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Relevance logics are a misunderstood lot. Despite being the subject of intense study for nearly a century, they remain maligned as too complicated, too abstruse, or too silly to be worth learning much about. This Element aims to dispel these misunderstandings. By focusing on the weak relevant logic B, the discussion provides an entry point into a rich and diverse family of logics. Also, it contains the first-ever textbook treatment of quantification in relevance logics, as well as an overview of the cutting edge on variable sharing results and a guide to further topics in the field.
This book introduces the reader to relevant logic and provides it with a philosophical interpretation. The defining feature of relevant logic is that it forces the premises of an argument to be really used ('relevant') in deriving its conclusion. The logic is placed in the context of possible world semantics and situation semantics, which are then applied to provide an understanding of the various logical particles (especially implication and negation) and natural language conditionals. The book ends by examining various applications of relevant logic and presenting some interesting open problems.
In spite of a powerful tradition, more than two thousand years old, that in a valid argument the premises must be relevant to the conclusion, twentieth-century logicians neglected the concept of relevance until the publication of Volume I of this monumental work. Since that time relevance logic has achieved an important place in the field of philosophy: Volume II of Entailment brings to a conclusion a powerful and authoritative presentation of the subject by most of the top people working in the area. Originally the aim of Volume II was simply to cover certain topics not treated in the first volume--quantification, for example--or to extend the coverage of certain topics, such as semantics. However, because of the technical progress that has occurred since the publication of the first volume, Volume II now includes other material. The book contains the work of Alasdair Urquhart, who has shown that the principal sentential systems of relevance logic are undecidable, and of Kit Fine, who has demonstrated that, although the first-order systems are incomplete with respect to the conjectured constant domain semantics, they are still complete with respect to a semantics based on "arbitrary objects." Also presented is important work by the other contributing authors, who are Daniel Cohen, Steven Giambrone, Dorothy L. Grover, Anil Gupta, Glen Helman, Errol P. Martin, Michael A. McRobbie, and Stuart Shapiro. Robert G. Wolf's bibliography of 3000 items is a valuable addition to the volume. Originally published in 1992. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
PRAISE FOR THE BOOK:"Dejnozka's erudition continues to astound me." - Nicholas Griffin.As Canada Research Chair and Director of the Bertrand Russell Research Centre at McMaster University, Professor Griffin directs the editing of the ongoing editions of The Collected Papers of Bertrand Russell, currently at 16 volumes. He also edited The Cambridge Companion to Bertrand Russell, and has written several books and articles."Dejnozka challenges the reader to open his mind for a new interpretation of Russell's work, in particular that relevance notions have a greater place in his philosophy of logic than has been stressed before. Dejnozka's work is full of material which stimulates one to rethink Russell's philosophy of logic, and it is greatly to the author's credit that he brings to light such a wealth of crucial issues in the history and philosophy of logic." - Shahid Rahman.Professor Rahman teaches at the Université de Lille (France). He has served as dean and supervised many dissertations. He is the author of several books and the editor of several anthologies in logic and the philosophy of logic. He recently edited a book on Hugh MacColl. He has also written many articles and reviews, and read papers at various congresses.PUBLISHED REVIEW:"Dejnozka's defense of his view is well articulated and strongly supported by citing thinkers of the caliber of Quine, Russell and Wittgenstein, among others. Moreover, the defense is presented in a clear and explicit way, making evident the role played by relevance logic and diagrams.... Finally, a very positive aspect is the presence of many explanatory notes, placed at the end of the book, that shed light on the discussion in the text." Edgar L. B. Almeida, Logic and Logical Philosophy (2013).PUBLISHED REVIEW:"The main argument of the book is interesting for suggesting that truth ground containment, i.e. the classical notion of consequence, embodies a meaningful notion of a connection between the assumptions and the conclusion of a valid argument.... I do think that the book's main claims hold.... Yes, classical validity can be seen as involving a...notion of containment - containment of truth grounds. Yes, this notion can be found in the writings of outstanding modern classical logicians such as Wittgenstein or Russell. Yes, the relevantist's notion of relevance...can be seen as a species of a broader genus. Perhaps the greatest merit of the present book is that it emphasizes these points explicitly." Igor Sedlár, Organon F (2014).BOOK DESCRIPTION:In the first volume of their monumental work, Entailment, Alan Ross Anderson and Nuel D. Belnap say that the "modern classical tradition[,] stemming from Frege and Whitehead-Russell, gave no consideration whatsoever to the classical notion of relevance." But just what is this classical notion? I argue that the relevance tradition is implicitly most deeply concerned with the containment of truth-grounds. Thus modern classical logicians such as Peirce, Frege, Russell, Wittgenstein, and Quine are implicit relevantists on the deepest level. In showing this, I reunite two fields of logic which have become basically separated from each other: relevance logic and diagram logic. I argue that there are two main concepts of relevance, intensional and extensional. The first is that of the relevantists. The second is the concept of truth-ground containment as following from in Wittgenstein's Tractatus. I show that this second concept belongs to the diagram tradition of showing that the premisses contain the conclusion by the fact that the conclusion is diagrammed in the very act of diagramming the premisses. I argue that the extensional concept is primary, with at least five usable modern classical filters or constraints, and indefinitely many secondary intensional filters or constraints. In this way, I argue for a major reunion of purpose in logic between relevantists and modern classical logicians.
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.
The papers presented in this volume examine topics of central interest in contemporary philosophy of logic. They include reflections on the nature of logic and its relevance for philosophy today, and explore in depth developments in informal logic and the relation of informal to symbolic logic, mathematical metatheory and the limiting metatheorems, modal logic, many-valued logic, relevance and paraconsistent logic, free logics, extensional v. intensional logics, the logic of fiction, epistemic logic, formal logical and semantic paradoxes, the concept of truth, the formal theory of entailment, objectual and substitutional interpretation of the quantifiers, infinity and domain constraints, the Löwenheim-Skolem theorem and Skolem paradox, vagueness, modal realism v. actualism, counterfactuals and the logic of causation, applications of logic and mathematics to the physical sciences, logically possible worlds and counterpart semantics, and the legacy of Hilbert's program and logicism. The handbook is meant to be both a compendium of new work in symbolic logic and an authoritative resource for students and researchers, a book to be consulted for specific information about recent developments in logic and to be read with pleasure for its technical acumen and philosophical insights.- Written by leading logicians and philosophers- Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic- Clear, in-depth expositions of technical detail- Progressive organization from general considerations to informal to symbolic logic to nonclassical logics- Presents current work in symbolic logic within a unified framework- Accessible to students, engaging for experts and professionals- Insightful philosophical discussions of all aspects of logic- Useful bibliographies in every chapter
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.
A collection of papers proposing, developing, and implementing logical IR models. After an introductory chapter on non-classical logic as the appropriate formalism with which to build IR models, papers are divided into groups on three approaches: logical models, uncertainty models, and meta-models. Topics include preferential models of query by navigation, a logic for multimedia information retrieval, logical imaging and probabilistic information retrieval, and an axiomatic aboutness theory for information retrieval. Can be used as a text for a graduate course on information retrieval or database systems, and as a reference for researchers and practitioners in industry. Annotation copyrighted by Book News, Inc., Portland, OR
such questions for centuries (unrestricted by the capabilities of any hard ware). The principles governing the interaction of several processes, for example, are abstract an similar to principles governing the cooperation of two large organisation. A detailed rule based effective but rigid bureaucracy is very much similar to a complex computer program handling and manipulating data. My guess is that the principles underlying one are very much the same as those underlying the other. I believe the day is not far away in the future when the computer scientist will wake up one morning with the realisation that he is actually a kind of formal philosopher! The projected number of volumes for this Handbook is about 18. The subject has evolved and its areas have become interrelated to such an extent that it no longer makes sense to dedicate volumes to topics. However, the volumes do follow some natural groupings of chapters. I would like to thank our authors are readers for their contributions and their commitment in making this Handbook a success. Thanks also to our publication administrator Mrs J. Spurr for her usual dedication and excellence and to Kluwer Academic Publishers for their continuing support for the Handbook.