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This is Volume I of the proceedings of the 2nd European Conference on Argumentation: Argumentation and Inference, held at the University of Fribourg, Switzerland, in June 2017. The European Conference on Argumentation (ECA) is an established pan-European initiative aiming to consolidate and advance various streaks of research into argumentation and reasoning: philosophy, communication, linguistics, discourse analysis, computer science, psychology, cognitive studies, legal theory, etc. These proceedings reflect the current state of the art of argumentation scholarship across these disciplines and, as such, are a testimony to the vigour of the field. A majority of contributions presented in these volumes frontally tackle the conference theme, thereby offering a valuable and focused discussion on various aspects of inference and on its role in argumentative practices to scholars interested in the topic but also, more broadly, in argumentation theory.This is Volume I of the proceedings of the 2nd European Conference on Argumentation: Argumentation and Inference, held at the University of Fribourg, Switzerland, in June 2017. The European Conference on Argumentation (ECA) is an established pan-European initiative aiming to consolidate and advance various streaks of research into argumentation and reasoning: philosophy, communication, linguistics, discourse analysis, computer science, psychology, cognitive studies, legal theory, etc. These proceedings reflect the current state of the art of argumentation scholarship across these disciplines and, as such, are a testimony to the vigour of the field. A majority of contributions presented in these volumes frontally tackle the conference theme, thereby offering a valuable and focused discussion on various aspects of inference and on its role in argumentative practices to scholars interested in the topic but also, more broadly, in argumentation theory.

This text, volume II of a two-volume work, examines in depth the so-called "standard" predicate logic. Including a foundational lexicon of terms and a detour through the classical propositional logic, this volume can be used independently of the first. As a means toward teasing out theoretical subtleties and negotiating formal and philosophic challenges, this work uses detailed examples and exercises; because of this feature, the text can also be used to study formal logic in a rigorous fashion. Given its expressive power, predicate logic is deemed as minimally adequate for formalization of such fundamental languages as that of Mathematics and for translations of the meanings of English (or other natural-language) sentences. Laying foundations in this area is key to a technical understanding of deductive reasoning and to honing rigorous critical thinking and problem-solving skills. Notable (some of them unusual) features that are covered in the present volume include the following: The overview of propositional logic includes positive semantic trees, in addition to the negative semantic tree method. Prenex forms and conversion to equivalent prenex forms. Relational (ultimately polyadic) predicate symbols, function symbols and identity are made available. The decision problem and the L¿wenheim Result are discussed. Proof-theoretic methods are presented analytically and extensive justifications are offered for the required restrictions on the deduction rules. The semantics of predicate logic modeling are presented in analytical detail along with inquiries into the logical-philosophical significance of predicate logic. Translation from English into the predicate logic idiom (formalization, symbolization) is examined thoroughly, accompanied by motivating linguistic observations and thorough scrutiny of available options; aspects of this inquiry include translations under restricted and unrestricted domains, translations of compacted predicates, rendering of non-classically quantified phrases, translations of numerical statements, definite descriptions and regimentation, and guidance on how to render existential presuppositions. Disambiguation is imposed on translations and an extensive list of examples is presented. Translations of idiomatic linguistic expressions are studied. Semantic tree decision procedures (for finitarian domains) - including negative and positive semantic tree systems - are constructed and applied. Appendices on Set Theory, Mathematical Induction and Dialogical Logic are presented.

This text, volume I of a two-volume work, examines in depth the standard (also called classical) propositional logic. This is a theoretical work that aims at a philosophically exploratory and technically rigorous presentation. Detailed examples and exercises are used to tease out technical minutiae, solidify understanding, and point to logical-philosophical puzzles and challenges; because of this feature, the text can also be used to study formal logic in a rigorous fashion. The study of propositional logic can reward the dedicated and patient student by unveiling technical mysteries of critical thinking and problem-solving, by shedding light on relevant concepts in the study of reasoning, by showing how the powerful formal tools and methods work in applications, and by unlocking the crypts of logical analysis. It can hone insights that further contribute both to understanding how logic works and to preparing for future pursuits in the study of formal reasoning.This text encompasses certain topics and decision mechanisms that are usually absent from Logic texts and can be canvassed only through acquaintance with ever larger chunks of the extant bibliography. Rarely covered topics of the present text include: possible-worlds analysis, analyticity and non-cognitivism, detailed investigations of logical relations, alternative grammatical and computational systems, truth tables for dynamic flow of information and corrected truth tables, negative and positive semantic trees, normal forms and Karnaugh maps, Intuitionistic natural deduction, normalization and harmony in proof-theoretic systems, and dialogical logic.

The objective of the present work is to develop a theory of meaning based on the method of transcendental phenomenology. The key idea of the project is to explain the constitution of the meaning by means of the analyses of the intentionality. We have investigated different intentional acts which are functioning in the expression and in constructing the meanings. In this regard we have studied, first, the act of the primordial expression, in which a content of an intuition is raised to the realm of the ideal, and then the acts of the categorial synthesis, in which further meanings are constituted in the absence of their proper intuition. We have investigated the effects of the phenomenological theory of meaning to the conception of pure logic. Dialogical semantics is shown to be an adequate framework, from the phenomenological point of view, to interpret logical reasoning and to explain the meaning of the logical constants as well. We have also discussed the meanings of some logical connectives, and their formalizations, using our phenomenologico-dialogical method. In particular, the meaning explanations of negation(s), strict implication and necessity are given in a way which is not model theoretic nor proof theoretic, but based on the transcendental intentionality as manifested in the course of the dialogue.

The 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 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.