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The Many Valued And Nonmonotonic Turn In Logic

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The Many Valued and Nonmonotonic Turn in Logic

The Many Valued and Nonmonotonic Turn in Logic Book
Author : Dov M. Gabbay,John Woods
Publisher : Elsevier
Release : 2007-08-13
ISBN : 9780080549392
Language : En, Es, Fr & De

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Book Description :

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.

Pluralism Transnationalism and Culture in Asian Law

Pluralism  Transnationalism and Culture in Asian Law Book
Author : Gary F Bell
Publisher : Flipside Digital Content Company Inc.
Release : 2018-02-14
ISBN : 9814786675
Language : En, Es, Fr & De

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Book Description :

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 Book
Author : Alex Citkin,UrszulaWybraniec-Skardowska
Publisher : MDPI
Release : 2020-11-18
ISBN : 303943358X
Language : En, Es, Fr & De

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Book Description :

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.

Coherent Systems

Coherent Systems Book
Author : Karl Schlechta
Publisher : Elsevier
Release : 2004-09-21
ISBN : 9780080502199
Language : En, Es, Fr & De

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Book Description :

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

Conditionals and Modularity in General Logics

Conditionals and Modularity in General Logics Book
Author : Dov M. Gabbay,Karl Schlechta
Publisher : Springer Science & Business Media
Release : 2011-08-19
ISBN : 9783642190681
Language : En, Es, Fr & De

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Book Description :

This text centers around three main subjects. The first is the concept of modularity and independence in classical logic and nonmonotonic and other nonclassical logic, and the consequences on syntactic and semantical interpolation and language change. In particular, we will show the connection between interpolation for nonmonotonic logic and manipulation of an abstract notion of size. Modularity is essentially the ability to put partial results achieved independently together for a global result. The second aspect of the book is the authors' uniform picture of conditionals, including many-valued logics and structures on the language elements themselves and on the truth value set. The third topic explained by the authors is neighbourhood semantics, their connection to independence, and their common points and differences for various logics, e.g., for defaults and deontic logic, for the limit version of preferential logics, and for general approximation. The book will be of value to researchers and graduate students in logic and theoretical computer science.

Proof Theory for Fuzzy Logics

Proof Theory for Fuzzy Logics Book
Author : George Metcalfe,Nicola Olivetti,Dov M. Gabbay
Publisher : Springer Science & Business Media
Release : 2008-11-27
ISBN : 1402094094
Language : En, Es, Fr & De

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Book Description :

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 from Russell to Church

Logic from Russell to Church Book
Author : Dov M. Gabbay,John Woods
Publisher : Elsevier
Release : 2009-06-16
ISBN : 0080885470
Language : En, Es, Fr & De

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Book Description :

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

Logic Programming and Nonmonotonic Reasoning

Logic Programming and Nonmonotonic Reasoning Book
Author : Thomas Eiter,Wolfgang Faber,Miroslaw Trusczynksi
Publisher : Springer
Release : 2003-08-06
ISBN : 3540454020
Language : En, Es, Fr & De

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Book Description :

This book constitutes the refereed proceedings of the 6th International Conference on Logic Programming and Nonmonotonic Reasoning, LPNMR 2001, held in Vienna, Austria in September 2001. The 22 revised full papers and eleven system descriptions presented with five invited papers were carefully reviewed and rigorously selected. Among the topics addressed are computational logic, declarative information extraction, model checking, inductive logic programming, default theories, stable logic programming, program semantics, incomplete information processing, concept learning, declarative specification, Prolog programming, many-valued logics, etc.

Greek Indian and Arabic Logic

Greek  Indian and Arabic Logic Book
Author : Dov M. Gabbay,John Woods
Publisher : Elsevier
Release : 2004-02-06
ISBN : 9780080532868
Language : En, Es, Fr & De

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Book Description :

Greek, Indian and Arabic Logic marks the initial appearance of the multi-volume Handbook of the History of Logic. Additional volumes will be published when ready, rather than in strict chronological order. Soon to appear are The Rise of Modern Logic: From Leibniz to Frege. Also in preparation are Logic From Russell to Gödel, Logic and the Modalities in the Twentieth Century, and The Many-Valued and Non-Monotonic Turn in Logic. Further volumes will follow, including Mediaeval and Renaissance Logic and Logic: A History of its Central. In designing the Handbook of the History of Logic, the Editors have taken the view that the history of logic holds more than an antiquarian interest, and that a knowledge of logic's rich and sophisticated development is, in various respects, relevant to the research programmes of the present day. Ancient logic is no exception. The present volume attests to the distant origins of some of modern logic's most important features, such as can be found in the claim by the authors of the chapter on Aristotle's early logic that, from its infancy, the theory of the syllogism is an example of an intuitionistic, non-monotonic, relevantly paraconsistent logic. Similarly, in addition to its comparative earliness, what is striking about the best of the Megarian and Stoic traditions is their sophistication and originality. Logic is an indispensably important pivot of the Western intellectual tradition. But, as the chapters on Indian and Arabic logic make clear, logic's parentage extends more widely than any direct line from the Greek city states. It is hardly surprising, therefore, that for centuries logic has been an unfetteredly international enterprise, whose research programmes reach to every corner of the learned world. Like its companion volumes, Greek, Indian and Arabic Logic is the result of a design that gives to its distinguished authors as much space as would be needed to produce highly authoritative chapters, rich in detail and interpretative reach. The aim of the Editors is to have placed before the relevant intellectual communities a research tool of indispensable value. Together with the other volumes, Greek, Indian and Arabic Logic, will be essential reading for everyone with a curiosity about logic's long development, especially researchers, graduate and senior undergraduate students in logic in all its forms, argumentation theory, AI and computer science, cognitive psychology and neuroscience, linguistics, forensics, philosophy and the history of philosophy, and the history of ideas.

Protoalgebraic Logics

Protoalgebraic Logics Book
Author : Janusz Czelakowski
Publisher : Boom Koninklijke Uitgevers
Release : 2001-04-30
ISBN : 9780792369400
Language : En, Es, Fr & De

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Book Description :

The main aim of this monograph is to provide a structured study of the algebraic method in metalogic. In contrast to traditional algebraic logic, where the focus is on the algebraic forms of specific deductive systems, abstract algebraic logic is concerned with the process of algebraization itself. This book presents in a systematic way recent ideas in abstract algebraic logic centered around the notion of the Leibniz operator. The stress is put on the taxonomy of deductive systems. Isolating a list of plausible properties of the Leibniz operator serves as a basis for distinguishing certain natural classes of sentential logics. The hierarchy of deductive systems presented in the book comprises, among others, the following classes: protoalgebraic logics, equivalential logics, algebraizable logics, and Fregean logics. Because of the intimate connection between algebraic and logical structures, the book also provides a uniform treatment of various topics concerning deduction theorems and quasivarieties of algebras. The presentation of the above classes of logics is accompanied by a wealth of examples illustrating the general theory. An essential part of the book is formed by the numerous exercises integrated into the text. This book is both suitable for logically and algebraically minded graduate and advanced graduate students of mathematics, computer science and philosophy, and as a reference work for the expert.

Encyclopedia of Philosophy

Encyclopedia of Philosophy Book
Author : Donald M. Borchert
Publisher : Thomson Gale/MacMillan Reference USA
Release : 2006
ISBN : 9780028657851
Language : En, Es, Fr & De

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Book Description :

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.

Fuzzy Equational Logic

Fuzzy Equational Logic Book
Author : Radim Belohlávek,Radim B?lohlávek,Vilem Vychodil
Publisher : Springer Science & Business Media
Release : 2005-08-26
ISBN : 9783540262541
Language : En, Es, Fr & De

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Book Description :

Fuzzy Relational Systems

Fuzzy Relational Systems Book
Author : Radim Belohlávek,Radim Belohlavek
Publisher : Taylor & Francis US
Release : 2002-06-30
ISBN : 9780306467776
Language : En, Es, Fr & De

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Book Description :

This book deals with fuzzy relational systems, i.e. with systems of fuzzy relations defined on a set. Fuzzy relational systems represent mathematical framework for fuzzy relational modeling which is the most successful part of fuzzy logic. The book deals with foundational aspects of fuzzy relational systems. It starts (Chapter 2) with motivations and discussions about fuzzy approach. The result of this are some requirements for the structures of truth values for fuzzy logic. These structures are analyzed in subsequent sections. Chapter 3 is a key one and develops a general theory of fuzzy relational systems, paying special attention to issues which are degenerate in classical "non-fuzzy" case. Chapter 4 deals with binary fuzzy relations and particularly with similarity and order, two most frequently used types of binary relations. Chapter 5 deals with binary fuzzy relations (interpreted as fuzzy relations between a set of objects and a set of attributes) and formal analysis of such relations. Chapter 6 focuses on the problem of composition and decomposition of binary fuzzy relations. Chapter 7 contains miscellaneous topics: fuzzy closure operators, similarity spaces, selected applications, and a formal deductive system of fuzzy logic. Each Chapter is closed by bibliographical remarks. The book contains a bibliography and an index of key terms. The book provides a general framework for dealing with fuzzy relational systems and brings several new results.

Non Monotonic Extensions of Logic Programming

Non Monotonic Extensions of Logic Programming Book
Author : Jurgen Dix,Louis M. Pereira,Teodor C. Przymusinski
Publisher : Springer Science & Business Media
Release : 1995-06-20
ISBN : 9783540594673
Language : En, Es, Fr & De

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Book Description :

This volume is based on papers presented during the ICLP '94 Workshop on Nonmonotonic Extensions of Logic Programming and on papers solicited afterwards from key researchers participating in the workshop. In total 10 carefully refereed, revised, full research papers on semantics and computational aspects of logic programs are included. Logic programs rely on a nonmonotonic operator often referred to as negation by failure or negation by default. The nonmonoticity of this operator allows to apply results from the area of nonmonotonic theories to the investigation of logic programs (and vice versa). This volume is devoted to the interdependence of nonmonotonic formalisms and logic programming.

Hyperbolic Systems of Conservation Laws

Hyperbolic Systems of Conservation Laws Book
Author : Philippe G. LeFloch
Publisher : Springer Science & Business Media
Release : 2002-07-01
ISBN : 9783764366872
Language : En, Es, Fr & De

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Book Description :

This book examines the well-posedness theory for nonlinear hyperbolic systems of conservation laws, recently completed by the author together with his collaborators. It covers the existence, uniqueness, and continuous dependence of classical entropy solutions. It also introduces the reader to the developing theory of nonclassical (undercompressive) entropy solutions. The systems of partial differential equations under consideration arise in many areas of continuum physics.

Non Monotonic Extensions of Logic Programming

Non Monotonic Extensions of Logic Programming Book
Author : Germany) NMELP'96 (2nd : 1996 : Bad Honnef,Juergen Dix,Luis Moniz Pereira,Teodor C. Przymusinski
Publisher : Springer Science & Business Media
Release : 1997-04-09
ISBN : 9783540628439
Language : En, Es, Fr & De

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Book Description :

This book constitutes the thoroughly refereed post-workshop proceedings of the 6th International Workshop on Non-Monotonic Extensions of Logic Programming, NMELP '96, held in Bad Honnef, Germany, in September 1996. The nine full papers presented in the volume in revised version were carefully reviewed and selected from a total of 18 submissions; the set of papers addresses theoretical, applicational and implementational issues and reflects the current state of the art in the area of non-monotonic extensions of logic programming. An introductory survey by the volume editors entitled "Prolegomena to Logic Programming for Non-Monotonic Reasoning" deserves special mentioning; it contains a bibliography listing 136 entries.

Logics in AI

Logics in AI Book
Author : Jan van Eijck
Publisher : Springer Science & Business Media
Release : 1991-02-26
ISBN : 9783540536864
Language : En, Es, Fr & De

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Book Description :

The European Workshop on Logics in Artificial Intelligence was held at the Centre for Mathematics and Computer Science in Amsterdam, September 10-14, 1990. This volume includes the 29 papers selected and presented at the workshop together with 7 invited papers. The main themes are: - Logic programming and automated theorem proving, - Computational semantics for natural language, - Applications of non-classical logics, - Partial and dynamic logics.