Quantification in Nonclassical Logic Book

Quantification in Nonclassical Logic


  • Author : Dov M. Gabbay
  • Publisher : Elsevier
  • Release Date : 2009-06-20
  • Genre: Mathematics
  • Pages : 640
  • ISBN 10 : 9780080931128
  • Total Read : 63
  • File Size : 10,9 Mb

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Quantification in Nonclassical Logic Summary:

Quantification and modalities have always been topics of great interest for logicians. These two themes emerged from philosophy and language in ancient times; they were studied by traditional informal methods until the 20th century. In the last century the tools became highly mathematical, and both modal logic and quantification found numerous applications in Computer Science. At the same time many other kinds of nonclassical logics were investigated and applied to Computer Science. Although there exist several good books in propositional modal logics, this book is the first detailed monograph in nonclassical first-order quantification. It includes results obtained during the past thirty years. The field is very large, so we confine ourselves with only two kinds of logics: modal and superintuitionistic. The main emphasis of Volume 1 is model-theoretic, and it concentrates on descriptions of different sound semantics and completeness problem --- even for these seemingly simple questions we have our hands full. The major part of the presented material has never been published before. Some results are very recent, and for other results we either give new proofs or first proofs in full detail.

An Introduction to Non Classical Logic Book
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An Introduction to Non Classical Logic


  • Author : Graham Priest
  • Publisher : Cambridge University Press
  • Release Date : 2008-04-10
  • Genre: Science
  • Pages : null
  • ISBN 10 : 1139469673
  • Total Read : 90
  • File Size : 13,5 Mb

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An Introduction to Non Classical Logic Summary:

This revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area.

V A  Yankov on Non Classical Logics  History and Philosophy of Mathematics Book

V A Yankov on Non Classical Logics History and Philosophy of Mathematics


  • Author : Alex Citkin
  • Publisher : Springer Nature
  • Release Date : 2022-11-08
  • Genre: Mathematics
  • Pages : 319
  • ISBN 10 : 9783031068430
  • Total Read : 83
  • File Size : 20,9 Mb

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V A Yankov on Non Classical Logics History and Philosophy of Mathematics Summary:

This book is dedicated to V.A. Yankov’s seminal contributions to the theory of propositional logics. His papers, published in the 1960s, are highly cited even today. The Yankov characteristic formulas have become a very useful tool in propositional, modal and algebraic logic. The papers contributed to this book provide the new results on different generalizations and applications of characteristic formulas in propositional, modal and algebraic logics. In particular, an exposition of Yankov’s results and their applications in algebraic logic, the theory of admissible rules and refutation systems is included in the book. In addition, the reader can find the studies on splitting and join-splitting in intermediate propositional logics that are based on Yankov-type formulas which are closely related to canonical formulas, and the study of properties of predicate extensions of non-classical propositional logics. The book also contains an exposition of Yankov’s revolutionary approach to constructive proof theory. The editors also include Yankov’s contributions to history and philosophy of mathematics and foundations of mathematics, as well as an examination of his original interpretation of history of Greek philosophy and mathematics.

Classical and Nonclassical Logics Book

Classical and Nonclassical Logics


  • Author : Eric Schechter
  • Publisher : Princeton University Press
  • Release Date : 2005-08-28
  • Genre: Mathematics
  • Pages : 530
  • ISBN 10 : 0691122792
  • Total Read : 74
  • File Size : 6,6 Mb

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Classical and Nonclassical Logics Summary:

Classical logic is traditionally introduced by itself, but that makes it seem arbitrary and unnatural. This text introduces classical alongside several nonclassical logics (relevant, constructive, quantative, paraconsistent).

Structural Analysis of Non Classical Logics Book

Structural Analysis of Non Classical Logics


  • Author : Syraya Chin-Mu Yang
  • Publisher : Springer
  • Release Date : 2015-10-16
  • Genre: Philosophy
  • Pages : 278
  • ISBN 10 : 9783662483572
  • Total Read : 95
  • File Size : 20,9 Mb

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Structural Analysis of Non Classical Logics Summary:

This volume brings together a group of logic-minded philosophers and philosophically oriented logicians to address a diversity of topics on the structural analysis of non-classical logics. It mainly focuses on the construction of different types of models for various non-classical logics of current interest, including modal logics, epistemic logics, dynamic logics, and observational predicate logic. The book presents a wide range of applications of two well-known approaches in current research: (i) structural modeling of certain philosophical issues in the framework of non-classic logics, such as admissible models for modal logic, structural models for modal epistemology and for counterfactuals, and epistemological models for common knowledge and for public announcements; (ii) conceptual analysis of logical properties of, and formal semantics for, non-classical logics, such as sub-formula property, truthmaking, epistemic modality, behavioral strategies, speech acts and assertions. The structural analysis provided in this volume will appeal not only to graduate students and experts in non-classic logics, but also to readers from a wide range of disciplines, including computer science, cognitive science, linguistics, game theory and theory of action, to mention a few.

An Introduction to Non Classical Logic Book

An Introduction to Non Classical Logic


  • Author : Graham Priest
  • Publisher : Cambridge University Press
  • Release Date : 2008-04-10
  • Genre: Science
  • Pages : 646
  • ISBN 10 : 0521854334
  • Total Read : 90
  • File Size : 10,7 Mb

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An Introduction to Non Classical Logic Summary:

This revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area.

Modal Logic for Philosophers Book

Modal Logic for Philosophers


  • Author : James W. Garson
  • Publisher : Cambridge University Press
  • Release Date : 2006-08-14
  • Genre: Philosophy
  • Pages : null
  • ISBN 10 : 9781107321038
  • Total Read : 89
  • File Size : 12,9 Mb

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Modal Logic for Philosophers Summary:

Designed for use by philosophy students, this 2006 book provides an accessible, yet technically sound treatment of modal logic and its philosophical applications. Every effort has been made to simplify the presentation by using diagrams in place of more complex mathematical apparatus. These and other innovations provide philosophers with easy access to a rich variety of topics in modal logic, including a full coverage of quantified modal logic, non-rigid designators, definite descriptions, and the de-re de-dictio distinction. Discussion of philosophical issues concerning the development of modal logic is woven into the text. The book uses natural deduction systems and also includes a diagram technique that extends the method of truth trees to modal logic. This feature provides a foundation for a novel method for showing completeness, one that is easy to extend to systems that include quantifiers.

Logics for Computer Science Book

Logics for Computer Science


  • Author : Anita Wasilewska
  • Publisher : Springer
  • Release Date : 2018-11-03
  • Genre: Computers
  • Pages : 535
  • ISBN 10 : 9783319925912
  • Total Read : 73
  • File Size : 17,5 Mb

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Logics for Computer Science Summary:

Providing an in-depth introduction to fundamental classical and non-classical logics, this textbook offers a comprehensive survey of logics for computer scientists. Logics for Computer Science contains intuitive introductory chapters explaining the need for logical investigations, motivations for different types of logics and some of their history. They are followed by strict formal approach chapters. All chapters contain many detailed examples explaining each of the introduced notions and definitions, well chosen sets of exercises with carefully written solutions, and sets of homework. While many logic books are available, they were written by logicians for logicians, not for computer scientists. They usually choose one particular way of presenting the material and use a specialized language. Logics for Computer Science discusses Gentzen as well as Hilbert formalizations, first order theories, the Hilbert Program, Godel's first and second incompleteness theorems and their proofs. It also introduces and discusses some many valued logics, modal logics and introduces algebraic models for classical, intuitionistic, and modal S4 and S5 logics. The theory of computation is based on concepts defined by logicians and mathematicians. Logic plays a fundamental role in computer science, and this book explains the basic theorems, as well as different techniques of proving them in classical and some non-classical logics. Important applications derived from concepts of logic for computer technology include Artificial Intelligence and Software Engineering. In addition to Computer Science, this book may also find an audience in mathematics and philosophy courses, and some of the chapters are also useful for a course in Artificial Intelligence.