Consequence Relations

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Consequence Relations

Author : Alex Citkin
Publisher : Oxford University Press
ISBN 13 : 019269149X
Total Pages : 353 pages
Book Rating : 4.1/5 (926 download)

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Book Synopsis Consequence Relations by : Alex Citkin

Download or read book Consequence Relations written by Alex Citkin and published by Oxford University Press. This book was released on 2022-06-30 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: The publication of Rasiowa and Sikorski's The Mathematics of Metamathematics (1970), Rasiowa's An Algebraic Approach to Non-Classical Logics (1974), and Wójcicki's Theory of Logical Calculi (1988) created a niche in the field of mathematical and philosophical logic. This in-depth study of the concept of a consequence relation, culminating in the concept of a Lindenbaum-Tarski algebra, fills this niche. Citkin and Muravitsky consider the problem of obtaining confirmation that a statement is a consequence of a set of statements as prerequisites, on the one hand, and the problem of demonstrating that such confirmation does not exist in the structure under consideration, on the other hand. For the second part of this problem, the concept of the Lindenbaum-Tarski algebra plays a key role, which becomes even more important when the considered consequence relation is placed in the context of decidability. This role is traced in the book for various formal objective languages. The work also includes helpful exercises to aid the reader's assimilation of the book's material. Intended for advanced undergraduate and graduate students in mathematics and philosophy, this book can be used to teach special courses in logic with an emphasis on algebraic methods, for self-study, and also as a reference work.

Principles of Knowledge Representation and Reasoning

Author : Jon Doyle
Publisher : Morgan Kaufmann
ISBN 13 :
Total Pages : 680 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Principles of Knowledge Representation and Reasoning by : Jon Doyle

Download or read book Principles of Knowledge Representation and Reasoning written by Jon Doyle and published by Morgan Kaufmann. This book was released on 1994 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: The proceedings of KR '94 comprise 55 papers on topics including deduction an search, description logics, theories of knowledge and belief, nonmonotonic reasoning and belief revision, action and time, planning and decision-making and reasoning about the physical world, and the relations between KR

Foundations of Logical Consequence

Author : Colin R. Caret
Publisher : Mind Association Occasional
ISBN 13 : 0198715692
Total Pages : 368 pages
Book Rating : 4.1/5 (987 download)

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Book Synopsis Foundations of Logical Consequence by : Colin R. Caret

Download or read book Foundations of Logical Consequence written by Colin R. Caret and published by Mind Association Occasional. This book was released on 2015 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Logical consequence is the relation that obtains between premises and conclusion(s) in a valid argument. Orthodoxy has it that valid arguments are necessarily truth-preserving, but this platitude only raises a number of further questions, such as: how does the truth of premises guarantee the truth of a conclusion, and what constraints does validity impose on rational belief? This volume presents thirteen essays by some of the most important scholars in the field of philosophical logic. The essays offer ground-breaking new insights into the nature of logical consequence; the relation between logic and inference; how the semantics and pragmatics of natural language bear on logic; the relativity of logic; and the structural properties of the consequence relation.

Between Saying and Doing

Author : Robert Brandom
Publisher : Oxford University Press
ISBN 13 : 0199542872
Total Pages : 278 pages
Book Rating : 4.1/5 (995 download)

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Book Synopsis Between Saying and Doing by : Robert Brandom

Download or read book Between Saying and Doing written by Robert Brandom and published by Oxford University Press. This book was released on 2008-04-24 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Between Saying and Doing aims to reconcile pragmatism with analytic philosophy. Robert Brandom investigates the relations between the meaning of linguistic expressions (logical, indexical, modal, normative, and intentional, among others) and their use. He offers new ways of thinking about empiricism, naturalism, and functionalism.

Explanatory Nonmonotonic Reasoning

Author : Alexander Bochman
Publisher : World Scientific
ISBN 13 : 9812561013
Total Pages : 424 pages
Book Rating : 4.8/5 (125 download)

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Book Synopsis Explanatory Nonmonotonic Reasoning by : Alexander Bochman

Download or read book Explanatory Nonmonotonic Reasoning written by Alexander Bochman and published by World Scientific. This book was released on 2005 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many approaches in the field of nonmonotonic and ?commonsense? reasoning are actually different representations of the same basic ideas and constructions. This book gives a logical formalization of the original, explanatory approach to nonmonotonic reasoning. It uses the basic formalism of biconsequence relations, as well as derived systems of default, autoepistemic and causal inference, to cover in a single framework such diverse systems as default logic, autoepistemic and modal nonmonotonic logics, input/output and causal logics, argumentation theory, and semantics of general logic programs with negation as failure. This approach provides a clear separation between logical (monotonic) and nonmonotonic aspects of nonmonotonic reasoning. The separation allows, in particular, to single out the logics underlying modern logic programming and restore thereby the connection between logic programming and logic.

One True Logic

Author : Owen Griffiths
Publisher : Oxford University Press
ISBN 13 : 0192565249
Total Pages : 336 pages
Book Rating : 4.1/5 (925 download)

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Book Synopsis One True Logic by : Owen Griffiths

Download or read book One True Logic written by Owen Griffiths and published by Oxford University Press. This book was released on 2022-05-26 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Logical monism is the claim that there is a single correct logic, the 'one true logic' of our title. The view has evident appeal, as it reflects assumptions made in ordinary reasoning as well as in mathematics, the sciences, and the law. In all these spheres, we tend to believe that there are determinate facts about the validity of arguments. Despite its evident appeal, however, logical monism must meet two challenges. The first is the challenge from logical pluralism, according to which there is more than one correct logic. The second challenge is to determine which form of logical monism is the correct one. One True Logic is the first monograph to explicitly articulate a version of logical monism and defend it against the first challenge. It provides a critical overview of the monism vs pluralism debate and argues for the former. It also responds to the second challenge by defending a particular monism, based on a highly infinitary logic. It breaks new ground on a number of fronts and unifies disparate discussions in the philosophical and logical literature. In particular, it generalises the Tarski-Sher criterion of logicality, provides a novel defence of this generalisation, offers a clear new argument for the logicality of infinitary logic and replies to recent pluralist arguments.

Logica Universalis

Author : Jean-Yves Beziau
Publisher : Springer Science & Business Media
ISBN 13 : 3764373040
Total Pages : 225 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Logica Universalis by : Jean-Yves Beziau

Download or read book Logica Universalis written by Jean-Yves Beziau and published by Springer Science & Business Media. This book was released on 2005-12-06 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: Universal Logic is not a new logic, but a general theory of logics, considered as mathematical structures. The name was introduced about ten years ago, but the subject is as old as the beginning of modern logic. It was revived after the flowering of thousands of new logics during the last thirty years: there was a need for a systematic theory of logics to put some order in this chaotic multiplicity. The present book contains recent works on universal logic by first-class researchers from all around the world. The book is full of new and challenging ideas that will guide the future of this exciting subject. It will be of interest for people who want to better understand what logic is. It will help those who are lost in the jungle of heterogeneous logical systems to find a way. Tools and concepts are provided here for those who want to study classes of already existing logics or want to design and build new ones.

A Logical Theory of Nonmonotonic Inference and Belief Change

Author : Alexander Bochman
Publisher : Springer Science & Business Media
ISBN 13 : 3662045605
Total Pages : 439 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis A Logical Theory of Nonmonotonic Inference and Belief Change by : Alexander Bochman

Download or read book A Logical Theory of Nonmonotonic Inference and Belief Change written by Alexander Bochman and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book that integrates nonmonotonic reasoning and belief change into a single framework from an artificial intelligence logic point-of-view. The approach to both these subjects is based on a powerful notion of an epistemic state that subsumes both existing models for nonmonotonic inference and current models for belief change. Many results and constructions in the book are completely new and have not appeared earlier in the literature.

Reflections on the Liar

Author : Bradley Armour-Garb
Publisher : Oxford University Press
ISBN 13 : 0190672277
Total Pages : 401 pages
Book Rating : 4.1/5 (96 download)

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Book Synopsis Reflections on the Liar by : Bradley Armour-Garb

Download or read book Reflections on the Liar written by Bradley Armour-Garb and published by Oxford University Press. This book was released on 2017-06-23 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years there have been a number of books-both anthologies and monographs-that have focused on the Liar Paradox and, more generally, on the semantic paradoxes, either offering proposed treatments to those paradoxes or critically evaluating ones that occupy logical space. At the same time, there are a number of people who do great work in philosophy, who have various semantic, logical, metaphysical and/or epistemological commitments that suggest that they should say something about the Liar Paradox, yet who have said very little, if anything, about that paradox or about the extant projects involving it. The purpose of this volume is to afford those philosophers the opportunity to address what might be described as reflections on the Liar.

Concise Encyclopedia of Semantics

Author : Keith Allan
Publisher : Elsevier
ISBN 13 : 0080959695
Total Pages : 1103 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Concise Encyclopedia of Semantics by : Keith Allan

Download or read book Concise Encyclopedia of Semantics written by Keith Allan and published by Elsevier. This book was released on 2010-04-06 with total page 1103 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise Encyclopedia of Semantics is a comprehensive new reference work aiming to systematically describe all aspects of the study of meaning in language. It synthesizes in one volume the latest scholarly positions on the construction, interpretation, clarification, obscurity, illustration, amplification, simplification, negotiation, contradiction, contraction and paraphrasing of meaning, and the various concepts, analyses, methodologies and technologies that underpin their study. It examines not only semantics but the impact of semantic study on related fields such as morphology, syntax, and typologically oriented studies such as 'grammatical semantics', where semantics has made a considerable contribution to our understanding of verbal categories like tense or aspect, nominal categories like case or possession, clausal categories like causatives, comparatives, or conditionals, and discourse phenomena like reference and anaphora. COSE also examines lexical semantics and its relation to syntax, pragmatics, and cognitive linguistics; and the study of how 'logical semantics' develops and thrives, often in interaction with computational linguistics. As a derivative volume from Encyclopedia of Language and Linguistics, Second Edition, it comprises contributions from 150 of the foremost scholars of semantics in their various specializations and draws on 20+ years of development in the parent work in a compact and affordable format. Principally intended for tertiary level inquiry and research, this will be invaluable as a reference work for undergraduate and postgraduate students as well as academics inquiring into the study of meaning and meaning relations within languages. As semantics is a centrally important and inherently cross-cutting area within linguistics it will therefore be relevant not just for semantics specialists, but for most linguistic audiences. - The first encyclopedia ever published in this fascinating and diverse field - Combines the talents of the world's leading semantics specialists - The latest trends in the field authoritatively reviewed and interpreted in context of related disciplines - Drawn from the richest, most authoritative, comprehensive and internationally acclaimed reference resource in the linguistics area - Compact and affordable single volume reference format

Logic: A History of its Central Concepts

Author : Dov M. Gabbay
Publisher : Newnes
ISBN 13 : 0080931707
Total Pages : 706 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Logic: A History of its Central Concepts by : Dov M. Gabbay

Download or read book Logic: A History of its Central Concepts written by Dov M. Gabbay and published by Newnes. This book was released on 2012-12-31 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of the History of Logic is a multi-volume research instrument that brings to the development of logic the best in modern techniques of historical and interpretative scholarship. It is the first work in English in which the history of logic is presented so extensively. The volumes are numerous and large. Authors have been given considerable latitude to produce chapters of a length, and a level of detail, that would lay fair claim on the ambitions of the project to be a definitive research work. Authors have been carefully selected with this aim in mind. They and the Editors join in the conviction that a knowledge of the history of logic is nothing but beneficial to the subject's present-day research programmes. One of the attractions of the Handbook's several volumes is the emphasis they give to the enduring relevance of developments in logic throughout the ages, including some of the earliest manifestations of the subject. - Covers in depth the notion of logical consequence - Discusses the central concept in logic of modality - Includes the use of diagrams in logical reasoning

The Many Valued and Nonmonotonic Turn in Logic

Author : Dov M. Gabbay
Publisher : Elsevier
ISBN 13 : 008054939X
Total Pages : 691 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis The Many Valued and Nonmonotonic Turn in Logic by : Dov M. Gabbay

Download or read book The Many Valued and Nonmonotonic Turn in Logic written by Dov M. Gabbay and published by Elsevier. This book was released on 2007-08-13 with total page 691 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume of the Handbook of the History of Logic brings together two of the most important developments in 20th century non-classical logic. These are many-valuedness and non-monotonicity. On the one approach, in deference to vagueness, temporal or quantum indeterminacy or reference-failure, sentences that are classically non-bivalent are allowed as inputs and outputs to consequence relations. Many-valued, dialetheic, fuzzy and quantum logics are, among other things, principled attempts to regulate the flow-through of sentences that are neither true nor false. On the second, or non-monotonic, approach, constraints are placed on inputs (and sometimes on outputs) of a classical consequence relation, with a view to producing a notion of consequence that serves in a more realistic way the requirements of real-life inference. Many-valued logics produce an interesting problem. Non-bivalent inputs produce classically valid consequence statements, for any choice of outputs. A major task of many-valued logics of all stripes is to fashion an appropriately non-classical relation of consequence.The chief preoccupation of non-monotonic (and default) logicians is how to constrain inputs and outputs of the consequence relation. In what is called "left non-monotonicity, it is forbidden to add new sentences to the inputs of true consequence-statements. The restriction takes notice of the fact that new information will sometimes override an antecedently (and reasonably) derived consequence. In what is called "right non-monotonicity, limitations are imposed on outputs of the consequence relation. Most notably, perhaps, is the requirement that the rule of or-introduction not be given free sway on outputs. Also prominent is the effort of paraconsistent logicians, both preservationist and dialetheic, to limit the outputs of inconsistent inputs, which in classical contexts are wholly unconstrained.In some instances, our two themes coincide. Dialetheic logics are a case in point. Dialetheic logics allow certain selected sentences to have, as a third truth value, the classical values of truth and falsity together. So such logics also admit classically inconsistent inputs. A central task is to construct a right non-monotonic consequence relation that allows for these many-valued, and inconsistent, inputs.The Many Valued and Non-Monotonic Turn in Logic is an indispensable research tool for anyone interested in the development of logic, including researchers, graduate and senior undergraduate students in logic, history of logic, mathematics, history of mathematics, computer science, AI, linguistics, cognitive science, argumentation theory, and the history of ideas. - Detailed and comprehensive chapters covering the entire range of modal logic. - Contains the latest scholarly discoveries and interprative insights that answers many questions in the field of logic.

Handbook of Philosophical Logic

Author : Dov M. Gabbay
Publisher : Springer Science & Business Media
ISBN 13 : 9401704643
Total Pages : 377 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Handbook of Philosophical Logic by : Dov M. Gabbay

Download or read book Handbook of Philosophical Logic written by Dov M. Gabbay and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is with great pleasure that we are presenting to the community the second edition of this extraordinary handbook. It has been over 15 years since the publication of the first edition and there have been great changes in the landscape of philosophical logic since then. The first edition has proved invaluable to generations of students and researchers in formal philosophy and language, as well as to consumers of logic in many applied areas. The main logic article in the Encyclopaedia Britannica 1999 has described the first edition as 'the best starting point for exploring any of the topics in logic'. We are confident that the second edition will prove to be just as good! The first edition was the second handbook published for the logic com- nity. It followed the North Holland one volume Handbook of Mathematical Logic, published in 1977, edited by the late Jon Barwise. The four volume Handbook of Philosophical Logic, published 1983-1989 came at a fortunate temporal junction at the evolution of logic. This was the time when logic was gaining ground in computer science and artificial intelligence circles. These areas were under increasing commercial pressure to provide devices which help and/or replace the human in his daily activity. This pressure required the use of logic in the modelling of human activity and organi- tion on the one hand and to provide the theoretical basis for the computer program constructs on the other.

A Logical Theory of Causality

Author : Alexander Bochman
Publisher : MIT Press
ISBN 13 : 0262362244
Total Pages : 367 pages
Book Rating : 4.2/5 (623 download)

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Book Synopsis A Logical Theory of Causality by : Alexander Bochman

Download or read book A Logical Theory of Causality written by Alexander Bochman and published by MIT Press. This book was released on 2021-08-17 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: A general formal theory of causal reasoning as a logical study of causal models, reasoning, and inference. In this book, Alexander Bochman presents a general formal theory of causal reasoning as a logical study of causal models, reasoning, and inference, basing it on a supposition that causal reasoning is not a competitor of logical reasoning but its complement for situations lacking logically sufficient data or knowledge. Bochman also explores the relationship of this theory with the popular structural equation approach to causality proposed by Judea Pearl and explores several applications ranging from artificial intelligence to legal theory, including abduction, counterfactuals, actual and proximate causality, dynamic causal models, and reasoning about action and change in artificial intelligence. As logical preparation, before introducing causal concepts, Bochman describes an alternative, situation-based semantics for classical logic that provides a better understanding of what can be captured by purely logical means. He then presents another prerequisite, outlining those parts of a general theory of nonmonotonic reasoning that are relevant to his own theory. These two components provide a logical background for the main, two-tier formalism of the causal calculus that serves as the formal basis of his theory. He presents the main causal formalism of the book as a natural generalization of classical logic that allows for causal reasoning. This provides a formal background for subsequent chapters. Finally, Bochman presents a generalization of causal reasoning to dynamic domains.

Making Semantics Pragmatic

Author : Ken Turner
Publisher : BRILL
ISBN 13 : 085724910X
Total Pages : 240 pages
Book Rating : 4.8/5 (572 download)

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Book Synopsis Making Semantics Pragmatic by : Ken Turner

Download or read book Making Semantics Pragmatic written by Ken Turner and published by BRILL. This book was released on 2011-06-08 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of especially invited papers aims to explore the nature of the semantics/pragmatics interface by examining the extent to which the analysis of certain expressions or constructions can be pragmaticised. As the title of the collection implicates, it is anticipated that the theoretical and descriptive burden will move from semantics to pragmatics. However not all parts of a linguistic system will yield to a pragmatic treatment. The possibility remains that certain expressions or constructions are more economically and elegantly treated in semantic terms. Thus, this collection also contains papers that address the topic of 'making pragmatics semantic'. This collection contributes to the current interest in examining the division of labour between semantics and pragmatics in the analysis of meaning. All of the papers are at the forefront of knowledge in these matters and each contains original empirical analyses and/or novel theoretical perspectives. This book is relevant to courses in university departments of linguistics, modern languages, philosophy and psychology and to a wide range of university teaching and research.

Principles of Knowledge Representation and Reasoning

Author : Anthony G. Cohn
Publisher : Morgan Kaufmann
ISBN 13 :
Total Pages : 680 pages
Book Rating : 4.:/5 (37 download)

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Book Synopsis Principles of Knowledge Representation and Reasoning by : Anthony G. Cohn

Download or read book Principles of Knowledge Representation and Reasoning written by Anthony G. Cohn and published by Morgan Kaufmann. This book was released on 1998 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Logical Pluralism

Author : JC Beall
Publisher : Clarendon Press
ISBN 13 : 0191537144
Total Pages : 152 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Logical Pluralism by : JC Beall

Download or read book Logical Pluralism written by JC Beall and published by Clarendon Press. This book was released on 2005-11-24 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, arguing that the notion of logical consequence doesn't pin down one deductive consequence relation; it allows for many of them. In particular, they argue that broadly classical, intuitionistic, and relevant accounts of deductive logic are genuine logical consequence relations; we should not search for one true logic, since there are many. Their conclusions have profound implications for many linguists as well as for philosophers.