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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.
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.
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.
Directions in Relevant Logic by J. Norman,R. Sylvan Pdf
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.
Logic, Rationality, and Interaction by Wiebe van der Hoek,Wesley H. Holliday,Wen-fang Wang Pdf
FoLLI-LNCS is the publication platform for the Association of Logic, Language and Information (FoLLI, www.folli.org). The Association was founded in 1991 to advance research and education on the interface between logic, linguistics, computer science, and cognitive science. The FoLLI Publications on Logic, Language and Information aim to disseminate results of cutting-edge research and tutorial materials in these interdisciplinary areas. This LNCS volume is part of FoLLi book serie and contains the papers presented at the 5th International Workshop on Logic, Rationality and Interaction/ (LORI-V), held in October 2015 in Taipei, Taiwan. The topics covered in this program well represent the span and depth that hasby now become a trademark of the LORI workshop series, where logic interfaceswith disciplines as diverse as game theory and decision theory, philosophyand epistemology, linguistics, computer science and artificial intelligence.
A Practical Logic of Cognitive Systems by Dov M. Gabbay,John Woods Pdf
The present work is a continuation of the authors' acclaimed multi-volume APractical Logic of Cognitive Systems. After having investigated the notion ofrelevance in their previous volume, Gabbay and Woods now turn to abduction. Inthis highly original approach, abduction is construed as ignorance-preservinginference, in which conjecture plays a pivotal role. Abduction is a response to acognitive target that cannot be hit on the basis of what the agent currently knows.The abducer selects a hypothesis which were it true would enable the reasoner to attain his target. He concludes from this fact that the hypothesis may be conjectured. In allowing conjecture to stand in for the knowledge he fails to have, the abducer reveals himself to be a satisficer, since an abductive solution is not a solution from knowledge. Key to the authors' analysis is the requirement that a conjectured proposition is not just what a reasoner might allow himself to assume, but a proposition he must defeasibly release as a premiss for further inferences in the domain of enquiry in which the original abduction problem has arisen. The coverage of the book is extensive, from the philosophy of science tocomputer science and AI, from diagnostics to the law, from historical explanation to linguistic interpretation. One of the volume's strongest contributions is its exploration of the abductive character of criminal trials, with special attention given to the standard of proof beyond a reasonable doubt. Underlying their analysis of abductive reasoning is the authors' conception ofpractical agency. In this approach, practical agency is dominantly a matter of thecomparative modesty of an agent's cognitive agendas, together with comparatively scant resources available for their advancement. Seen in these ways, abduction has a significantly practical character, precisely because it is a form of inference that satisfices rather than maximizes its response to the agent's cognitive target. The Reach of Abduction will be necessary reading for researchers, graduatestudents and senior undergraduates in logic, computer science, AI, belief dynamics, argumentation theory, cognitive psychology and neuroscience, linguistics, forensic science, legal reasoning and related areas. Key features: - Reach of Abduction is fully integrated with a background logic of cognitive systems.- The most extensive coverage compared to competitive works.- Demonstrates not only that abduction is a form of ignorance preservinginference but that it is a mode of inference that is wholly rational.- Demonstrates the satisficing rather than maximizing character ofabduction.- The development of formal models of abduction is considerably more extensive than one finds in existing literature. It is an especially impressive amalgam of sophisticatedconceptual analysis and extensive logical modelling. · Reach of Abduction is fully integrated with a background logic of cognitive systems.· The most extensive coverage compared to competitive works· Demonstrates not only that abduction is a form of ignorance preservinginference but that it is a mode of inference that is wholly rational.· Demonstrates the satisficing rather than maximizing character ofabduction.· The development of formal models of abduction is considerably more extensive than one finds in existing literature. It is an especially impressive amalgam of sophisticatedconceptual analysis and extensive logical modelling.
Handbook of Philosophical Logic by Dov M. Gabbay,Franz Guenthner Pdf
This volume presents a number of systems of logic which can be considered as alternatives to classical logic. The notion of what counts as an alternative is a somewhat problematic one. There are extreme views on the matter of what is the 'correct' logical system and whether one logical system (e. g. classical logic) can represent (or contain) all the others. The choice of the systems presented in this volume was guided by the following criteria for including a logic as an alternative: (i) the departure from classical logic in accepting or rejecting certain theorems of classical logic following intuitions arising from significant application areas and/or from human reasoning; (ii) the alternative logic is well-established and well-understood mathematically and is widely applied in other disciplines such as mathematics, physics, computer science, philosophy, psychology, or linguistics. A number of other alternatives had to be omitted for the present volume (e. g. recent attempts to formulate so-called 'non-monotonic' reason ing systems). Perhaps these can be included in future extensions of the Handbook of Philosophical Logic. Chapter 1 deals with partial logics, that is, systems where sentences do not always have to be either true or false, and where terms do not always have to denote. These systems are thus, in general, geared towards reasoning in partially specified models. Logics of this type have arisen mainly from philo sophical and linguistic considerations; various applications in theoretical computer science have also been envisaged.
The Logic of Entailment and its History by Edwin Mares Pdf
What follows from what, and how do we make statements (whether true or false) about which inferences are correct? In this book, Edwin Mares provides a new philosophical, semantical and historical analysis of and justification for the relevant logic of entailment. In the first half of the book he examines some key ideas in the historical development of the logic of entailment, looking in particular at the notion 'is derivable from' and at how symbolic logic has attempted to capture this notion. In the second half of the book he develops his own theory connecting ideas from the traditions in mathematical logic with some ideas in the philosophy of science. The book's fresh and original perspective on the logic of entailment will be valuable for all who want to know more about the historical and philosophical origins of modern symbolic logic.
A Companion to Philosophical Logic by Dale Jacquette Pdf
This collection of newly comissioned essays by international contributors offers a representative overview of the most important developments in contemporary philosophical logic. Presents controversies in philosophical implications and applications of formal symbolic logic. Surveys major trends and offers original insights.
Papers in Philosophical Logic: Volume 1 by David Lewis Pdf
This is the first of a three-volume collection of David Lewis's most recent papers in all the areas to which he has made significant contributions. The purpose of this collection (and the two volumes to follow) is to disseminate even more widely the work of a preeminent and influential late twentieth-century philosopher. The papers are now offered in a readily accessible format. This first volume is devoted to Lewis's work on philosophical logic from the last twenty-five years. The topics covered include: deploying the methods of formal semantics from artificial formalised languages to natural languages, model-theoretic investigations of intensional logic, contradiction, relevance, the differences between analog and digital representation, and questions arising from the construction of ambitious formalised philosophical systems. The volume will serve as an important reference tool for all philosophers and their students.
The Bloomsbury Companion to Philosophical Logic by Leon Horsten,Richard Pettigrew Pdf
Logical methods are used in all area of philosophy. By introducing and advancing central to topics in the discipline, The Bloomsbury Companion to Philosophical Logic emphasizes the crucial role logic plays in understanding philosophical problems. Covering stages in the history of logic and of modern logic, this comprehensive Companion looks ahead to new areas of research and explores issues pertaining to classical logic and its rivals, semantics for parts of natural language, and the application of logic in the theory of rationality. Experts in the field provide a mix of technical chapters that offer excellent encyclopaedias of results in the area and chapters of philosophical discussions that survey a range of philosophical positions. To facilitate further study, this volumes also includes a series of research tools such as a detailed index, an up-to-date list of resources and an annotated bibliography. Balancing technical exposition with philosophical discussion, The Bloomsbury Companion to Philosophical Logic not only provides students and lecturers with the basis of a course in philosophical logic, it offers anyone working in this key area of contemporary philosophy a valuable research resource.
Logical pluralism is the view that different logics are equally appropriate, or equally correct. Logical relativism is a pluralism according to which validity and logical consequence are relative to something. In Varieties of Logic, Stewart Shapiro develops several ways in which one can be a pluralist or relativist about logic. One of these is an extended argument that words and phrases like 'valid' and 'logical consequence' are polysemous or, perhaps better, are cluster concepts. The notions can be sharpened in various ways. This explains away the 'debates' in the literature between inferentialists and advocates of a truth-conditional, model-theoretic approach, and between those who advocate higher-order logic and those who insist that logic is first-order. A significant kind of pluralism flows from an orientation toward mathematics that emerged toward the end of the nineteenth century, and continues to dominate the field today. The theme is that consistency is the only legitimate criterion for a theory. Logical pluralism arises when one considers a number of interesting and important mathematical theories that invoke a non-classical logic, and are rendered inconsistent, and trivial, if classical logic is imposed. So validity is relative to a theory or structure. The perspective raises a host of important questions about meaning. The most significant of these concern the semantic content of logical terminology, words like 'or', 'not', and 'for all', as they occur in rigorous mathematical deduction. Does the intuitionistic 'not', for example, have the same meaning as its classical counterpart? Shapiro examines the major arguments on the issue, on both sides, and finds them all wanting. He then articulates and defends a thesis that the question of meaning-shift is itself context-sensitive and, indeed, interest-relative. He relates the issue to some prominent considerations concerning open texture, vagueness, and verbal disputes. Logic is ubiquitous. Whenever there is deductive reasoning, there is logic. So there are questions about logical pluralism that are analogous to standard questions about global relativism. The most pressing of these concerns foundational studies, wherein one compares theories, sometimes with different logics, and where one figures out what follows from what in a given logic. Shapiro shows that the issues are not problematic, and that is usually easy to keep track of the logic being used and the one mentioned.
A Protocol-theoretic Framework for the Logic of Epistemic Norms by Ralph Jenkins Pdf
This book defines a logical system called the Protocol-theoretic Logic of Epistemic Norms (PLEN), it develops PLEN into a formal framework for representing and reasoning about epistemic norms, and it shows that PLEN is theoretically interesting and useful with regard to the aims of such a framework. In order to motivate the project, the author defends an account of epistemic norms called epistemic proceduralism. The core of this view is the idea that, in virtue of their indispensable, regulative role in cognitive life, epistemic norms are closely intertwined with procedural rules that restrict epistemic actions, procedures, and processes. The resulting organizing principle of the book is that epistemic norms are protocols for epistemic planning and control. The core of the book is developing PLEN, which is essentially a novel variant of propositional dynamic logic (PDL) distinguished by more or less elaborate revisions of PDL’s syntax and semantics. The syntax encodes the procedural content of epistemic norms by means of the well-known protocol or program constructions of dynamic and epistemic logics. It then provides a novel language of operators on protocols, including a range of unique protocol equivalence relations, syntactic operations on protocols, and various procedural relations among protocols in addition to the standard dynamic (modal) operators of PDL. The semantics of the system then interprets protocol expressions and expressions embedding protocols over a class of directed multigraph-like structures rather than the standard labeled transition systems or modal frames. The intent of the system is to better represent epistemic dynamics, build a logic of protocols atop it, and then show that the resulting logic of protocols is useful as a logical framework for epistemic norms. The resulting theory of epistemic norms centers on notions of norm equivalence derived from theories of process equivalence familiar from the study of dynamic and modal logics. The canonical account of protocol equivalence in PLEN turns out to possess a number of interesting formal features, including satisfaction of important conditions on hyperintensional equivalence, a matter of recently recognized importance in the logic of norms, generally. To show that the system is interesting and useful as a framework for representing and reasoning about epistemic norms, the author applies the logical system to the analysis of epistemic deontic operators, and, partly on the basis of this, establishes representation theorems linking protocols to the action-guiding content of epistemic norms. The protocol-theoretic logic of epistemic norms is then shown to almost immediately validate the main principles of epistemic proceduralism.
