Download or read book Logic Foundations of Mathematics and Computability Theory written by Robert E. Butts and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Fifth International Congress of Logic, Methodology and Philosophy of Science was held at the University of Western Ontario, London, Canada, 27 August to 2 September 1975. The Congress was held under the auspices of the International Union of History and Philosophy of Science, Division of Logic, Methodology and Philosophy of Science, and was sponsored by the National Research Council of Canada and the University of Western Ontario. As those associated closely with the work of the Division over the years know well, the work undertaken by its members varies greatly and spans a number of fields not always obviously related. In addition, the volume of work done by first rate scholars and scientists in the various fields of the Division has risen enormously. For these and related reasons it seemed to the editors chosen by the Divisional officers that the usual format of publishing the proceedings of the Congress be abandoned in favour of a somewhat more flexible, and hopefully acceptable, method of pre sentation. Accordingly, the work of the invited participants to the Congress has been divided into four volumes appearing in the University of Western Ontario Series in Philosophy of Science. The volumes are entitled, Logic, Foundations of Mathematics and Computability Theory, Foun dational Problems in the Special Sciences, Basic Problems in Methodol ogy and Linguistics, and Historical and Philosophical Dimensions of Logic, Methodology and Philosophy of Science.
Download or read book Computability Theory And Foundations Of Mathematics Proceedings Of The 9th International Conference On Computability Theory And Foundations Of Mathematics written by Ningning Peng and published by World Scientific. This book was released on 2022-05-18 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume features the latest scientific developments in the fields of computability theory and logical foundations of mathematics as well as applications. The scope involves the topics of Computability Theory, Reverse Mathematics, Nonstandard Analysis, Proof Theory, Set Theory, Philosophy of Mathematics, Constructive Mathematics, Theory of Randomness and Computational Complexity Theory.
Download or read book Proceedings Logic foundations of mathematics and computability theory written by Robert E. Butts and published by . This book was released on 1977 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Logic Foundations of Mathematics and Computability Theory written by Robert E. Butts and published by . This book was released on 1977 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computability written by Richard L. Epstein and published by . This book was released on 2004 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computability Theory and Foundations of Mathematics written by Kazuyuki Tanaka and published by . This book was released on 2022-05-18 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume features the latest scientific developments in the fields of computability theory and logical foundations of mathematics as well as applications. The scope involves the topics of Computability Theory, Reverse Mathematics, Nonstandard Analysis, Proof Theory, Set Theory, Philosophy of Mathematics, Constructive Mathematics, Theory of Randomness and Computational Complexity Theory.
Download or read book Proceedings of the Fifth International Congress of Logic Methodology and Philosophy of Science London Ontario Canada 1975 Logic foundations of mathematics and computability theory written by Robert E. Butts and published by . This book was released on 1977 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Logic Foundations of Mathematics and Computability Theory written by Robert E. Butts and published by . This book was released on 1977 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computability written by Richard L Epstein and published by Advanced Reasoning Forum. This book was released on 2018-10-24 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in a new edition!--the classic presentation of the theory of computable functions in the context of the foundations of mathematics. Part I motivates the study of computability with discussions and readings about the crisis in the foundations of mathematics in the early 20th century while presenting the basic ideas of whole number, function, proof, and real number. Part II starts with readings from Turing and Post leading to the formal theory of recursive functions. Part III presents sufficient formal logic to give a full development of Gödel's incompleteness theorems. Part IV considers the significance of the technical work with a discussion of Church's Thesis and readings on the foundations of mathematics. This new edition contains the timeline "Computability and Undecidability" as well as the essay "On mathematics".
Download or read book Logic Foundations of Mathematics and Computability Theory written by Robert E. Butts and published by . This book was released on 1977 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Logic written by Wei Li and published by Springer Science & Business Media. This book was released on 2010-02-26 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical logic is a branch of mathematics that takes axiom systems and mathematical proofs as its objects of study. This book shows how it can also provide a foundation for the development of information science and technology. The first five chapters systematically present the core topics of classical mathematical logic, including the syntax and models of first-order languages, formal inference systems, computability and representability, and Gödel’s theorems. The last five chapters present extensions and developments of classical mathematical logic, particularly the concepts of version sequences of formal theories and their limits, the system of revision calculus, proschemes (formal descriptions of proof methods and strategies) and their properties, and the theory of inductive inference. All of these themes contribute to a formal theory of axiomatization and its application to the process of developing information technology and scientific theories. The book also describes the paradigm of three kinds of language environments for theories and it presents the basic properties required of a meta-language environment. Finally, the book brings these themes together by describing a workflow for scientific research in the information era in which formal methods, interactive software and human invention are all used to their advantage. This book represents a valuable reference for graduate and undergraduate students and researchers in mathematics, information science and technology, and other relevant areas of natural sciences. Its first five chapters serve as an undergraduate text in mathematical logic and the last five chapters are addressed to graduate students in relevant disciplines.
Download or read book Logical Foundations of Computer Science written by Sergei Artemov and published by Springer Nature. This book was released on 2021-12-16 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2022, held in Deerfield Beach, FL, USA, in January 2022. The 23 revised full papers were carefully reviewed and selected from 35 submissions. The scope of the Symposium is broad and includes constructive mathematics and type theory; homotopy type theory; logic, automata, and automatic structures; computability and randomness; logical foundations of programming; logical aspects of computational complexity; parameterized complexity; logic programming and constraints; automated deduction and interactive theorem proving; logical methods in protocol and program verification; logical methods in program specification and extraction; domain theory logics; logical foundations of database theory; equational logic and term rewriting; lambda and combinatory calculi; categorical logic and topological semantics; linear logic; epistemic and temporal logics; intelligent and multiple-agent system logics; logics of proof and justification; non-monotonic reasoning; logic in game theory and social software; logic of hybrid systems; distributed system logics; mathematical fuzzy logic; system design logics; other logics in computer science.
Download or read book Logic Methodology and Philosophy of Science Proceedings of the 3rd International Congress 27 Aug 2 Sept 1975 written by Logic, methodology and philosophy of science and published by . This book was released on 1977 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Foundations of Logic and Theory of Computation written by A. Sernadas and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a self-contained introduction to mathematical logic and computability theory for students of mathematics or computer science. It is organized around the failures and successes of Hilbert's programme for the formalization of Mathematics. It is widely known that the programme failed with Gödel's incompleteness theorems and related negative results about arithmetic. Unfortunately, the positive outcomes of the programme are less well known, even among mathematicians. The book covers key successes, like Gödel's proof of the completeness of first-order logic, Gentzen's proof of its consistency by purely symbolic means, and the decidability of a couple of useful theories. The book also tries to convey the message that Hilbert's programme made a significant contribution to the advent of the computer as it is nowadays understood and, thus, to the latest industrial revolution. Part I of the book addresses Hilbert's programme and computability. Part II presents first-order logic, including Gödel's completeness theorem and Gentzen's consistency theorem. Part III is focused on arithmetic, representability of computable maps, Gödel's incompleteness theorems and decidability of Presburger arithmetic. Part IV provides detailed answers to selected exercises. The book can be used at late undergraduate level or early graduate level. An undergraduate course would concentrate on Parts I and II, leaving out the Gentzen calculus, and sketching the way to the 1st incompleteness theorem. A more advanced course might skip early material already known to the students and concentrate on the positive and negative results of Hilbert's programme, thus covering Gentzen's proof of consistency and Part III in full.
Download or read book Logic Methodology and Philosophy of Science written by and published by . This book was released on 1975 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Logic and Theory of Algorithms written by Arnold Beckmann and published by Springer. This book was released on 2008-06-11 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt: CiE 2008: Logic and Theory of Algorithms Athens, Greece, June 15–20, 2008 Computability in Europe (CiE) is an informal network of European scientists working on computability theory, including its foundations, technical devel- ment, and applications. Among the aims of the network is to advance our t- oretical understanding of what can and cannot be computed, by any means of computation. Its scienti?c vision is broad: computations may be performed with discrete or continuous data by all kinds of algorithms, programs, and - chines. Computations may be made by experimenting with any sort of physical system obeying the laws of a physical theory such as Newtonian mechanics, quantum theory, or relativity. Computations may be very general, depending on the foundations of set theory; or very speci?c, using the combinatorics of ?nite structures. CiE also works on subjects intimately related to computation, especially theories of data and information, and methods for formal reasoning about computations. The sources of new ideas and methods include practical developments in areas such as neural networks, quantum computation, natural computation, molecular computation, computational learning. Applications are everywhere,especially, in algebra,analysisand geometry, or data types and p- gramming. Within CiE there is general recognition of the underlying relevance of computability to physics and a broad range of other sciences, providing as it does a basic analysis of the causal structure of dynamical systems. Thisvolume,Logic andTheory of Algorithms,istheproceedingsofthefourth in a series of conferences of CiE that was held at the University of Athens, June 15–20, 2008.
Download or read book Provability Computability and Reflection written by Lev D. Beklemishev and published by Elsevier. This book was released on 2000-04-01 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provability, Computability and Reflection
