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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.

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 Book
Author : Dov M. Gabbay,John Hayden Woods
Publisher : Unknown
Release : 2004
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Handbook of the History of Logic The many valued and nonmonotonic turn in logic book written by Dov M. Gabbay,John Hayden Woods, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Handbook of the History of Logic

Handbook of the History of Logic Book
Author : Dov M. Gabbay,John Woods
Publisher : Unknown
Release : 2004
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Handbook of the History of Logic book written by Dov M. Gabbay,John Woods, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

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.

Conditionals and Modularity in General Logics

Conditionals and Modularity in General Logics Book
Author : Dov M. Gabbay,Karl Schlechta
Publisher : Springer
Release : 2013-11-27
ISBN : 9783642270659
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.

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.

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.

New Directions in Paraconsistent Logic

New Directions in Paraconsistent Logic Book
Author : Jean-Yves Beziau,Mihir Chakraborty,Soma Dutta
Publisher : Springer
Release : 2016-02-08
ISBN : 8132227190
Language : En, Es, Fr & De

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Book Description :

The present book discusses all aspects of paraconsistent logic, including the latest findings, and its various systems. It includes papers by leading international researchers, which address the subject in many different ways: development of abstract paraconsistent systems and new theorems about them; studies of the connections between these systems and other non-classical logics, such as non-monotonic, many-valued, relevant, paracomplete and fuzzy logics; philosophical interpretations of these constructions; and applications to other sciences, in particular quantum physics and mathematics. Reasoning with contradictions is the challenge of paraconsistent logic. The book will be of interest to graduate students and researchers working in mathematical logic, computer science, philosophical logic, linguistics and physics.

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.

Advances in Fuzzy Logic and Technology 2017

Advances in Fuzzy Logic and Technology 2017 Book
Author : Janusz Kacprzyk,Eulalia Szmidt,Slawomir Zadrożny,K. T. Atanassov,Maciej Krawczak
Publisher : Springer
Release : 2017-08-29
ISBN : 3319668242
Language : En, Es, Fr & De

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Book Description :

This volume constitutes the proceedings of two collocated international conferences: EUSFLAT-2017 – the 10th edition of the flagship Conference of the European Society for Fuzzy Logic and Technology held in Warsaw, Poland, on September 11–15, 2017, and IWIFSGN’2017 – The Sixteenth International Workshop on Intuitionistic Fuzzy Sets and Generalized Nets, held in Warsaw on September 13–15, 2017. The conferences were organized by the Systems Research Institute, Polish Academy of Sciences, Department IV of Engineering Sciences, Polish Academy of Sciences, and the Polish Operational and Systems Research Society in collaboration with the European Society for Fuzzy Logic and Technology (EUSFLAT), the Bulgarian Academy of Sciences and various European universities. The aim of the EUSFLAT-2017 was to bring together theoreticians and practitioners working on fuzzy logic, fuzzy systems, soft computing and related areas and to provide a platform for exchanging ideas and discussing the l atest trends and ideas, while the aim of IWIFSGN’2017 was to discuss new developments in extensions of the concept of a fuzzy set, such as an intuitionistic fuzzy set, as well as other concepts, like that of a generalized net. The papers included, written by leading international experts, as well as the special sessions and panel discussions contribute to the development the field, strengthen collaborations and intensify networking.

Handbook of the History of Logic

Handbook of the History of Logic Book
Author : Dov M. Gabbay,John Woods
Publisher : Unknown
Release : 2004
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Handbook of the History of Logic book written by Dov M. Gabbay,John Woods, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Relations Concrete Abstract And Applied An Introduction

Relations  Concrete  Abstract  And Applied   An Introduction Book
Author : Herbert Toth
Publisher : World Scientific
Release : 2020-06-22
ISBN : 9811220360
Language : En, Es, Fr & De

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Book Description :

The book is intended as an invitation to the topic of relations on a rather general basis. It fills the gap between the basic knowledge offered in countless introductory papers and books (usually comprising orders and equivalences) and the highly specialized monographs on mainly relation algebras, many-valued (fuzzy) relations, or graphs. This is done not only by presenting theoretical results but also by giving hints to some of the many interesting application areas (also including their respective theoretical basics).This book is a new — and the first of its kind — compilation of known results on binary relations. It offers relational concepts in both reasonable depth and broadness, and also provides insight into the vast diversity of theoretical results as well as application possibilities beyond the commonly known examples.This book is unique by the spectrum of the topics it handles. As indicated in its title these are:

Proposal for the Formalization of Dialectical Logic

Proposal for the Formalization of Dialectical Logic Book
Author : José Luis Usó-Doménech ,Josué Antonio Nescolarde-Selva ,Lorena Segura-Abad
Publisher : Infinite Study
Release : 2021-09-18
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Classical logic is typically concerned with abstract analysis. The problem for a synthetic logic is to transcend and unify available data to reconstruct the object as a totality. Three rules are proposed to pass from classic logic to synthetic logic. We present the category logic of qualitative opposition using examples from various sciences. This logic has been defined to include the neuter as part of qualitative opposition.

Transnational Law

Transnational Law Book
Author : Miguel Maduro,Kaarlo Tuori,Suvi Sankari
Publisher : Cambridge University Press
Release : 2014-05-01
ISBN : 1107028310
Language : En, Es, Fr & De

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Book Description :

Examination of the effects of law's de-nationalisation by placing European law in the context of transnational law.

Modeling Decisions for Artificial Intelligence

Modeling Decisions for Artificial Intelligence Book
Author : Vicenç Torra,Yasuo Narukawa,Isabel Aguiló,Manuel González-Hidalgo
Publisher : Springer
Release : 2018-10-08
ISBN : 3030002020
Language : En, Es, Fr & De

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Book Description :

This book constitutes the proceedings of the 15th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2018, held in Mallorca, Spain, in October 2018. The 24 papers presented in this volume were carefully reviewed and selected from 43 submissions. The book also contains one invited talk in full paper length. The papers were organized in topical sections named: aggregation operators, fuzzy measures and integrals; decision making; clustering and classification; and data privacy and security.

Lattice Valued Logic

Lattice Valued Logic Book
Author : Yang Xu,Da Ruan,Keyun Qin,Jun Liu
Publisher : Springer
Release : 2012-11-02
ISBN : 3540448470
Language : En, Es, Fr & De

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Book Description :

Lattice-valued Logic aims at establishing the logical foundation for uncertain information processing routinely performed by humans and artificial intelligence systems. In this textbook for the first time a general introduction on lattice-valued logic is given. It systematically summarizes research from the basic notions up to recent results on lattice implication algebras, lattice-valued logic systems based on lattice implication algebras, as well as the corresponding reasoning theories and methods. The book provides the suitable theoretical logical background of lattice-valued logic systems and supports newly designed intelligent uncertain-information-processing systems and a wide spectrum of intelligent learning tasks.

The History and Philosophy of Polish Logic

The History and Philosophy of Polish Logic Book
Author : K. Mulligan,K. Kijania-PLacek,T. Placek,Katarzyna Kijania-Placek
Publisher : Springer
Release : 2016-01-26
ISBN : 1137030895
Language : En, Es, Fr & De

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Book Description :

The book presents the state of the art of research into the legacy of interwar Polish analytic philosophy and exemplifies different approaches to the history of philosophy. It contains discussions and reconstructions of aspects of Polish philosophy and logic as well as reactions to and developments of this tradition.

A Logical Theory of Causality

A Logical Theory of Causality Book
Author : Alexander Bochman
Publisher : MIT Press
Release : 2021-08-17
ISBN : 0262362244
Language : En, Es, Fr & De

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Book Description :

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.

Reason Method and Value

Reason  Method  and Value Book
Author : Dale Jacquette
Publisher : Walter de Gruyter
Release : 2013-05-02
ISBN : 3110329050
Language : En, Es, Fr & De

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Book Description :

Nicholas Rescher has enjoyed a long and distinguished career in philosophy, writing on many different areas from logic to philosophy of language, epistemology, pragmatism, ethics and political philosophy, and metaphilosophy. Reason, Method, and Value: A Reader on the Philosophy of Nicholas Rescher offers a selection of Rescher's writings over a span of decades representing the core of his prodigious research interests in six key areas. Each section of the *Reader* is accompanied by a compact critical introduction written by a leading philosophical scholar with spezial expertise in Rescher's philosophy, and the volume opens with an appreciative introduction written by the editor and a concluding retrospective by Rescher, looking back over his oeuvre and explaining connecting themes and the unity of system contained in this extensive body of work. Taken together, the volume encapsulates the heart of Rescher's impressive lifelong contributions to philosophy between two covers, in a single volume that provides a solid overview of his thought while serving to direct readers to the corpus of Rescher's writings for amore complete picture.