This second volume of a collection of papers offers new perspectives and challenges in the study of logic. It is presented in honor of the fiftieth birthday of Jean-Yves Béziau. The papers touch upon a wide range of topics including paraconsistent logic, quantum logic, geometry of oppositions, categorical logic, computational logic, fundamental logic notions (identity, rule, quantification) and history of logic (Leibniz, Peirce, Hilbert). The volume gathers personal recollections about Jean-Yves Béziau and an autobiography, followed by 25 papers written by internationally distinguished logicians, mathematicians, computer scientists, linguists and philosophers, including Irving Anellis, Dov Gabbay, Ivor Grattan-Guinness, Istvan Németi, Henri Prade. These essays will be of interest to all students and researchers interested in the nature and future of logic.

Many systems of logic diagrams have been offered both historically and more recently. Each of them has clear limitations. An original alternative system is offered here. It is simpler, more natural, and more expressively and inferentially powerful. It can be used to analyze not only syllogisms but arguments involving relational terms and unanalyzed statement terms.

Relevance logics came of age with the one and only International Conference on relevant logics in 1974. They did not however become accepted, or easy to promulgate. In March 1981 we received most of the typescript of IN MEMORIAM: ALAN ROSS ANDERSON Proceedings of the International Conference of Relevant Logic from the original editors, Kenneth W. Collier, Ann Gasper and Robert G. Wolf of Southern Illinois University. 1 They had, most unfortunately, failed to find a publisher - not, it appears, because of overall lack of merit of the essays, but because of the expense of producing the collection, lack of institutional subsidization, and doubts of publishers as to whether an expensive collection of essays on such an esoteric, not to say deviant, subject would sell. We thought that the collection of essays was still (even after more than six years in the publishing trade limbo) well worth publishing, that the subject would remain undeservedly esoteric in North America while work on it could not find publishers (it is not so esoteric in academic circles in Continental Europe, Latin America and the Antipodes) and, quite important, that we could get the collection published, and furthermore, by resorting to local means, published comparatively cheaply. It is indeed no ordinary collection. It contains work by pioneers of the main types of broadly relevant systems, and by several of the most innovative non-classical logicians of the present flourishing logical period. We have slowly re-edited and reorganised the collection and made it camera-ready.

In Relevance in Argumentation, author Douglas Walton presents a new method for critically evaluating arguments for relevance. This method enables a critic to judge whether a move can be said to be relevant or irrelevant, and is based on case studies of argumentation in which an argument, or part of an argument, has been criticized as irrelevant. Walton's method is based on a new theory of relevance that incorporates techniques of argumentation theory, logic, and artificial intelligence. The work uses a case-study approach with numerous examples of controversial arguments, strategies of attack in argumentation, and fallacies. Walton reviews ordinary cases of irrelevance in argumentation, and uses them as a basis to advance and develop his new theory of irrelevance and relevance. The volume also presents a clear account of the technical problems in the previous attempts to define relevance, including an analysis of formal systems of relevance logic and an explanation of the Grecian notion of conversational relevance. This volume is intended for graduate and advanced undergraduate courses in those fields using argumentation theory--especially philosophy, linguistics, cognitive science and communication studies, in addition to argumentation. The work also has practical use, as it applies theory directly to familiar examples of argumentation in daily and professional life. With a clear and comprehensive method for determining relevance and irrelevance, it can be convincingly applied to highly significant practical problems about relevance, including those in legal and political argumentation.

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This book constitutes the refereed proceedings of the Second International Conference Diagrams 2002, held in Callaway Gardens, Georgia, USA, in April 2002. The 21 revised full papers and 19 posters presented were carefully reviewed and selected from 77 submissions. The papers are organized in topical sections on understanding and communicating with diagrams, diagrams in mathematics, computational aspects of diagrammatic representation and reasoning, logic and diagrams, diagrams in human-computer interaction, tracing the process of diagrammatic reasoning, visualizing information with diagrams, diagrams and software engineering, and cognitive aspects.

A lively and engaging look at logic puzzles and their role in mathematics, philosophy, and recreation Logic puzzles were first introduced to the public by Lewis Carroll in the late nineteenth century and have been popular ever since. Games like Sudoku and Mastermind are fun and engrossing recreational activities, but they also share deep foundations in mathematical logic and are worthy of serious intellectual inquiry. Games for Your Mind explores the history and future of logic puzzles while enabling you to test your skill against a variety of puzzles yourself. In this informative and entertaining book, Jason Rosenhouse begins by introducing readers to logic and logic puzzles and goes on to reveal the rich history of these puzzles. He shows how Carroll's puzzles presented Aristotelian logic as a game for children, yet also informed his scholarly work on logic. He reveals how another pioneer of logic puzzles, Raymond Smullyan, drew on classic puzzles about liars and truthtellers to illustrate Kurt Gödel's theorems and illuminate profound questions in mathematical logic. Rosenhouse then presents a new vision for the future of logic puzzles based on nonclassical logic, which is used today in computer science and automated reasoning to manipulate large and sometimes contradictory sets of data. Featuring a wealth of sample puzzles ranging from simple to extremely challenging, this lively and engaging book brings together many of the most ingenious puzzles ever devised, including the "Hardest Logic Puzzle Ever," metapuzzles, paradoxes, and the logic puzzles in detective stories.