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The Journal of Applied Logics - IfCoLog Journal of Logics and their Applications (FLAP) covers all areas of pure and applied logic, broadly construed. All papers published are open access, and available via the College Publications website. This Journal is open access, and available in both printed and electronic formats. It is published by College Publications, on behalf of IfCoLog (www.ifcolog.net).

The Talmud introduces a specific logical hermeneutics, completely different from the Ancient Greek logic. This hermeneutics first appeared within the Babylonian legal tradition established by the Sumerians and Akkadians to interpret the first legal codes in the world and to deduce trial decisions from the codes by logical inference rules. The purpose of this book is (i) to examine the Talmudic hermeneutics from the point of view of its meaning for contemporary philosophy and logic as well as (ii) to evaluate the genesis of Talmudic hermeneutics which began with the Sumerian/Akkadian legal tradition. The logical hermeneutics of the Talmud is a part of the Oral Torah that was well expressed by the Tannaim, the first Judaic commentators of the Bible, for inferring Judaic laws from the Holy Book.The authors who have contributed to this volume were asked, first of all, to consider the Talmudic hermeneutics from the standpoint of modern philosophy: symbolic logic, rhetoric, analytic philosophy, pragmatics and so on. On the one hand, the authors are interested in possibilities to import some modern philosophical and logical methods into the Talmudic study, and on the other, are interested in possibilities to export new logical principles from the Talmud which are innovative to contemporary philosophy and logic.

La lógica de la Edad Media se presenta a los lógicos contemporáneos, filósofos medievalistas, historiadores yfilósofos de la lógica, como un campo tan fascinante como de difícil acceso. Parece demasiado intrincado paracasi cualquier investigador de estas áreas encontrar la punta del ovillo que lo conduzca a transitar unapresentación ordenada e inteligible de la lógica medieval. Este libro pretende solucionar este problema. Paraello, presenta de manera ordenada y autocontenida los desarrollos lógicos de la parte técnicamente másevolucionada de la lógica de la Edad Media: el siglo XIV. A diferencia de otras presentaciones no evade loshechos históricos y culturales que conforman el panorama de la época ni las cuestiones filosóficas detrás delos desarrollos lógicos, a fin de entender cabalmente las cuestiones técnicas y no desnaturalizar la propuestamedieval.Los primeros tres capítulos se abocan a cuestiones introductorias, históricas y a la genealogía de los tópicosmás importantes. El cuarto capítulo está dedicado a la presentación sintáctica del lenguaje de la lógicamedieval. El quinto y el sexto a la metateoría de esta lógica. El séptimo explora y presenta la semántica. Losdos últimos nos brindan una reconstrucción racional, en términos del lenguaje simbólico contemporáneo, dela lógica de finales del siglo XIV.

The Handbook of Formal Argumentation is a community effort aimed at providing a comprehensive and up-to-date view of the state of the art and current trends in the lively research field of formal argumentation.The first volume of the Handbook is organised into five parts, containing nineteen chapters in all, each written by leading experts in the field.The first part provides a general and historical perspective on the field.The second part gives a comprehensive coverage of the argumentation formalisms available in the literature at various levels of abstraction.The third part is devoted to cover some of the many dialogical aspects of argumentation, while the fourth one deals withalgorithmic, computational and implementation issues.Finally, the fifth part provides some deeper analyses on the previously introduced topics.The Handbook of Formal Argumentation is an open-ended initiative of which the present volume is the first outcome. Further volumes are planned to cover topics not included in the present one and the initiative is conceived to grow by the support and feeding it receives from the community members.

The concept of measuring inconsistency in information was developed by John Grant in a 1978 paper in the context of first-order logic. For more than 20 years very little was done in this area until in the early 2000s a number of AI researchers started to formulate new inconsistency measures primarily in the context of propositional logic knowledge bases. The aim of this volume is to survey what has been done so far, to expand inconsistency measurement to other formalisms, to connect it with related topics, and to provide ideas for further research in a topic that is particularly relevant now in view of the many inconsistencies in the massive amount of information available.The book contains 11 chapters. The first chapter, by John Grant, gives his original motivation for starting this field, explains why it was formulated in a highly mathematical manner, presents important material that was omitted from the original paper, and provides ideas about the use of dimensions in measuring inconsistency. The second chapter, by Matthias Thimm, is a survey that covers most of the research on inconsistency measures up to 2017. The other 9 chapters, all by experts either in inconsistency measures, or in the topic under consideration, or both, connect inconsistency measures with argumentation, disjunctive logic programming, fuzzy logic systems, modal logics, multiset representation, paraconsistent consequence, probabilistic logic, relational databases, and spatio-temporal databases.

The present work offers an original approach on the legal notions developed by Hans Kelsen in his attempts towards a "pure" theory of Law, based on a philosophical analysis of the main legal concepts that have a strong philosophical feature, namely those notions which are somehow "shared" between the two fields in their name, but not always in their meaning. While the most striking notion to be approached via a philosophical perspective wouldprobably be that of legal validity (since validity is a central term also in Logic), we aim, in thesame way, to approach the notions of legal fictions, the notion of science in Law, normativeconflicts or "contradictions" as they are commonly - and wrongly - named, and the rule ofinference as it is applied in the context of normative creation, giving place to the wrong notion of practical reasoning. The notion of practical reasoning is very rich in this context ofcomparison, and will be a special one, as it serves for us to analyze traditional problems oflegal theory, such as Jørgensen's dilemma, as well as it offers the opportunity of providing our own alternative of a legitimate logical treatment of the process of legal justification in the context of the creation of a norm. We aim to analyze the notion of legal and logical conditions as well, which represent a changing in Kelsen's perspective on the utility and legitimacy of the application of logic to the legal domain. Such a comparative study, even if it appears to be fundamental for clarifying those notions in their respective fields, is a task never before developed in this systematic manner.The objective of such a study is to provide a clear overview of the boundaries between thefields of philosophy (especially logic) and the legal norms. A clear understanding of therelations between those "homonym" notions may explain why they are - most of the time -misused when philosophers talk about law, as well as when lawyers and jurists try to justifythe concepts composing their legal theories. The context of this study is the legal positivism as it is explained by the legal-philosopher Hans Kelsen. This choice is justified by the fact that Kelsen's legal theory appears to be the most suitable frame for an analytical, logic-oriented investigation. The work emphasized will be the General Theory of Norms (1979), mainly because of the fact that this book represents how intensively Kelsen dedicated himself to the legal problems mostly related to philosophy or logic, namely the question of the application of logic to norms and the clarification ofproblematic notions such as the Basic Norm as a fiction or, still, the notion of "modallyindifferent substrate", that we consider to be a path towards a conciliation between logic and law.

Dans ce long article, paru en allemand en 1964, Kurt Ebbinghaus propose, dans la lignée des travaux de Paul Lorenzen, une reconstruction de la théorie du syllogisme à partir d'un modèle calculatoire. Dans ce modèle, les syllogismes sont pensés comme des règles et la question de la validité logique est formulée en termes de « procédure » et non en termes de « vérité ». L'intérêt de le traduire aujourd'hui pour la première fois n'est pas seulement qu'il offre de quoi mesurer combien Aristote est un grand logicien, parfaitement maître des outils formels qu'il élabore dans les Premiers Analytiques. Il permet d'attribuer à Kurt Ebbinghaus la véritable paternité de l'approche inférentialiste des écrits logiques d'Aristote, approche plus connue depuis les travaux de J. Corcoran ou de R. Smith, pourtant plus tardifs. Il ouvre enfin, à travers le concept de « preuve d'admissibilité », une perspective proprement constructiviste sur la question de la complétude chez Aristote.

This is a great book. Against the background of the dogmatism of much of modern economics, Fullbrook has produced an innovative, wide-ranging argument for narrative pluralism. The timely book is beautifully written, accessible to all, provocative, extraordinarily insightful, and extremely compelling.Tony Lawson, Cambridge University, UK This fascinating and profound work should be read … by anyone who is taken in by mainstream economics' false claims of scientific objectivity. Fullbrook's erudite, systematic and thoughtful investigation into the philosophical and conceptual bases of the "singular narrative" exposes the limitations of neoclassical economics and its degenerate practice, and provides a powerful critique of different models of economic rationality.Jayati Ghosh, Jawaharlal Nehru University, India For anyone interested in the state of modern (mainstream) economics, and especially in how and why the neoclassical school has remained so dominant since the Crash of 2008, Fullbrook's book is a must-read. It goes far beyond other treatments in the way that it compares (unfavourably) the prevailing "mono-epistemology" in economics with the norms of epistemological pluralism in the natural sciences. Robert H. Wade, London School of Economics This genuinely original book… scrutinizes the weird make-believe world of mainstream economics and its narrative dogmatism, determinism and atomism, it constitutes a powerful plaidoyer for real pluralism in economics. Fullbrook brings bold new perspectives on the logic of economic choice, rationality, ideology, naturalism, and microfoundations. Whether you agree with him or not, he forces you to think.Lars P Syll, Malmö University, Sweden This book is provocative and highly convincing. It shows us that there is no such thing as a one and unique truth, neither in natural sciences, nor in social sciences. Because reality is multifaceted, narrative pluralism is essential for the advancement of knowledge and for the good health of a democratic society. Fullbrook changes our understanding of what is science and what is ideology.André Orléan, l'École des hautes études en sciences sociales, Paris The neoclassical monopoly in economics necessarily ignores most of what really counts, and locks out competitors. Fullbrook establishes this persuasively in a thoughtful, grounded, and accessible study. To be adequate, economic understanding requires a plurality of approaches. This book shows conclusively that no other position is tenable.Anver Offer, All Souls College, Oxford University, UK Edward Fullbrook's Narrative Fixation in Economics is an exceptionally erudite exploration of the descent of economics into scientism and anti-knowledge.Julie Nelson, University of Massachusetts, Boston

The Theory of Inconsistency has a long lineage, stretching back to Herakleitos, Hegel and Marx. In the late twentieth-century, it was placed on a rigorous footing with the discovery of paraconsistent logic and inconsistent mathematics. Paraconsistent logics, many of which are now known, are "inconsistency tolerant", that is, they lack the rule of Boolean logic that a contradiction implies every proposition. When this constricting rule was seen to be arbitrary, inconsistent mathematical structures were free to be described. This book continues the development of inconsistent mathematics by taking up inconsistent geometry, hitherto largely undeveloped. It has two main goals. First, various geometrical structures are shown to deliver models for paraconsistent logics. Second, the "impossible pictures" of Reutersvaard, Escher, the Penroses and others are addressed. The idea is to derive inconsistent mathematical descriptions of the content of impossible pictures, so as to explain rigorously how they can be impossible and yet classifiable into several basic types. The book will be of interest to logicians, mathematicians, philosophers, psychologists, cognitive scientists, and artists interested in impossible images. It contains a gallery of previously-unseen coloured images, which illustrates the possibilities available in representing impossible geometrical shapes. Chris Mortensen is Emeritus Professor of Philosophy at the University of Adelaide. He is the author of Inconsistent Mathrmatics (Kluwer 1995), and many articles in the Theory of Inconsistency.

Elementary Logic with Applications is written for undergraduate logic and logic programming courses. Logic has been applied to a wide variety of subjects such as software engineering and hardware design, to programming and artificial intelligence. In this way, it has served to stimulate the search for clear conceptual foundations. Recently many extensions of classical logic such as temporal, modal, relevance, fuzzy and non-monotonic logics have been widely used in computer science, therefore requiring a new formulation of classic logic which can be modified to yield the effect of non-classical logics. This text aims to introduce classical logic in such a way that one can easily deviate into discussing non-classical logics. It defines a number of different types of logics and the differences between them, starting with the basic notions of the most common logic. Elementary Logic with Applications develops a theorem prover for classical logic in a way that maintains a procedural point of view and presents the reader with the real challenges facing applied logic. Dov Gabbay and Odinaldo Rodrigues have been teaching logic and computer science for many years. Dov Gabbay has written numerous other titles on the subject of logic and is a world authority on non-classical logics. Odinaldo Rodrigues is widely known for his work on logic, belief revision and argumentation. The "Elementary Logic with Applications" course is currently taught at the Department of Informatics, King's College London.

This book sets out to encourage a debate about the role that economic theory and philosophy of economics can play. A good part of economics consists of theoretical developments which describe completely imaginary worlds and have no connections to actual market economies. If the purpose of theoretical and philosophical analysis in economics is to make a contribution to find out how modern market economies work and which kind of theoretical practice will be useful for the implementation of successful economic policies, a shift both in philosophy of economics and economics itself is needed. Exposing the ungrounded pretensions of the mainstream philosophy of economics, Marqués' carefully argued book is a major contribution to the ongoing debate on contemporary mainstream economics and its methodological and philosophical underpinnings. Even those who disagree with his conclusions will benefit from his thorough and deep critique of the modeling strategies used in modern economics. Lars Pålsson Syll, Malmö University, Sweden Is 'mainstream philosophy of economics' only about models and imaginary worlds created to represent economic theories? Marqués questions this epistemic focus and calls for the ontological examination of real world economic processes. This book is a serious challenge to standard thinking and an alternative program for a pluralist philosophy of economics.John Davis, Marquette University, USA and University of Amsterdam In recent decades economists have focused heavily on the development and use of models. In this scholarly but accessible book Marqués clearly describes the limitations of this approach and suggests alternative directions. It is a valuable addition to the armoury of anyone concerned about the nature of mainstream economics. Stuart Birks, Massey University, New Zealand In this book Gustavo Marqués, one of our discipline's most dexterous and acute minds, calmly investigates in depth economics' most persistent methodological enigmas. Chapter Three alone is sufficient reason for owning this book. Edward Fullbrook, University of the West of England

This book is a collection of Steve Keen's influential papers published over the last fifteenyears. The topics covered include methodology, microeconomics, and the monetary approachto macroeconomics that Keen - along with many other non-mainstream economists - hasbeen developing."Economics still awaits its Darwin. Keynes came close, but not close enough. Keen comes closerstill and this collection of his papers shows how. Developing an economics for the post-crisisworld focuses simultaneously on the recent global crisis and the underlying structures ofcontemporary economies.Edward Fullbrook, Editor of Real-World Economics Review

This book introduces 40 critical pointers for those who wish to see the theory in a broader, more realistic context. The material is suitable for introductory and intermediate courses and can be included selectively by students for additional reading or in lectures or tutorials as discussion points."Students of mainstream economics need a guide like this to help them understand the underlying assumptions, limitations and inbuilt biases of what they are studying. It helps them open their eyes to a broader view of how real economies work."Emeritus Professor Frank Stilwell, University of Sydney"...different approaches are required to move from Neo-classical Theory's artificial world of economics to Real Life Economics, the invitational style that Birks has used is likely to be one of the most productive ones. He enters into the students' comfort zone and takes them along pointing out the limitations of what is familiar and its inadequacies to deal seriously with policy issues."C T Kurien"This book... critiques the traditional market-focused world of economics in a systematic fashion, with copious well-chosen examples from everyday life to underscore the anomalies and weaknesses involved in the understanding of problems and seeking their solutions. ...it would be a 'good read', not just to the existing or aspiring economist, but also to those who are not particularly concerned about the state of affairs in the discipline of economics. It is refreshingly enlightening."Emeritus Professor Srikanta Chatterjee"The real benefit of the text is that it is critical about the underlying assumptions that we implicitly hide behind when we create our models. The more honest and critical we are when we teach our students then the more effective economic policy will be in the future, which surely we, as a discipline, should be striving towards. I'd recommend this book to those who don't realise the severity of the assumptions that they hide behind, to students who can use these ideas to engage in debate with each other and with their lecturers, and to honest and critical lecturers who can refer to it simply to remind themselves why they already do it the honest way. It should be mandatory for all economics departments to have at least one copy."Professor Don Webber

Les philosophes ont souvent traité de la fiction comme d'un problème collatéral, dont l'intérêt est limité à la logique et la philosophie du langage. Ce livre affirme en revanche que la fiction joue un rôle central en métaphysique. En développant une théorie « artefactuelle » de la fiction il aboutit ainsi à l'esquisse d'un nouveau système de catégories, « multidimensionnel ». L'on comprend ainsi que les personnages fictionnels sont des artefacts abstraits, des entités tout aussi ordinaires que les lois, les symphonies ou les ¿uvres littéraires : des entités dont l'existence dépend, d'un côté, des actes intentionnels humains (les actes créateurs d'au moins un auteur et les compétences linguistiques et culturelles d'une communauté de lecteurs) et, de l'autre, de l'existence de certaines entités spatio-temporels (des livres, des enregistrements etc.). Les conséquences métaphysiques d'une telle théorie sont importantes : l'identification d'un ensemble de catégories ontologiques de base, une meilleure compréhension de la différence entre vraie et fausse parcimonie ontologique et la formulation d'une base adéquate pour une ontologique du monde quotidien. Philosophers have often treated fiction as a sideshow issue, whose interest is limited to logic and philosophy of language. By contrast, this book maintains that fiction plays a central role in metaphysics. Through an "artifactual" theory of fiction it leads to the sketch of a new "multidimensional" system of categories. Fictional characters are recognized as abstract artifacts, as ordinary as laws or symphonies or works of literature, i.e. entities whose existence depends on intentional human acts on the one hand (the creative acts of at least one author, and the linguistic and cultural competence of a community of readers) and on the other hand on the existence of some spatiotemporal particulars (such as books, records etc.). The metaphysical consequences of this theory are far reaching: the identification of a set of basic ontological categories, a better understanding of the difference between genuine and false ontological parsimony and the formulation of an adequate basis for an ontology of the everyday world.

The book provides a self-contained introduction to computability theory for advanced undergraduate or early graduate students of mathematics and computer science. The technical material is illustrated with plenty of examples, problems with fully worked solutions as well as a range of proposed exercises.Part I is centered around fundamental computability notions and results, starting with the pillar concepts of computational model (an abstract high-level programming language), computable function, decidable and listable set, proper universal function, decision problem and the reduction technique for transferring decidability and listability properties. The essential results namely Rice's Theorem, Rice-Shapiro's Theorem, Rice-Shapiro-McNaughton-Myhill's Theorem as well as Rogers' Theorem and the Recursion Theorem are presented and illustrated. Many-to-one reducibility and many-to-one degrees are investigated. A short introduction to computation with oracles is also included. Computable as well as non-computable operators are introduced as well as monotonic and finitary operators. The relationship between them is discussed, in particular via Myhill-Shepherdson's Theorem. Kleene's Least Fixed Point Theorem is also presented. Finally, Part I terminates with a briefi ng on the Turing computational model, Turing reducibility and Turing degrees.Part II of the book concentrates on applications of computability in several areas namely in logic (undecidability of arithmetic, satisfiability in propositional logic, decidability in modal logic), Euclidean geometry, graphs and Kolmogorov complexity. Nevertheless no previous knowledge of these subjects is required. The essential details for understanding the applications are provided.

Contemporary argumentation studies continue a tradition founded by Aristotle, Cicero, Quintilian and others. Since the end of the Second World War, they have been vigorously taken over and reoriented by different schools of thought, stressing their link to the renovated disciplines of logic, dialectic, rhetoric or grammar. Anscombre, Blair, Ducrot, van Eemeren, Grize, Grootendorst, Hamblin, Johnson, Olbrechts-Tyteca, Perelman, Toulmin, Walton, Woods, and many others, have reconceptualized the field, reconnected it to contemporary scholarship and opened up rigorous and innovative avenues of research. At the turn of the century, argumentation in science education and argumentation about socio-scientific issues emerged as new fields within the larger area of argumentation studies. Within this diverse and challenging context, this comprehensive Dictionary makes a significant contribution to the construction of a common culture and shared vocabulary of argumentation. Argumentation is approached as an all-pervasive linguistic-cognitive activity, and argumentation studies are posited as a multidisciplinary field. This Dictionary of Argumentation defines 301 concepts. The 223 main entries define, comment upon, and illustrate a specific concept or a set of interrelated concepts. The 78 secondary entries refer to the relevant main entry (-ies). The relationships between the entries are marked by a system of cross-references, which strengthen the conceptual coherence of the Dictionary as a whole. This is the first dictionary of its kind to be published in English.