April 14, 2021

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The Many Valued and Nonmonotonic Turn in Logic

The Many Valued and Nonmonotonic Turn in Logic
Author : Dov M. Gabbay,John Woods
Publisher : Elsevier
Release Date : 2007-08-13
Category : Mathematics
Total pages :690
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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 the History of Logic: The many valued and nonmonotonic turn in logic

Handbook of the History of Logic: The many valued and nonmonotonic turn in logic
Author : Dov M. Gabbay,John Hayden Woods
Publisher : Unknown
Release Date : 2004
Category : Logic
Total pages :129
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Encyclopedia of Philosophy

Encyclopedia of Philosophy
Author : Donald M. Borchert
Publisher : Thomson Gale/MacMillan Reference USA
Release Date : 2006
Category : Electronic books
Total pages :742
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This volume, covering entries from "Kabbalah" to "Marxist philosophy," presents articles on Eastern and Western philosophies, medical and scientific ethics, the Holocaust, terrorism, censorship, biographical entries, and much more.

Pluralism, Transnationalism and Culture in Asian Law

Pluralism, Transnationalism and Culture in Asian Law
Author : Gary F Bell
Publisher : Flipside Digital Content Company Inc.
Release Date : 2018-02-14
Category : Law
Total pages :129
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This book stems from a symposium held at the Faculty of Law of the National University of Singapore in honour of the pioneer in the field of legal pluralism, Professor M.B. Hooker. It gathers essays from admirers and friends who add their own contributions on legal pluralism, transnationalism and culture in Asia. The book opens with an account of M.B. Hooker colourful and prolific career. The authors then approach legal pluralism through legal theory, legal anthropology, comparative law, law and religion, constitutional law, even Islamic art, thus reflecting the broad approaches of Professor Hooker's scholarship. While most of the book focuses mainly on Southeast Asia, it also reaches out to all of Asia up to Israel, and even includes a chapter comparing Indonesia and Egypt.

Deductive Systems in Traditional and Modern Logic

Deductive Systems in Traditional and Modern Logic
Author : Alex Citkin,UrszulaWybraniec-Skardowska
Publisher : MDPI
Release Date : 2020-11-18
Category : Mathematics
Total pages :298
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The book provides a contemporary view on different aspects of the deductive systems in various types of logics including term logics, propositional logics, logics of refutation, non-Fregean logics, higher order logics and arithmetic.

A Treatise on Many-valued Logics

A Treatise on Many-valued Logics
Author : Siegfried Gottwald
Publisher : Research Studies PressLtd
Release Date : 2001
Category : Mathematics
Total pages :604
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A growing interest in many-valued logic has developed which to a large extent is based on applications, intended as well as already realised ones. These applications range from the field of computer science, e.g. in the areas of automated theorem proving, approximate reasoning, multi-agent systems, switching theory, and program verification, through the field of pure mathematics, e.g. in independence of consistency proofs, in generalized set theories, or in the theory of particular algebraic structures, into the fields of humanities, linguistics and philosophy.

Fundamenta Informaticae

Fundamenta Informaticae
Author : Polskie Towarzystwo Matematyczne
Publisher : Unknown
Release Date : 2002
Category : Artificial intelligence
Total pages :129
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Non-monotonic Extensions of Logic Programming

Non-monotonic Extensions of Logic Programming
Author : Anonim
Publisher : Unknown
Release Date : 1996
Category : Logic programming
Total pages :129
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Mathematical Reviews

Mathematical Reviews
Author : Anonim
Publisher : Unknown
Release Date : 2008
Category : Mathematics
Total pages :129
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Logic from Russell to Church

Logic from Russell to Church
Author : Dov M. Gabbay,John Woods
Publisher : Elsevier
Release Date : 2009-06-16
Category : Mathematics
Total pages :1068
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This volume is number five in the 11-volume Handbook of the History of Logic. It covers the first 50 years of the development of mathematical logic in the 20th century, and concentrates on the achievements of the great names of the period--Russell, Post, Gödel, Tarski, Church, and the like. This was the period in which mathematical logic gave mature expression to its four main parts: set theory, model theory, proof theory and recursion theory. Collectively, this work ranks as one of the greatest achievements of our intellectual history. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, and artificial intelligence, for whom the historical background of his or her work is a salient consideration. • The entire range of modal logic is covered • Serves as a singular contribution to the intellectual history of the 20th century • Contains the latest scholarly discoveries and interpretative insights

Non-monotonic Reasoning

Non-monotonic Reasoning
Author : Yao Hua Tan
Publisher : Unknown
Release Date : 1992
Category : Commonsense reasoning
Total pages :198
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Coherent Systems

Coherent Systems
Author : Karl Schlechta
Publisher : Elsevier
Release Date : 2004-09-21
Category : Computers
Total pages :468
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One aspect of common sense reasoning is reasoning about normal cases, e.g. a physician will first try to interpret symptoms by a common disease, and will take more exotic possibilities only later into account. Such "normality" can be encoded, e.g. by a relation, where case A is considered more normal than case B. This gives a standard semantics or interpretation to nonmonotonic reasoning (a branch of common sense reasoning), or, more formally, to nonmonotonic logics. We consider in this book the repercussions such normality relations and similar constructions have on the resulting nonmonotonic logics, i.e. which types of logic are adequate for which kind of relation, etc. We show in this book that some semantics correspond nicely to some logics, but also that other semantics do not correspond to any logics of the usual form. Provides a coherent picture of several formalisms of nonmonotonic logics Gives completeness and incompleteness results for many variants of preferential, distance based, and other semantics Gives probably the first systematic investigation of definability preservation and its consequences Gives new proof techniques for completeness results Is centered on semantics

Proof Theory for Fuzzy Logics

Proof Theory for Fuzzy Logics
Author : George Metcalfe,Nicola Olivetti,Dov M. Gabbay
Publisher : Springer Science & Business Media
Release Date : 2008-11-27
Category : Mathematics
Total pages :276
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Fuzzy logics are many-valued logics that are well suited to reasoning in the context of vagueness. They provide the basis for the wider field of Fuzzy Logic, encompassing diverse areas such as fuzzy control, fuzzy databases, and fuzzy mathematics. This book provides an accessible and up-to-date introduction to this fast-growing and increasingly popular area. It focuses in particular on the development and applications of "proof-theoretic" presentations of fuzzy logics; the result of more than ten years of intensive work by researchers in the area, including the authors. In addition to providing alternative elegant presentations of fuzzy logics, proof-theoretic methods are useful for addressing theoretical problems (including key standard completeness results) and developing efficient deduction and decision algorithms. Proof-theoretic presentations also place fuzzy logics in the broader landscape of non-classical logics, revealing deep relations with other logics studied in Computer Science, Mathematics, and Philosophy. The book builds methodically from the semantic origins of fuzzy logics to proof-theoretic presentations such as Hilbert and Gentzen systems, introducing both theoretical and practical applications of these presentations.

Logic Programming and Non-monotonic Reasoning

Logic Programming and Non-monotonic Reasoning
Author : Anonim
Publisher : Unknown
Release Date : 2004
Category : Logic programming
Total pages :129
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Handbook of the History of Logic

Handbook of the History of Logic
Author : Dov M. Gabbay,John Woods
Publisher : Unknown
Release Date : 2004
Category : Logic
Total pages :129
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