The Many Valued and Nonmonotonic Turn in Logic Book
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The Many Valued and Nonmonotonic Turn in Logic


  • Author : Dov M. Gabbay
  • Publisher : Elsevier
  • Release Date : 2007-08-13
  • Genre: Mathematics
  • Pages : 690
  • ISBN 10 : 008054939X
  • Total Read : 77
  • File Size : 19,9 Mb

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The Many Valued and Nonmonotonic Turn in Logic Summary:

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 i

R Calculus  II Book

R Calculus II


  • Author : Wei Li
  • Publisher : Springer Nature
  • Release Date : 2022-12-02
  • Genre: Big data
  • Pages : 281
  • ISBN 10 : 9789811692949
  • Total Read : 74
  • File Size : 19,9 Mb

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R Calculus II Summary:

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 Book

Pluralism Transnationalism and Culture in Asian Law


  • Author : Gary F Bell
  • Publisher : Flipside Digital Content Company Inc.
  • Release Date : 2018-02-14
  • Genre: Law
  • Pages : 318
  • ISBN 10 : 9789814786676
  • Total Read : 88
  • File Size : 19,7 Mb

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Pluralism Transnationalism and Culture in Asian Law Summary:

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 Book

R Calculus III Post Three Valued Logic


  • Author : Wei Li
  • Publisher : Springer Nature
  • Release Date : 2022-12-21
  • Genre: Mathematics
  • Pages : 284
  • ISBN 10 : 9789811942709
  • Total Read : 84
  • File Size : 7,5 Mb

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R Calculus III Post Three Valued Logic Summary:

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 Book

Deductive Systems in Traditional and Modern Logic


  • Author : Alex Citkin
  • Publisher : MDPI
  • Release Date : 2020-11-18
  • Genre: Mathematics
  • Pages : 298
  • ISBN 10 : 9783039433582
  • Total Read : 74
  • File Size : 20,5 Mb

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Deductive Systems in Traditional and Modern Logic Summary:

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 Book

Advances in Fuzzy Logic and Technology 2017


  • Author : Janusz Kacprzyk
  • Publisher : Springer
  • Release Date : 2017-08-29
  • Genre: Technology & Engineering
  • Pages : 628
  • ISBN 10 : 9783319668246
  • Total Read : 77
  • File Size : 8,7 Mb

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Advances in Fuzzy Logic and Technology 2017 Summary:

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.

Consequence Relations Book

Consequence Relations


  • Author : Alex Citkin
  • Publisher : Oxford University Press
  • Release Date : 2022-06-30
  • Genre: Young Adult Nonfiction
  • Pages : 353
  • ISBN 10 : 9780192691491
  • Total Read : 97
  • File Size : 10,9 Mb

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Consequence Relations Summary:

The publication of Rasiowa and Sikorski's The Mathematics of Metamathematics (1970), Rasiowa's An Algebraic Approach to Non-Classical Logics (1974), and Wójcicki's Theory of Logical Calculi (1988) created a niche in the field of mathematical and philosophical logic. This in-depth study of the concept of a consequence relation, culminating in the concept of a Lindenbaum-Tarski algebra, fills this niche. Citkin and Muravitsky consider the problem of obtaining confirmation that a statement is a consequence of a set of statements as prerequisites, on the one hand, and the problem of demonstrating that such confirmation does not exist in the structure under consideration, on the other hand. For the second part of this problem, the concept of the Lindenbaum-Tarski algebra plays a key role, which becomes even more important when the considered consequence relation is placed in the context of decidability. This role is traced in the book for various formal objective languages. The work also includes helpful exercises to aid the reader's assimilation of the book's material. Intended for advanced undergraduate and graduate students in mathematics and philosophy, this book can be used to teach special courses in logic with an emphasis on algebraic methods, for self-study, and also as a reference work.

Proposal for the Formalization of Dialectical Logic Book

Proposal for the Formalization of Dialectical Logic


  • Author : José Luis Usó-Doménech
  • Publisher : Infinite Study
  • Release Date : 2022-12-02
  • Genre: Uncategoriezed
  • Pages : 11
  • ISBN 10 : 978186723xxxx
  • Total Read : 74
  • File Size : 14,5 Mb

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Proposal for the Formalization of Dialectical Logic Summary:

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.