Intuitionistic Set Theory
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Intuitionistic Set Theory
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Author : John L. Bell
language : en
Publisher:
Release Date : 2014-02-28
Intuitionistic Set Theory written by John L. Bell and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-28 with Mathematics categories.
While intuitionistic (or constructive) set theory IST has received a certain attention from mathematical logicians, so far as I am aware no book providing a systematic introduction to the subject has yet been published. This may be the case in part because, as a form of higher-order intuitionistic logic - the internal logic of a topos - IST has been chiefly developed in a tops-theoretic context. In particular, proofs of relative consistency with IST for mathematical assertions have been (implicitly) formulated in topos- or sheaf-theoretic terms, rather than in the framework of Heyting-algebra-valued models, the natural extension to IST of the well-known Boolean-valued models for classical set theory. In this book I offer a brief but systematic introduction to IST which develops the subject up to and including the use of Heyting-algebra-valued models in relative consistency proofs. I believe that IST, presented as it is in the familiar language of set theory, will appeal particularly to those logicians, mathematicians and philosophers who are unacquainted with the methods of topos theory.
Intuitionistic Type Theory
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Author : Per Martin-Löf
language : en
Publisher:
Release Date : 1984
Intuitionistic Type Theory written by Per Martin-Löf and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
A Short Introduction To Intuitionistic Logic
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Author : Grigori Mints
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-20
A Short Introduction To Intuitionistic Logic written by Grigori Mints and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-20 with Mathematics categories.
Intuitionistic logic is presented here as part of familiar classical logic which allows mechanical extraction of programs from proofs. to make the material more accessible, basic techniques are presented first for propositional logic; Part II contains extensions to predicate logic. This material provides an introduction and a safe background for reading research literature in logic and computer science as well as advanced monographs. Readers are assumed to be familiar with basic notions of first order logic. One device for making this book short was inventing new proofs of several theorems. The presentation is based on natural deduction. The topics include programming interpretation of intuitionistic logic by simply typed lambda-calculus (Curry-Howard isomorphism), negative translation of classical into intuitionistic logic, normalization of natural deductions, applications to category theory, Kripke models, algebraic and topological semantics, proof-search methods, interpolation theorem. The text developed from materal for several courses taught at Stanford University in 1992-1999.
Terminological Dif Culties In Fuzzy Set Theory The Case Of Intuitionistic Fuzzy Sets
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Author : Didier Dubois
language : en
Publisher: Infinite Study
Release Date :
Terminological Dif Culties In Fuzzy Set Theory The Case Of Intuitionistic Fuzzy Sets written by Didier Dubois 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.
This note points out a terminological clash between Atanassov’s “intuitionistic fuzzy sets” and what is currently understood as intuitionistic logic.
Intuitionistic Fuzzy Sets
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Author : Krassimir T. Atanassov
language : en
Publisher: Physica
Release Date : 2013-03-20
Intuitionistic Fuzzy Sets written by Krassimir T. Atanassov and has been published by Physica this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-20 with Mathematics categories.
In the beginning of 1983, I came across A. Kaufmann's book "Introduction to the theory of fuzzy sets" (Academic Press, New York, 1975). This was my first acquaintance with the fuzzy set theory. Then I tried to introduce a new component (which determines the degree of non-membership) in the definition of these sets and to study the properties of the new objects so defined. I defined ordinary operations as "n", "U", "+" and "." over the new sets, but I had began to look more seriously at them since April 1983, when I defined operators analogous to the modal operators of "necessity" and "possibility". The late George Gargov (7 April 1947 - 9 November 1996) is the "god father" of the sets I introduced - in fact, he has invented the name "intu itionistic fuzzy", motivated by the fact that the law of the excluded middle does not hold for them. Presently, intuitionistic fuzzy sets are an object of intensive research by scholars and scientists from over ten countries. This book is the first attempt for a more comprehensive and complete report on the intuitionistic fuzzy set theory and its more relevant applications in a variety of diverse fields. In this sense, it has also a referential character.
Mathematical Intuitionism Introduction To Proof Theory
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Author : Al'bert Grigor'evi_ Dragalin
language : en
Publisher: American Mathematical Soc.
Release Date : 1988-12-31
Mathematical Intuitionism Introduction To Proof Theory written by Al'bert Grigor'evi_ Dragalin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-12-31 with Mathematics categories.
In the area of mathematical logic, a great deal of attention is now being devoted to the study of nonclassical logics. This book intends to present the most important methods of proof theory in intuitionistic logic and to acquaint the reader with the principal axiomatic theories based on intuitionistic logic.
Intuitionistic Fuzzy Measures
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Author : Adrian I. Ban
language : en
Publisher: Nova Publishers
Release Date : 2006
Intuitionistic Fuzzy Measures written by Adrian I. Ban and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
This book is the outcome of about eight years of work performed by the author largely in the field of intuitionistic fuzzy set theory and more in depth on intuitionistic fuzzy measures presented from a point of view characteristic for pure mathematics. The purpose of the book is to present a continuation of studies conducted focusing mainly on measures that evaluate intuitionistic fuzzy sets by real values and crisp sets by intuitionistic fuzzy values.
Foundations Of Set Theory
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Author : A.A. Fraenkel
language : en
Publisher: Elsevier
Release Date : 1973-12-01
Foundations Of Set Theory written by A.A. Fraenkel and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973-12-01 with Computers categories.
Foundations of Set Theory discusses the reconstruction undergone by set theory in the hands of Brouwer, Russell, and Zermelo. Only in the axiomatic foundations, however, have there been such extensive, almost revolutionary, developments. This book tries to avoid a detailed discussion of those topics which would have required heavy technical machinery, while describing the major results obtained in their treatment if these results could be stated in relatively non-technical terms. This book comprises five chapters and begins with a discussion of the antinomies that led to the reconstruction of set theory as it was known before. It then moves to the axiomatic foundations of set theory, including a discussion of the basic notions of equality and extensionality and axioms of comprehension and infinity. The next chapters discuss type-theoretical approaches, including the ideal calculus, the theory of types, and Quine's mathematical logic and new foundations; intuitionistic conceptions of mathematics and its constructive character; and metamathematical and semantical approaches, such as the Hilbert program. This book will be of interest to mathematicians, logicians, and statisticians.
Intuitionistic Set Theory Or How To Construct A Proof
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Author : Conrad Kuck
language : en
Publisher: Verlag Dr. Kovac
Release Date : 1998-01-01
Intuitionistic Set Theory Or How To Construct A Proof written by Conrad Kuck and has been published by Verlag Dr. Kovac this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Proof theory categories.
On Intuitionistic Fuzzy Sets Theory
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Author : Krassimir T. Atanassov
language : en
Publisher: Springer
Release Date : 2012-04-28
On Intuitionistic Fuzzy Sets Theory written by Krassimir T. Atanassov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-28 with Technology & Engineering categories.
This book aims to be a comprehensive and accurate survey of state-of-art research on intuitionistic fuzzy sets theory and could be considered a continuation and extension of the author ́s previous book on Intuitionistic Fuzzy Sets, published by Springer in 1999 (Atanassov, Krassimir T., Intuitionistic Fuzzy Sets, Studies in Fuzziness and soft computing, ISBN 978-3-7908-1228-2, 1999). Since the aforementioned book has appeared, the research activity of the author within the area of intuitionistic fuzzy sets has been expanding into many directions. The results of the author ́s most recent work covering the past 12 years as well as the newest general ideas and open problems in this field have been therefore collected in this new book.
