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

The Many Valued and Nonmonotonic Turn in Logic Excerpt :

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

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 : null
  • ISBN 10 : 9789814786676

Pluralism Transnationalism and Culture in Asian Law Excerpt :

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 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

Deductive Systems in Traditional and Modern Logic Excerpt :

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.

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

Consequence Relations Excerpt :

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 : 2022-09-29
  • Genre: Uncategoriezed
  • Pages : 11
  • ISBN 10 : 978186723xxxx

Proposal for the Formalization of Dialectical Logic Excerpt :

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.

Probabilistic Extensions of Various Logical Systems Book

Probabilistic Extensions of Various Logical Systems

  • Author : Zoran Ognjanović
  • Publisher : Springer Nature
  • Release Date : 2020-07-17
  • Genre: Computers
  • Pages : 238
  • ISBN 10 : 9783030529543

Probabilistic Extensions of Various Logical Systems Excerpt :

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.

A Logical Theory of Causality Book

A Logical Theory of Causality

  • Author : Alexander Bochman
  • Publisher : MIT Press
  • Release Date : 2021-08-17
  • Genre: Computers
  • Pages : 366
  • ISBN 10 : 9780262362245

A Logical Theory of Causality Excerpt :

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.

Relations  Concrete  Abstract  And Applied   An Introduction Book

Relations Concrete Abstract And Applied An Introduction

  • Author : Herbert Toth
  • Publisher : World Scientific
  • Release Date : 2020-06-22
  • Genre: Mathematics
  • Pages : 572
  • ISBN 10 : 9789811220364

Relations Concrete Abstract And Applied An Introduction Excerpt :

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:

Transnational Law Book

Transnational Law

  • Author : Miguel Maduro
  • Publisher : Cambridge University Press
  • Release Date : 2014-05-01
  • Genre: Law
  • Pages : 409
  • ISBN 10 : 9781107028319

Transnational Law Excerpt :

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

Modeling Decisions for Artificial Intelligence Book

Modeling Decisions for Artificial Intelligence

  • Author : Vicenç Torra
  • Publisher : Springer
  • Release Date : 2018-10-08
  • Genre: Computers
  • Pages : 319
  • ISBN 10 : 9783030002022

Modeling Decisions for Artificial Intelligence Excerpt :

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.

The History and Philosophy of Polish Logic Book

The History and Philosophy of Polish Logic

  • Author : K. Mulligan
  • Publisher : Springer
  • Release Date : 2016-01-26
  • Genre: Philosophy
  • Pages : 308
  • ISBN 10 : 9781137030894

The History and Philosophy of Polish Logic Excerpt :

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.

Reason  Method  and Value Book

Reason Method and Value

  • Author : Dale Jacquette
  • Publisher : Walter de Gruyter
  • Release Date : 2013-05-02
  • Genre: Philosophy
  • Pages : 643
  • ISBN 10 : 9783110329056

Reason Method and Value Excerpt :

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.