Topology Via Logic

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Topology Via Logic

Author : Steven Vickers
Publisher : Cambridge University Press
ISBN 13 : 9780521576512
Total Pages : 224 pages
Book Rating : 4.5/5 (765 download)

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Book Synopsis Topology Via Logic by : Steven Vickers

Download or read book Topology Via Logic written by Steven Vickers and published by Cambridge University Press. This book was released on 1989 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in paperback, Topology via Logic is an advanced textbook on topology for computer scientists. Based on a course given by the author to postgraduate students of computer science at Imperial College, it has three unusual features. First, the introduction is from the locale viewpoint, motivated by the logic of finite observations: this provides a more direct approach than the traditional one based on abstracting properties of open sets in the real line. Second, the methods of locale theory are freely exploited. Third, there is substantial discussion of some computer science applications. Although books on topology aimed at mathematics exist, no book has been written specifically for computer scientists. As computer scientists become more aware of the mathematical foundations of their discipline, it is appropriate that such topics are presented in a form of direct relevance and applicability. This book goes some way towards bridging the gap.

Experiments in Topology

Author : Stephen Barr
Publisher : Courier Corporation
ISBN 13 : 048615274X
Total Pages : 244 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Experiments in Topology by : Stephen Barr

Download or read book Experiments in Topology written by Stephen Barr and published by Courier Corporation. This book was released on 2012-12-04 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classic, lively explanation of one of the byways of mathematics. Klein bottles, Moebius strips, projective planes, map coloring, problem of the Koenigsberg bridges, much more, described with clarity and wit.

Frames and Locales

Author : Jorge Picado
Publisher : Springer Science & Business Media
ISBN 13 : 3034801548
Total Pages : 412 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Frames and Locales by : Jorge Picado

Download or read book Frames and Locales written by Jorge Picado and published by Springer Science & Business Media. This book was released on 2011-10-21 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Until the mid-twentieth century, topological studies were focused on the theory of suitable structures on sets of points. The concept of open set exploited since the twenties offered an expression of the geometric intuition of a "realistic" place (spot, grain) of non-trivial extent. Imitating the behaviour of open sets and their relations led to a new approach to topology flourishing since the end of the fifties.It has proved to be beneficial in many respects. Neglecting points, only little information was lost, while deeper insights have been gained; moreover, many results previously dependent on choice principles became constructive. The result is often a smoother, rather than a more entangled, theory. No monograph of this nature has appeared since Johnstone's celebrated Stone Spaces in 1983. The present book is intended as a bridge from that time to the present. Most of the material appears here in book form for the first time or is presented from new points of view. Two appendices provide an introduction to some requisite concepts from order and category theories.

Topology

Author : Tai-Danae Bradley
Publisher : MIT Press
ISBN 13 : 0262359626
Total Pages : 167 pages
Book Rating : 4.2/5 (623 download)

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Book Synopsis Topology by : Tai-Danae Bradley

Download or read book Topology written by Tai-Danae Bradley and published by MIT Press. This book was released on 2020-08-18 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate-level textbook that presents basic topology from the perspective of category theory. This graduate-level textbook on topology takes a unique approach: it reintroduces basic, point-set topology from a more modern, categorical perspective. Many graduate students are familiar with the ideas of point-set topology and they are ready to learn something new about them. Teaching the subject using category theory--a contemporary branch of mathematics that provides a way to represent abstract concepts--both deepens students' understanding of elementary topology and lays a solid foundation for future work in advanced topics.

Homotopy Type Theory: Univalent Foundations of Mathematics

Author :
Publisher : Univalent Foundations
ISBN 13 :
Total Pages : 484 pages
Book Rating : 4./5 ( download)

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Book Synopsis Homotopy Type Theory: Univalent Foundations of Mathematics by :

Download or read book Homotopy Type Theory: Univalent Foundations of Mathematics written by and published by Univalent Foundations. This book was released on with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Stone Spaces

Author : Peter T. Johnstone
Publisher : Cambridge University Press
ISBN 13 : 9780521337793
Total Pages : 398 pages
Book Rating : 4.3/5 (377 download)

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Book Synopsis Stone Spaces by : Peter T. Johnstone

Download or read book Stone Spaces written by Peter T. Johnstone and published by Cambridge University Press. This book was released on 1982 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified treatment of the corpus of mathematics that has developed out of M. H. Stone's representation theorem for Boolean algebras (1936) which has applications in almost every area of modern mathematics.

Infinite Words

Author : Dominique Perrin
Publisher : Academic Press
ISBN 13 : 9780125321112
Total Pages : 560 pages
Book Rating : 4.3/5 (211 download)

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Book Synopsis Infinite Words by : Dominique Perrin

Download or read book Infinite Words written by Dominique Perrin and published by Academic Press. This book was released on 2004-02-18 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infinite Words is an important theory in both Mathematics and Computer Sciences. Many new developments have been made in the field, encouraged by its application to problems in computer science. Infinite Words is the first manual devoted to this topic. Infinite Words explores all aspects of the theory, including Automata, Semigroups, Topology, Games, Logic, Bi-infinite Words, Infinite Trees and Finite Words. The book also looks at the early pioneering work of Büchi, McNaughton and Schützenberger. Serves as both an introduction to the field and as a reference book. Contains numerous exercises desgined to aid students and readers. Self-contained chapters provide helpful guidance for lectures.

Extensions of First-Order Logic

Author : Maria Manzano
Publisher : Cambridge University Press
ISBN 13 : 9780521354356
Total Pages : 414 pages
Book Rating : 4.3/5 (543 download)

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Book Synopsis Extensions of First-Order Logic by : Maria Manzano

Download or read book Extensions of First-Order Logic written by Maria Manzano and published by Cambridge University Press. This book was released on 1996-03-29 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to many-sorted logic as an extension of first-order logic.

Categorical Foundations

Author : Maria Cristina Pedicchio
Publisher : Cambridge University Press
ISBN 13 : 9780521834148
Total Pages : 452 pages
Book Rating : 4.8/5 (341 download)

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Book Synopsis Categorical Foundations by : Maria Cristina Pedicchio

Download or read book Categorical Foundations written by Maria Cristina Pedicchio and published by Cambridge University Press. This book was released on 2004 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description

Topology of Tiling Spaces

Author : Lorenzo Adlai Sadun
Publisher : American Mathematical Soc.
ISBN 13 : 0821847279
Total Pages : 131 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Topology of Tiling Spaces by : Lorenzo Adlai Sadun

Download or read book Topology of Tiling Spaces written by Lorenzo Adlai Sadun and published by American Mathematical Soc.. This book was released on 2008 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is an introduction to the topology of tiling spaces, with a target audience of graduate students who wish to learn about the interface of topology with aperiodic order. It isn't a comprehensive and cross-referenced tome about everything having to do with tilings, which would be too big, too hard to read, and far too hard to write! Rather, it is a review of the explosion of recent work on tiling spaces as inverse limits, on the cohomology of tiling spaces, on substitution tilings and the role of rotations, and on tilings that do not have finite local complexity. Powerful computational techniques have been developed, as have new ways of thinking about tiling spaces." "The text contains a generous supply of examples and exercises."--BOOK JACKET.

Tame Topology and O-minimal Structures

Author : Lou Van den Dries
Publisher : Cambridge University Press
ISBN 13 : 0521598389
Total Pages : 196 pages
Book Rating : 4.5/5 (215 download)

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Book Synopsis Tame Topology and O-minimal Structures by : Lou Van den Dries

Download or read book Tame Topology and O-minimal Structures written by Lou Van den Dries and published by Cambridge University Press. This book was released on 1998-05-07 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes give a self-contained treatment of the theory of o-minimal structures from a geometric and topological viewpoint, assuming only rudimentary algebra and analysis. This book should be of interest to model theorists, analytic geometers and topologists.

Metamathematics, Machines and Gödel's Proof

Author : N. Shankar
Publisher : Cambridge University Press
ISBN 13 : 9780521585330
Total Pages : 224 pages
Book Rating : 4.5/5 (853 download)

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Book Synopsis Metamathematics, Machines and Gödel's Proof by : N. Shankar

Download or read book Metamathematics, Machines and Gödel's Proof written by N. Shankar and published by Cambridge University Press. This book was released on 1997-01-30 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes the use of computer programs to check several proofs in the foundations of mathematics.

Categorical Logic and Type Theory

Author : B. Jacobs
Publisher : Gulf Professional Publishing
ISBN 13 : 9780444508539
Total Pages : 784 pages
Book Rating : 4.5/5 (85 download)

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Book Synopsis Categorical Logic and Type Theory by : B. Jacobs

Download or read book Categorical Logic and Type Theory written by B. Jacobs and published by Gulf Professional Publishing. This book was released on 2001-05-10 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.

Epistemic Logic for AI and Computer Science

Author : John-Jules Ch Meyer
Publisher :
ISBN 13 : 9780521460149
Total Pages : 354 pages
Book Rating : 4.4/5 (61 download)

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Book Synopsis Epistemic Logic for AI and Computer Science by : John-Jules Ch Meyer

Download or read book Epistemic Logic for AI and Computer Science written by John-Jules Ch Meyer and published by . This book was released on 1995 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Epistemic logic has grown from its philosophical beginnings to find diverse applications in computer science, and as a means of reasoning about the knowledge and belief of agents. This book provides a broad introduction to the subject, along with many exercises and their solutions. The authors begin by presenting the necessary apparatus from mathematics and logic, including Kripke semantics and the well-known modal logics K, T, S4 and S5. Then they turn to applications in the context of distributed systems and artificial intelligence. These include the notions of common knowledge, distributed knowledge, explicit and implicit belief, the interplays between knowledge and time, and knowledge and action, as well as a graded (or numerical) variant of the epistemic operators. The authors also discuss extensively the problem of logical omniscience. They cover Halpern & Moses' theory of honest formulas, and they make a digression into the realm of nonmonotonic reasoning and preferential entailment. They discuss Moore's autoepistemic logic, together with Levesque's related logic of "all I know". Furthermore, they show how one can base default and counterfactual reasoning on epistemic logic. Graduate students in philosophy or in computer science, especially those with an interest in AI, will find this book useful.

Algebraic Topology

Author : Allen Hatcher
Publisher : Cambridge University Press
ISBN 13 : 9780521795401
Total Pages : 572 pages
Book Rating : 4.7/5 (954 download)

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Book Synopsis Algebraic Topology by : Allen Hatcher

Download or read book Algebraic Topology written by Allen Hatcher and published by Cambridge University Press. This book was released on 2002 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory textbook suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises.

A Computational Logic

Author : Robert S. Boyer
Publisher : Academic Press
ISBN 13 : 1483277887
Total Pages : 414 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis A Computational Logic by : Robert S. Boyer

Download or read book A Computational Logic written by Robert S. Boyer and published by Academic Press. This book was released on 2014-06-25 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: ACM Monograph Series: A Computational Logic focuses on the use of induction in proving theorems, including the use of lemmas and axioms, free variables, equalities, and generalization. The publication first elaborates on a sketch of the theory and two simple examples, a precise definition of the theory, and correctness of a tautology-checker. Topics include mechanical proofs, informal development, formal specification of the problem, well-founded relations, natural numbers, and literal atoms. The book then examines the use of type information to simplify formulas, use of axioms and lemmas as rewrite rules, and the use of definitions. Topics include nonrecursive functions, computing values, free variables in hypothesis, infinite backwards chaining, infinite looping, computing type sets, and type prescriptions. The manuscript takes a look at rewriting terms and simplifying clauses, eliminating destructors and irrelevance, using equalities, and generalization. Concerns include reasons for eliminating isolated hypotheses, precise statement of the generalization heuristic, restricting generalizations, precise use of equalities, and multiple destructors and infinite looping. The publication is a vital source of data for researchers interested in computational logic.

Independence-Friendly Logic

Author : Allen L. Mann
Publisher : Cambridge University Press
ISBN 13 : 1139495917
Total Pages : 215 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Independence-Friendly Logic by : Allen L. Mann

Download or read book Independence-Friendly Logic written by Allen L. Mann and published by Cambridge University Press. This book was released on 2011-05-05 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bringing together over twenty years of research, this book gives a complete overview of independence-friendly logic, an exciting logical formalism at the interface of logic and game theory. It is suitable for graduate students and advanced undergraduates who have taken a course on first-order logic.