The Many Valued And Nonmonotonic Turn In Logic
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The Many Valued And Nonmonotonic Turn In Logic
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Author : Dov M. Gabbay
language : en
Publisher: Elsevier
Release Date : 2007-08-13
The Many Valued And Nonmonotonic Turn In Logic written by Dov M. Gabbay and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-13 with Mathematics categories.
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.
Deductive Systems In Traditional And Modern Logic
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Author : Alex Citkin
language : en
Publisher: MDPI
Release Date : 2020-11-18
Deductive Systems In Traditional And Modern Logic written by Alex Citkin and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-18 with Mathematics categories.
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.
The Logic Of Gilles Deleuze
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Author : Corry Shores
language : en
Publisher: Bloomsbury Publishing
Release Date : 2020-10-15
The Logic Of Gilles Deleuze written by Corry Shores and has been published by Bloomsbury Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-15 with Philosophy categories.
French philosopher Gilles Deleuze wrote two 'logic' books: Francis Bacon: The Logic of Sensation and The Logic of Sense. However, in neither of these books nor in any other works does Deleuze articulate in a formal way the features of the logic he employs. He certainly does not use classical logic. And the best options for the non-classical logic that he may be implementing are: fuzzy, intuitionist, and many-valued. These are applicable to his concepts of heterogeneous composition and becoming, affirmative synthetic disjunction, and powers of the false. In The Logic of Gilles Deleuze: Basic Principles, Corry Shores examines the applicability of three non-classical logics to Deleuze's philosophy, by building from the philosophical and logical writings of Graham Priest, the world's leading proponent of dialetheism. Through so doing, Shores argues that Deleuze's logic is best understood as a dialetheic, paraconsistent, many-valued logic.
R Calculus Iii Post Three Valued Logic
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Author : Wei Li
language : en
Publisher: Springer Nature
Release Date : 2022-11-19
R Calculus Iii Post Three Valued Logic written by Wei Li and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-19 with Mathematics categories.
This third volume of the book series shows R-calculus is a Gentzen-typed deduction system which is non-monotonic, and is a concrete belief revision operator which is proved to satisfy the AGM postulates and the DP postulates. In this book, R-calculus is taken as Tableau-based/sequent-based/multisequent-based to preserve the satisfiability of the Theory/sequent/multisequent to revise, or sequent-based, to preserve the satisfiability of the sequent to revise. The R-calculi for Post and three-valued logic is given. This book offers a rich blend of theory and practice. It is suitable for students, researchers and practitioners in the field of logic.
The Bloomsbury Companion To Philosophical Logic
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Author : Leon Horsten
language : en
Publisher: Bloomsbury Publishing
Release Date : 2014-09-25
The Bloomsbury Companion To Philosophical Logic written by Leon Horsten and has been published by Bloomsbury Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-25 with Philosophy categories.
Logical methods are used in all area of philosophy. By introducing and advancing central to topics in the discipline, The Bloomsbury Companion to Philosophical Logic emphasizes the crucial role logic plays in understanding philosophical problems. Covering stages in the history of logic and of modern logic, this comprehensive Companion looks ahead to new areas of research and explores issues pertaining to classical logic and its rivals, semantics for parts of natural language, and the application of logic in the theory of rationality. Experts in the field provide a mix of technical chapters that offer excellent encyclopaedias of results in the area and chapters of philosophical discussions that survey a range of philosophical positions. To facilitate further study, this volumes also includes a series of research tools such as a detailed index, an up-to-date list of resources and an annotated bibliography. Balancing technical exposition with philosophical discussion, The Bloomsbury Companion to Philosophical Logic not only provides students and lecturers with the basis of a course in philosophical logic, it offers anyone working in this key area of contemporary philosophy a valuable research resource.
Pluralism Transnationalism And Culture In Asian Law
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Author : Gary F Bell
language : en
Publisher: Flipside Digital Content Company Inc.
Release Date : 2018-02-14
Pluralism Transnationalism And Culture In Asian Law written by Gary F Bell and has been published by Flipside Digital Content Company Inc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-14 with Law categories.
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.
Proposal For The Formalization Of Dialectical Logic
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Author : José Luis Usó-Doménech
language : en
Publisher: Infinite Study
Release Date :
Proposal For The Formalization Of Dialectical Logic written by José Luis Usó-Doménech and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
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.
Aristotle S Modal Syllogistic
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Author : Marko Malink
language : en
Publisher: Harvard University Press
Release Date : 2013-11-01
Aristotle S Modal Syllogistic written by Marko Malink and has been published by Harvard University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-01 with Philosophy categories.
Aristotle was the founder not only of logic but also of modal logic. In the Prior Analytics he developed a complex system of modal syllogistic which, while influential, has been disputed since antiquity--and is today widely regarded as incoherent. Combining analytic rigor with keen sensitivity to historical context, Marko Malink makes clear that the modal syllogistic forms a consistent, integrated system of logic, one that is closely related to other areas of Aristotle's philosophy. Aristotle's modal syllogistic differs significantly from modern modal logic. Malink considers the key to understanding the Aristotelian version to be the notion of predication discussed in the Topics--specifically, its theory of predicables (definition, genus, differentia, proprium, and accident) and the ten categories (substance, quantity, quality, and so on). The predicables introduce a distinction between essential and nonessential predication. In contrast, the categories distinguish between substantial and nonsubstantial predication. Malink builds on these insights in developing a semantics for Aristotle's modal propositions, one that verifies the ancient philosopher's claims of the validity and invalidity of modal inferences. While it acknowledges some limitations of this reconstruction, Aristotle's Modal Syllogistic brims with bold ideas, richly supported by close readings of the Greek texts.
Springer Handbook Of Computational Intelligence
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Author : Janusz Kacprzyk
language : en
Publisher: Springer
Release Date : 2015-05-28
Springer Handbook Of Computational Intelligence written by Janusz Kacprzyk and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-28 with Technology & Engineering categories.
The Springer Handbook for Computational Intelligence is the first book covering the basics, the state-of-the-art and important applications of the dynamic and rapidly expanding discipline of computational intelligence. This comprehensive handbook makes readers familiar with a broad spectrum of approaches to solve various problems in science and technology. Possible approaches include, for example, those being inspired by biology, living organisms and animate systems. Content is organized in seven parts: foundations; fuzzy logic; rough sets; evolutionary computation; neural networks; swarm intelligence and hybrid computational intelligence systems. Each Part is supervised by its own Part Editor(s) so that high-quality content as well as completeness are assured.
R Calculus Iv Propositional Logic
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Author : Wei Li
language : en
Publisher: Springer Nature
Release Date : 2023-03-27
R Calculus Iv Propositional Logic written by Wei Li and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-27 with Mathematics categories.
This fourth volume of the book series combines propositional logic and R-calculus for a new point of view to consider belief revision. It gives the R-calculi for propositional logic, description logics, propositional modal logic, logic programming, ⇝-propositional logic, semantic networks, and three-valued logic, etc.. Applications of R-calculus in logic of supersequents are also given. This book offers a rich blend of theory and practice. It is suitable for students, researchers and practitioners in the field of logic.