background for the work done by the PhiMSAMP network. It contains fully refereed versions of papers presented at the seventhinstallment of the conference series Foundations of the Formal Sciences (FotFS).

This volume is dedicated to a distinguished logician, Walter Alexandre Carnielli, celebrating his 60th birthday.The honoree's contributions to contemporary logic range from innovative tableaux techniques, to the development of the foundations and applications of paraconsistent logics, to the invention of creative semantical apparatus.In this book the reader will find brilliant contributions by prominent logicians and philosophers that discourse over a broad repertoire of topics related to the outstanding work of Walter Carnielli.

Larry Powers' Non-contradiction is an engaging, innovative,and delightful book. It re-tells the story of Greek philosophyfrom the novel starting point that Parmenides, Plato andAristotle took their primary philosophical task to be thedefence of the principle of non-contradiction.In the course of nine chapters devoted to ancient Westernphilosophy we see Powers as the ally of the Greeks, and weget the impression that he sees their project even moreclearly than they did.The book also includes a substantial chapter that takes onthe challenge of explaining the importance of Hegel to modernanalytical philosophers, and another chapter that comparesour logical ways with those of ancient Indian and Chinesethinkers, such as Dignaga and Chuang Tsu.Interwoven with Powers' exposition of the history of philosophyis a primer on his own meta-philosophy, a theory devoted to theanalysis and resolution of philosophical disagreements.Especially those with an interest in logic and metaphysics willwant to study this book: throughout, the argumentation isoriginal, insightful, provocative, persistent and stimulating.

Hilbert and Bernays' 'Grundlagen der Mathematik'appeared in two volumes in 1934 and 1939, asecond edition in 1968 and 1970. It offers afoundation for proof theory and is a major source onDavid Hilbert's formalist programme, Paul Bernays'philosophy, the epsilon operator, and much more.It has been a profound infl uence on mathematics,logic, and philosophy, and it covers formal groundand philosophical perspectives beyond the scope ofWhitehead and Russell's 'Principia Mathematica' andFrege's 'Grundlagen der Arithmetik'.This book is not only essential to any scholar of thehistory and philosophy of modern mathematics, but italso contains formal research - on the epsilon and iotaoperators - of contemporary relevance to logicians,mathematicians and computer science. For us, it isone of the most fascinating books ever written.This a bilingual German-English, commented editionof the 'Grundlagen'. It is the fi rst English publicationof these texts and shows the facsimile of the Germanoriginal text on the left-hand side of a double page,and its English translation on the right-hand side.In addition to extensive comments on the historyand the interpretation of the text's mathematicaland philosophical content, there are also carefulannotations regarding the differences between thetwo German editions (1934/39,1968/1970) of thistwo volume monograph.

Vague language and corresponding models of inference and information processing is an important and challenging topic as witnessed by a number of recent monographs and collections of essays devoted to the topic.This volume collects fifteen papers, the majority of which originated with talks presented at the conference "Logical Models of Reasoning with VagueInformation (LoMoReVI)", September 14-17, 2009, in ¿ejkovice, that initiated a EUROCORES/LogICCC project with the same title.At least two features set the current volume apart from other texts: first, the interdisciplinary nature of the topic is nicely reflected by the wide range ofinterests of the authors, who include philosophers, linguists, logicians, as well as mathematicians and computer scientists. Secondly, all the papers areaccompanied by comments written by other authors and a few outside experts. These comments and corresponding replies by the authors document the very lively ongoing debate on adequate models of vague language.

Hao Wang (1921-1995) was a prolific researcher andwriter in mathematical logic, computer science, andphilosophy. He is known for the close relation hedeveloped with Kurt G├╢del during the last decade of thelatter''s life and the two books about G├╢del that hepublished after G├╢del''s death. This volume of essayscovers to some extent each of these fields of Wang''sactivity but with greatest emphasis on philosophy.Wang spent the first twenty-five years of his life in Chinaand continued to identify himself as Chinese, and in lateryears he returned to China several times. The volumeadds to the picture of the Chinese side of Wang and hisengagement with the intellectual life of his own countryduring a turbulent period. Wang''s writings in Chineseare surveyed, and two translations are included of shortessays on two Chinese scholars, his teacher Jin Yuelinand his friend from student days He Zhaowu, as well asa short memoir of Wang by He, written shortly afterWang''s death.Another writing of Wang published for the first time isan edition with introduction of an exposition by Wang ofG├╢del''s views on sets and concepts. Essays on Wangand his work include a memoir of collaboration with himon G├╢del''s philosophy by Eckehart K├╢hler, an account oftwo classic contributions to computer science and logicby Martin Davis, and essays by Abner Shimony on hisdistinctive view of the nature and method of philosophyand by Juliet Floyd on his reflections on the philosophyof Wittgenstein, who fascinated Wang partly because ofthe contrast between his views and G├╢del''s.