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Author : Lev D. Beklemishev
Publisher : Elsevier
ISBN 13 : 0080954812
Total Pages : 333 pages
Book Rating : 4.0/5 (89 download)
Download or read book The Theory of Semisets written by Lev D. Beklemishev and published by Elsevier. This book was released on 2000-04-01 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Theory of Semisets
Author : Lev D. Beklemishev
Publisher : Elsevier
ISBN 13 : 008095474X
Total Pages : 467 pages
Book Rating : 4.0/5 (89 download)
Download or read book LOGIC COLLOQUIUM '69 written by Lev D. Beklemishev and published by Elsevier. This book was released on 2000-04-01 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: LOGIC COLLOQUIUM '69
Author : E. Casari
Publisher : Springer Science & Business Media
ISBN 13 : 3642110800
Total Pages : 283 pages
Book Rating : 4.6/5 (421 download)
Download or read book Aspects of Mathematical Logic written by E. Casari and published by Springer Science & Business Media. This book was released on 2011-06-06 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: H. Hermes: Basic notions and applications of the theory of decidability.- D. Kurepa: On several continuum hypotheses.- A. Mostowski: Models of set theory.- A. Robinson: Problems and methods of model theory.- S. Sochor, B. Balcar: The general theory of semisets. Syntactic models of the set theory.
Download or read book Canadian Mathematical Bulletin written by and published by . This book was released on 1975 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Dana S. Scott
Publisher : American Mathematical Soc.
ISBN 13 : 0821802453
Total Pages : 482 pages
Book Rating : 4.8/5 (218 download)
Download or read book Axiomatic Set Theory, Part 1 written by Dana S. Scott and published by American Mathematical Soc.. This book was released on 1971-12-31 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Franco Montagna
Publisher : Springer
ISBN 13 : 3319062336
Total Pages : 324 pages
Book Rating : 4.3/5 (19 download)
Download or read book Petr Hájek on Mathematical Fuzzy Logic written by Franco Montagna and published by Springer. This book was released on 2014-09-23 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume celebrates the work of Petr Hájek on mathematical fuzzy logic and presents how his efforts have influenced prominent logicians who are continuing his work. The book opens with a discussion on Hájek's contribution to mathematical fuzzy logic and with a scientific biography of him, progresses to include two articles with a foundation flavour, that demonstrate some important aspects of Hájek's production, namely, a paper on the development of fuzzy sets and another paper on some fuzzy versions of set theory and arithmetic. Articles in the volume also focus on the treatment of vagueness, building connections between Hájek's favorite fuzzy logic and linguistic models of vagueness. Other articles introduce alternative notions of consequence relation, namely, the preservation of truth degrees, which is discussed in a general context, and the differential semantics. For the latter, a surprisingly strong standard completeness theorem is proved. Another contribution also looks at two principles valid in classical logic and characterize the three main t-norm logics in terms of these principles. Other articles, with an algebraic flavour, offer a summary of the applications of lattice ordered-groups to many-valued logic and to quantum logic, as well as an investigation of prelinearity in varieties of pointed lattice ordered algebras that satisfy a weak form of distributivity and have a very weak implication. The last part of the volume contains an article on possibilistic modal logics defined over MTL chains, a topic that Hájek discussed in his celebrated work, Metamathematics of Fuzzy Logic, and another one where the authors, besides offering unexpected premises such as proposing to call Hájek's basic fuzzy logic HL, instead of BL, propose a very weak system, called SL as a candidate for the role of the really basic fuzzy logic. The paper also provides a generalization of the prelinearity axiom, which was investigated by Hájek in the context of fuzzy logic.
Author : Thomas Bedürftig
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110470772
Total Pages : 514 pages
Book Rating : 4.1/5 (14 download)
Download or read book Philosophy of Mathematics written by Thomas Bedürftig and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-10-26 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book is an introduction to the philosophy of mathematics. It asks philosophical questions concerning fundamental concepts, constructions and methods - this is done from the standpoint of mathematical research and teaching. It looks for answers both in mathematics and in the philosophy of mathematics from their beginnings till today. The reference point of the considerations is the introducing of the reals in the 19th century that marked an epochal turn in the foundations of mathematics. In the book problems connected with the concept of a number, with the infinity, the continuum and the infinitely small, with the applicability of mathematics as well as with sets, logic, provability and truth and with the axiomatic approach to mathematics are considered. In Chapter 6 the meaning of infinitesimals to mathematics and to the elements of analysis is presented. The authors of the present book are mathematicians. Their aim is to introduce mathematicians and teachers of mathematics as well as students into the philosophy of mathematics. The book is suitable also for professional philosophers as well as for students of philosophy, just because it approaches philosophy from the side of mathematics. The knowledge of mathematics needed to understand the text is elementary. Reports on historical conceptions. Thinking about today‘s mathematical doing and thinking. Recent developments. Based on the third, revised German edition. For mathematicians - students, teachers, researchers and lecturers - and readersinterested in mathematics and philosophy. Contents On the way to the reals On the history of the philosophy of mathematics On fundamental questions of the philosophy of mathematics Sets and set theories Axiomatic approach and logic Thinking and calculating infinitesimally – First nonstandard steps Retrospection
Author : H.W. Gottinger
Publisher : Springer Science & Business Media
ISBN 13 : 9400998384
Total Pages : 340 pages
Book Rating : 4.4/5 (9 download)
Download or read book Decision Theory and Social Ethics written by H.W. Gottinger and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ethics, as one of the most respectable disciplines of philosophy, has undergone a drastic and revolutionary change in recent time. There are three main trends of this development. The first trend can be described as a tendency towards a rigorous formal and analytical language. This means simply that ethics has created beside its own formalized set theoretical language a variety of new formalized, logical and mathemati cal methods and concepts. Thus ethics has become a formalized meta or epidiscipline which is going to replace the traditional concepts, principles and ethical methods in the realm of social sciences. It is clear that a formalized form of ethics can be used more easily in social, economic and political theories if there are ethical conflicts to be solved. This first trend can be regarded as a conditio sine qua non for application in, and imposing ethical solutions on, social scientific theories. The second trend may be characterized as an association- or unification-tendency of a formalized and analytical ethics with decision theory. Decision theory as a new interdiscipline of social sciences is actually an assemblage of a variety of subtheories such as value-utility theory, game theory, collective decision theory, etc. Harsanyi has called this complex of subtheories a general theory of human behavior. Analytical or formal ethics is actually using this general theory of human behavior as a vehicle simply because this theory deals from the beginning with conflict solution, i. e.
Author : A. Lachlan
Publisher : Springer
ISBN 13 : 3540370323
Total Pages : 353 pages
Book Rating : 4.5/5 (43 download)
Download or read book Set Theory and Hierarchy Theory V written by A. Lachlan and published by Springer. This book was released on 2006-11-15 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Manoranjan Kumar Singh
Publisher : Springer Nature
ISBN 13 : 9819732700
Total Pages : 680 pages
Book Rating : 4.8/5 (197 download)
Download or read book Concepts of Fuzzy Mathematics written by Manoranjan Kumar Singh and published by Springer Nature. This book was released on with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Petr Vopěnka
Publisher : Charles University in Prague, Karolinum Press
ISBN 13 : 8024646633
Total Pages : 352 pages
Book Rating : 4.0/5 (246 download)
Download or read book New Infinitary Mathematics written by Petr Vopěnka and published by Charles University in Prague, Karolinum Press. This book was released on 2022-08-01 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The dominant current of twentieth-century mathematics, which simultaneously explores and applies infinity (albeit in bizarre ideal worlds), relies on Cantor's classical theory of infinite sets. Cantor’s theory in turn relies on the problematic assumption of the existence of the set of all natural numbers, the only justification for which – a theological justification - is usually concealed and pushed into the collective unconscious. This book begins by surveying the theological background, emergence, and development of classical set theory. The author warns us about the dangers implicit in the construction of set theory, traceable in his own and other eminent mathematicians' seminal works on the subject. He then goes on to present an argument about the absurdity of the assumption of the existence of the set of all natural numbers. However, the author’s contribution is not just a negation of current views and assumptions. On the contrary, the new infinitary mathematics that he proceeds to propose and develop is driven by a cautious effort to transcend the horizon bounding the ancient geometric world and pre-set-theoretical mathematics, whilst allowing mathematics to correspond more closely to the natural real world surrounding us. The final parts are devoted to a discussion of real numbers and to demonstrating how, within the new infinitary mathematics, calculus can be rehabilitated in its original form employing infinitesimals.
Author : Pavel Pudlák
Publisher : Springer Science & Business Media
ISBN 13 : 3319001191
Total Pages : 699 pages
Book Rating : 4.3/5 (19 download)
Download or read book Logical Foundations of Mathematics and Computational Complexity written by Pavel Pudlák and published by Springer Science & Business Media. This book was released on 2013-04-22 with total page 699 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two main themes of this book, logic and complexity, are both essential for understanding the main problems about the foundations of mathematics. Logical Foundations of Mathematics and Computational Complexity covers a broad spectrum of results in logic and set theory that are relevant to the foundations, as well as the results in computational complexity and the interdisciplinary area of proof complexity. The author presents his ideas on how these areas are connected, what are the most fundamental problems and how they should be approached. In particular, he argues that complexity is as important for foundations as are the more traditional concepts of computability and provability. Emphasis is on explaining the essence of concepts and the ideas of proofs, rather than presenting precise formal statements and full proofs. Each section starts with concepts and results easily explained, and gradually proceeds to more difficult ones. The notes after each section present some formal definitions, theorems and proofs. Logical Foundations of Mathematics and Computational Complexity is aimed at graduate students of all fields of mathematics who are interested in logic, complexity and foundations. It will also be of interest for both physicists and philosophers who are curious to learn the basics of logic and complexity theory.
Author : W. Marek
Publisher : Springer
ISBN 13 : 3540381228
Total Pages : 344 pages
Book Rating : 4.5/5 (43 download)
Download or read book Set Theory and Hierarchy Theory written by W. Marek and published by Springer. This book was released on 2006-11-14 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Heinz-Dieter Ebbinghaus
Publisher : Springer Science & Business Media
ISBN 13 : 3662090589
Total Pages : 653 pages
Book Rating : 4.6/5 (62 download)
Download or read book Ω-Bibliography of Mathematical Logic written by Heinz-Dieter Ebbinghaus and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 653 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gert H. Müller The growth of the number of publications in almost all scientific areas, as in the area of (mathematical) logic, is taken as a sign of our scientifically minded culture, but it also has a terrifying aspect. In addition, given the rapidly growing sophistica tion, specialization and hence subdivision of logic, researchers, students and teachers may have a hard time getting an overview of the existing literature, partic ularly if they do not have an extensive library available in their neighbourhood: they simply do not even know what to ask for! More specifically, if someone vaguely knows that something vaguely connected with his interests exists some where in the literature, he may not be able to find it even by searching through the publications scattered in the review journals. Answering this challenge was and is the central motivation for compiling this Bibliography. The Bibliography comprises (presently) the following six volumes (listed with the corresponding Editors): I. Classical Logic W. Rautenberg 11. Non-classical Logics W. Rautenberg 111. Model Theory H.-D. Ebbinghaus IV. Recursion Theory P.G. Hinman V. Set Theory A.R. Blass VI. ProofTheory; Constructive Mathematics J.E. Kister; D. van Dalen & A.S. Troelstra.
Author : P. Hajek
Publisher : Springer Science & Business Media
ISBN 13 : 3642669433
Total Pages : 410 pages
Book Rating : 4.6/5 (426 download)
Download or read book Mechanizing Hypothesis Formation written by P. Hajek and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hypothesis formation is known as one of the branches of Artificial Intelligence, The general question of Artificial IntelligencE' ,"Can computers think?" is specified to the question ,"Can computers formulate and justify hypotheses?" Various attempts have been made to answer the latter question positively. The present book is one such attempt. Our aim is not to formalize and mechanize the whole domain of inductive reasoning. Our ultimate question is: Can computers formulate and justify scientific hypotheses? Can they comprehend empirical data and process them rationally, using the apparatus of modern mathematical logic and statistics to try to produce a rational image of the observed empirical world? Theories of hypothesis formation are sometimes called logics of discovery. Plotkin divides a logic of discovery into a logic of induction: studying the notion of justification of a hypothesis, and a logic of suggestion: studying methods of suggesting reasonable hypotheses. We use this division for the organization of the present book: Chapter I is introductory and explains the subject of our logic of discovery. The rest falls into two parts: Part A - a logic of induction, and Part B - a logic of suggestion.
Author : G. Eberlein
Publisher : Springer Science & Business Media
ISBN 13 : 9400938950
Total Pages : 333 pages
Book Rating : 4.4/5 (9 download)
Download or read book Theory and Decision written by G. Eberlein and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of articles contains contributions from a few of Werner Leinfellner's many friends and colleagues. Some of them are former students of Werner's. Others were colleagues of his at various American and European universities. Further, some have come to know Werner through his research, his long-standing editorship of Theory and Deci sion and his extensive participation in international conferences and congresses. The following articles are new to this volume. The areas covered are those in which Werner continues to play an active professional role. We offer them as a tribute to the many and multi-faceted contributions to the scientific enterprise for which Werner Leinfellner is so widely known. We believe such a festschrift to be fitting and long overdue. Because of the breadth of Werner's professional associations, it was difficult to select representatives from among his many spheres of influence. We apologize to the many scholars who could not be in cluded because of time and space considerations. Finally, we wish to express appreciation to Dean John Guilds of the University of Arkansas for providing financial support early on in the evolution of this project, to Jennifer Bauman for her bravura performance in copy-editing the manuscripts, and to our publisher at Reidel for bringing this volume to press.
Author :
Publisher :
ISBN 13 :
Total Pages : 352 pages
Book Rating : 4.:/5 (36 download)
Download or read book Fundamenta Mathematicae written by and published by . This book was released on 1976 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt:
