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.
Handbook Of The History Of Logic The Many Valued And Nonmonotonic Turn In Logic
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Author : Dov M. Gabbay
language : en
Publisher:
Release Date : 2004
Handbook Of The History Of Logic The Many Valued And Nonmonotonic Turn In Logic written by Dov M. Gabbay and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Logic categories.
R Calculus Ii Many Valued Logics
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Author : Wei Li
language : en
Publisher: Springer Nature
Release Date : 2022-04-12
R Calculus Ii Many Valued Logics 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 2022-04-12 with Mathematics categories.
This second volume of the book series shows R-calculus is a combination of one monotonic tableau proof system and one non-monotonic one. The R-calculus is a Gentzen-type 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. It discusses the algebraical and logical properties of tableau proof systems and R-calculi in many-valued logics. This book offers a rich blend of theory and practice. It is suitable for students, researchers and practitioners in the field of logic. Also it is very useful for all those who are interested in data, digitization and correctness and consistency of information, in modal logics, non monotonic logics, decidable/undecidable logics, logic programming, description logics, default logics and semantic inheritance networks.
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.
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.
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.
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.
R Calculus V Description Logics
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Author : Wei Li
language : en
Publisher: Springer Nature
Release Date : 2024-01-05
R Calculus V Description Logics 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 2024-01-05 with Mathematics categories.
This book series consists of two parts, decidable description logics and undecidable description logics. It gives the R-calculi for description logics. This book offers a rich blend of theory and practice. It is suitable for students, researchers and practitioners in the field of logic.
Probabilistic Extensions Of Various Logical Systems
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Author : Zoran Ognjanović
language : en
Publisher: Springer Nature
Release Date : 2020-07-17
Probabilistic Extensions Of Various Logical Systems written by Zoran Ognjanović and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-17 with Computers categories.
The contributions in this book survey results on combinations of probabilistic and various other classical, temporal and justification logical systems. Formal languages of these logics are extended with probabilistic operators. The aim is to provide a systematic overview and an accessible presentation of mathematical techniques used to obtain results on formalization, completeness, compactness and decidability. The book will be of value to researchers in logic and it can be used as a supplementary text in graduate courses on non-classical logics.
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.