An Introduction To Paraconsistent Logics

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An Introduction to Paraconsistent Logics

Author : Manuel Bremer
Publisher : Peter Lang Gmbh, Internationaler Verlag Der Wissenschaften
ISBN 13 : 9783631534137
Total Pages : 0 pages
Book Rating : 4.5/5 (341 download)

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Book Synopsis An Introduction to Paraconsistent Logics by : Manuel Bremer

Download or read book An Introduction to Paraconsistent Logics written by Manuel Bremer and published by Peter Lang Gmbh, Internationaler Verlag Der Wissenschaften. This book was released on 2005 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an overview of paraconsistent logics - that is logics which allow for inconsistency. Although allowing for inconsistency, paraconsistent logics are worth considering: Logical systems are worth considering in their own right since we can learn about very abstract structural properties of logics and the concepts employed within them such as negation, necessity and consistency. Some non-classical logics are especially of interest from a philosophical perspective since they alone offer the possibility of solving or even stating some philosophical problems. These introductory lectures argue from a philosophical perspective that some paraconsistent logics are of interest or even the best candidates for dealing with specific philosophical problems. Although logic is seen from the point of view of its philosophical use, various formal systems are described, compared and employed.

Paraconsistent Logic: Consistency, Contradiction and Negation

Author : Walter Carnielli
Publisher : Springer
ISBN 13 : 3319332058
Total Pages : 398 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Paraconsistent Logic: Consistency, Contradiction and Negation by : Walter Carnielli

Download or read book Paraconsistent Logic: Consistency, Contradiction and Negation written by Walter Carnielli and published by Springer. This book was released on 2016-06-14 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first in the field of paraconsistency to offer a comprehensive overview of the subject, including connections to other logics and applications in information processing, linguistics, reasoning and argumentation, and philosophy of science. It is recommended reading for anyone interested in the question of reasoning and argumentation in the presence of contradictions, in semantics, in the paradoxes of set theory and in the puzzling properties of negation in logic programming. Paraconsistent logic comprises a major logical theory and offers the broadest possible perspective on the debate of negation in logic and philosophy. It is a powerful tool for reasoning under contradictoriness as it investigates logic systems in which contradictory information does not lead to arbitrary conclusions. Reasoning under contradictions constitutes one of most important and creative achievements in contemporary logic, with deep roots in philosophical questions involving negation and consistency This book offers an invaluable introduction to a topic of central importance in logic and philosophy. It discusses (i) the history of paraconsistent logic; (ii) language, negation, contradiction, consistency and inconsistency; (iii) logics of formal inconsistency (LFIs) and the main paraconsistent propositional systems; (iv) many-valued companions, possible-translations semantics and non-deterministic semantics; (v) paraconsistent modal logics; (vi) first-order paraconsistent logics; (vii) applications to information processing, databases and quantum computation; and (viii) applications to deontic paradoxes, connections to Eastern thought and to dialogical reasoning.

An Introduction to Paraconsistent Logics

Author : Manuel Eugen Bremer
Publisher : Peter Lang Publishing
ISBN 13 : 9780820476711
Total Pages : 249 pages
Book Rating : 4.4/5 (767 download)

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Book Synopsis An Introduction to Paraconsistent Logics by : Manuel Eugen Bremer

Download or read book An Introduction to Paraconsistent Logics written by Manuel Eugen Bremer and published by Peter Lang Publishing. This book was released on 2005-01-01 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an overview of paraconsistent logics - that is logics which allow for inconsistency. Although allowing for inconsistency, paraconsistent logics are worth considering: Logical systems are worth considering in their own right since we can learn about very abstract structural properties of logics and the concepts employed within them such as negation, necessity and consistency. Some non-classical logics are especially of interest from a philosophical perspective since they alone offer the possibility of solving or even stating some philosophical problems. These introductory lectures argue from a philosophical perspective that some paraconsistent logics are of interest or even the best candidates for dealing with specific philosophical problems. Although logic is seen from the point of view of its philosophical use, various formal systems are described, compared and employed.

Paraconsistency: Logic and Applications

Author : Koji Tanaka
Publisher : Springer Science & Business Media
ISBN 13 : 9400744382
Total Pages : 380 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Paraconsistency: Logic and Applications by : Koji Tanaka

Download or read book Paraconsistency: Logic and Applications written by Koji Tanaka and published by Springer Science & Business Media. This book was released on 2012-07-26 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change this situation. The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more "big picture" ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics.

An Introduction to Non-Classical Logic

Author : Graham Priest
Publisher : Cambridge University Press
ISBN 13 : 9781139469678
Total Pages : pages
Book Rating : 4.4/5 (696 download)

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Book Synopsis An Introduction to Non-Classical Logic by : Graham Priest

Download or read book An Introduction to Non-Classical Logic written by Graham Priest and published by Cambridge University Press. This book was released on 2008-04-10 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area.

Logic, Epistemology, and the Unity of Science

Author : Shahid Rahman
Publisher : Springer Science & Business Media
ISBN 13 : 1402028083
Total Pages : 618 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Logic, Epistemology, and the Unity of Science by : Shahid Rahman

Download or read book Logic, Epistemology, and the Unity of Science written by Shahid Rahman and published by Springer Science & Business Media. This book was released on 2009-03-15 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first volume in this new series explores, through extensive co-operation, new ways of achieving the integration of science in all its diversity. The book offers essays from important and influential philosophers in contemporary philosophy, discussing a range of topics from philosophy of science to epistemology, philosophy of logic and game theoretical approaches. It will be of interest to philosophers, computer scientists and all others interested in the scientific rationality.

Handbook of Paraconsistency

Author : Jean-Yves Béziau
Publisher :
ISBN 13 :
Total Pages : 532 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Handbook of Paraconsistency by : Jean-Yves Béziau

Download or read book Handbook of Paraconsistency written by Jean-Yves Béziau and published by . This book was released on 2007 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: Paraconsistent logics are logics which allow solid deductive reasoning under contradictions by offering a mathematical and philosophical support to contradictory yet non-trivial theories. Due to its role in models of scientific reasoning and to its philosophical implications, as well as to its connections to topics such as abduction, automated reasoning, logic programming, and belief revision, paraconsistency has becoming a fast growing area. During the III World Congress on Paraconsistency (WCP3) held in Toulouse, France, in July, 2003, it became apparent that there is a need for a Handbook covering the most recent results on several aspects of paraconsistent logic, including philosophical debates on paraconsistency and its connections to philosophy of language, argumentation theory, computer science, information theory, and artificial intelligence. This book is a basic tool for those who want to know more about paraconsistent logic, its history and philosophy, the various systems of paraconsistent logic and their applications. The present volume is edited by Jean-Yves Beziau, Walter Carnielli and Dov Gabbay, expert logicians versed in a variety of logics.

Constructive Negations and Paraconsistency

Author : Sergei Odintsov
Publisher : Springer Science & Business Media
ISBN 13 : 1402068670
Total Pages : 241 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Constructive Negations and Paraconsistency by : Sergei Odintsov

Download or read book Constructive Negations and Paraconsistency written by Sergei Odintsov and published by Springer Science & Business Media. This book was released on 2008-03-19 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is an account of recent investigations into the two main concepts of negation developed in the constructive logic: the negation as reduction to absurdity, and the strong negation. These concepts are studied in the setting of paraconsistent logic.

An Introduction to Non-Classical Logic

Author : Graham Priest
Publisher : Cambridge University Press
ISBN 13 : 9780521794343
Total Pages : 268 pages
Book Rating : 4.7/5 (943 download)

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Book Synopsis An Introduction to Non-Classical Logic by : Graham Priest

Download or read book An Introduction to Non-Classical Logic written by Graham Priest and published by Cambridge University Press. This book was released on 2001-02-22 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to non-classical propositional logics. It brings together for the first time in a textbook a range of topics in logic, many of them of relatively recent origin, including modal, conditional, intuitionist, many-valued, paraconsistent, relevant and fuzzy logics. The material is unified by the underlying theme of world-semantics. All of the topics are explained clearly and accessibly, using devices such as tableaux proofs, and their relation to current philosophical issues and debates is discussed. Students with a basic understanding of classical logic will find this an invaluable introduction to an area that has become of central importance in both logic and philosophy, but which, until now, could be studied only through the research literature. It will interest those studying logic, those who need to know about non-classical logics because of their philosophical importance, and, more widely, readers working in mathematics and computer science.

An Introduction to Practical Formal Methods Using Temporal Logic

Author : Michael Fisher
Publisher : John Wiley & Sons
ISBN 13 : 9781119991465
Total Pages : 368 pages
Book Rating : 4.9/5 (914 download)

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Book Synopsis An Introduction to Practical Formal Methods Using Temporal Logic by : Michael Fisher

Download or read book An Introduction to Practical Formal Methods Using Temporal Logic written by Michael Fisher and published by John Wiley & Sons. This book was released on 2011-03-16 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: The name "temporal logic" may sound complex and daunting; but while they describe potentially complex scenarios, temporal logics are often based on a few simple, and fundamental, concepts - highlighted in this book. An Introduction to Practical Formal Methods Using Temporal Logic provides an introduction to formal methods based on temporal logic, for developing and testing complex computational systems. These methods are supported by many well-developed tools, techniques and results that can be applied to a wide range of systems. Fisher begins with a full introduction to the subject, covering the basics of temporal logic and using a variety of examples, exercises and pointers to more advanced work to help clarify and illustrate the topics discussed. He goes on to describe how this logic can be used to specify a variety of computational systems, looking at issues of linking specifications, concurrency, communication and composition ability. He then analyses temporal specification techniques such as deductive verification, algorithmic verification, and direct execution to develop and verify computational systems. The final chapter on case studies analyses the potential problems that can occur in a range of engineering applications in the areas of robotics, railway signalling, hardware design, ubiquitous computing, intelligent agents, and information security, and explains how temporal logic can improve their accuracy and reliability. Models temporal notions and uses them to analyze computational systems Provides a broad approach to temporal logic across many formal methods - including specification, verification and implementation Introduces and explains freely available tools based on temporal logics and shows how these can be applied Presents exercises and pointers to further study in each chapter, as well as an accompanying website providing links to additional systems based upon temporal logic as well as additional material related to the book.

How to Sell a Contradiction

Author : Francesco Berto
Publisher :
ISBN 13 : 9781904987437
Total Pages : 0 pages
Book Rating : 4.9/5 (874 download)

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Book Synopsis How to Sell a Contradiction by : Francesco Berto

Download or read book How to Sell a Contradiction written by Francesco Berto and published by . This book was released on 2007 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "There is a principle in things, about which we cannot be deceived, but must always, on the contrary, recognize the truth - viz. that the same thing cannot at one and the same time be and not be" with these words of the Metaphysics, Aristotle introduced the Law of Non-Contradiction, which was to become the most authoritative principle in the history of Western thought. However, things have recently changed, and nowadays various philosophers, called dialetheists, claim that this Law does not hold unrestrictedly - that in peculiar circumstances the same thing may at the same time be and not be, and contradictions may obtain in the world. This book opens with an examination of the famous logical paradoxes that appear to speak on behalf of contradictions (e.g., the Liar paradox, the set-theoretic paradoxes such as Cantor's and Russell's), and of the reasons for the failure of the standard attempts to solve them. It provides, then, an introduction to paraconsistent logics - non-classical logics in which the admission of contradictions does not lead to logical chaos -, and their astonishing applications, going from inconsistent data base management to contradictory arithmetics capable of circumventing Gödel's celebrated Incompleteness Theorem. The final part of the book discusses the philosophical motivations and difficulties of dialetheism, and shows how to extract from Aristotle's ancient words a possible reply to the dialetheic challenge. How to Sell a Contradiction will appeal to anyone interested in non-classical logics, analytic metaphysics, and philosophy of mathematics, and especially to those who consider challenging our most entrenched beliefs the main duty of philosophical inquiry. Francesco Berto is Lecturer in Logic and Metaphysics at the University of Venice, Italy. He has published articles in American Philosophical Quarterly, The Australasian Journal of Philosophy, Dialectica, Logique et Analyse, The European Journal of Philosophy, and the books La dialettica della struttura originaria [The Dialectics of the Basic Structure, Padua 2003], Che cos'è la dialettica hegeliana [What is Hegel's Dialectics?, Padua 2005], Teorie dell'assurdo [Theories of the Absurd, Rome 2006] and Logica da zero a Gödel [Logic, from Zero to Gödel, Rome 2007].

Philosophy of Logic

Author :
Publisher : Elsevier
ISBN 13 : 9780080466637
Total Pages : 1218 pages
Book Rating : 4.4/5 (666 download)

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Book Synopsis Philosophy of Logic by :

Download or read book Philosophy of Logic written by and published by Elsevier. This book was released on 2006-11-29 with total page 1218 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Kripke’s Worlds

Author : Olivier Gasquet
Publisher : Springer Science & Business Media
ISBN 13 : 3764385049
Total Pages : 208 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Kripke’s Worlds by : Olivier Gasquet

Download or read book Kripke’s Worlds written by Olivier Gasquet and published by Springer Science & Business Media. This book was released on 2013-11-20 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Possible worlds models were introduced by Saul Kripke in the early 1960s. Basically, a possible world's model is nothing but a graph with labelled nodes and labelled edges. Such graphs provide semantics for various modal logics (alethic, temporal, epistemic and doxastic, dynamic, deontic, description logics) and also turned out useful for other nonclassical logics (intuitionistic, conditional, several paraconsistent and relevant logics). All these logics have been studied intensively in philosophical and mathematical logic and in computer science, and have been applied increasingly in domains such as program semantics, artificial intelligence, and more recently in the semantic web. Additionally, all these logics were also studied proof theoretically. The proof systems for modal logics come in various styles: Hilbert style, natural deduction, sequents, and resolution. However, it is fair to say that the most uniform and most successful such systems are tableaux systems. Given logic and a formula, they allow one to check whether there is a model in that logic. This basically amounts to trying to build a model for the formula by building a tree. This book follows a more general approach by trying to build a graph, the advantage being that a graph is closer to a Kripke model than a tree. It provides a step-by-step introduction to possible worlds semantics (and by that to modal and other nonclassical logics) via the tableaux method. It is accompanied by a piece of software called LoTREC (www.irit.fr/Lotrec). LoTREC allows to check whether a given formula is true at a given world of a given model and to check whether a given formula is satisfiable in a given logic. The latter can be done immediately if the tableau system for that logic has already been implemented in LoTREC. If this is not yet the case LoTREC offers the possibility to implement a tableau system in a relatively easy way via a simple, graph-based, interactive language.

Contradictions, from Consistency to Inconsistency

Author : Walter Carnielli
Publisher : Springer
ISBN 13 : 3319987976
Total Pages : 324 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Contradictions, from Consistency to Inconsistency by : Walter Carnielli

Download or read book Contradictions, from Consistency to Inconsistency written by Walter Carnielli and published by Springer. This book was released on 2018-10-13 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume investigates what is beyond the Principle of Non-Contradiction. It features 14 papers on the foundations of reasoning, including logical systems and philosophical considerations. Coverage brings together a cluster of issues centered upon the variety of meanings of consistency, contradiction, and related notions. Most of the papers, but not all, are developed around the subtle distinctions between consistency and non-contradiction, as well as among contradiction, inconsistency, and triviality, and concern one of the above mentioned threads of the broadly understood non-contradiction principle and the related principle of explosion. Some others take a perspective that is not too far away from such themes, but with the freedom to tread new paths. Readers should understand the title of this book in a broad way,because it is not so obvious to deal with notions like contradictions, consistency, inconsistency, and triviality. The papers collected here present groundbreaking ideas related to consistency and inconsistency.

Theory of Effective Propositional Paraconsistent Logics

Author : Arnon Avron
Publisher :
ISBN 13 : 9781848902701
Total Pages : 576 pages
Book Rating : 4.9/5 (27 download)

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Book Synopsis Theory of Effective Propositional Paraconsistent Logics by : Arnon Avron

Download or read book Theory of Effective Propositional Paraconsistent Logics written by Arnon Avron and published by . This book was released on 2018-05-21 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: Perhaps the most counterintuitive property of classical logic (as well as of its most famous rival, intuitionistic logic) is the fact that it allows the inference of any proposition from a single pair of contradicting statements. A lot of work and efforts have been devoted over the years to develop alternatives to classical logic that do not have this drawback. Those alternatives are nowadays called `paraconsistent systems', and the corresponding research area --- paraconsistent reasoning. The purpose of this book is to provide a comprehensive methodological presentation of the rich mathematical theory that exists by now concerning the most fundamental part of paraconsistent reasoning: propositional (monotonic) logics. Among those logics it mainly concentrates on those which are effective (in the sense that they are decidable, have a concrete semantics, and can be equipped with implementable analytic proof systems). The first part of the book defines in precise terms all the basic notions that are related to paraconsistency, after reviewing all the necessary preliminaries. The other parts describe in detail all of the main approaches to the subject. This includes finite-valued semantics (both truth functional and non-deterministic); logics of formal inconsistency; relevant logics; constructive paraconsistent logics which are based on positive intuitionistic logic; and paraconsistent logics which are based on modal logics. The book covers thousands of paraconsistent logics, each of which is studied both from a semantical and from a proof theoretical points of view. In addition, most of those logics are characterized in terms of minimality or maximality properties that they may have.

Paraconsistent Logic

Author : Ayda Ignez Arruda
Publisher :
ISBN 13 :
Total Pages : 748 pages
Book Rating : 4.:/5 (44 download)

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Book Synopsis Paraconsistent Logic by : Ayda Ignez Arruda

Download or read book Paraconsistent Logic written by Ayda Ignez Arruda and published by . This book was released on 1989 with total page 748 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Analysis and Synthesis of Logics

Author : Walter Carnielli
Publisher : Springer Science & Business Media
ISBN 13 : 1402067828
Total Pages : 612 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Analysis and Synthesis of Logics by : Walter Carnielli

Download or read book Analysis and Synthesis of Logics written by Walter Carnielli and published by Springer Science & Business Media. This book was released on 2008-01-22 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting with simple examples showing the relevance of cutting and pasting logics, the monograph develops a mathematical theory of combining and decomposing logics, ranging from propositional and first-order based logics to higher-order based logics as well as to non-truth functional logics. The theory covers mechanisms for combining semantic structures and deductive systems either of the same or different nature. The issue of preservation of properties is addressed.