Galois Connections and Applications

Author: K. Denecke,M. Erné,S.L. Wismath

Publisher: Springer Science & Business Media

ISBN: 1402018983

Category: Mathematics

Page: 502

View: 6600

Galois connections provide the order- or structure-preserving passage between two worlds of our imagination - and thus are inherent in hu man thinking wherever logical or mathematical reasoning about cer tain hierarchical structures is involved. Order-theoretically, a Galois connection is given simply by two opposite order-inverting (or order preserving) maps whose composition yields two closure operations (or one closure and one kernel operation in the order-preserving case). Thus, the "hierarchies" in the two opposite worlds are reversed or transported when passing to the other world, and going forth and back becomes a stationary process when iterated. The advantage of such an "adjoint situation" is that information about objects and relationships in one of the two worlds may be used to gain new information about the other world, and vice versa. In classical Galois theory, for instance, properties of permutation groups are used to study field extensions. Or, in algebraic geometry, a good knowledge of polynomial rings gives insight into the structure of curves, surfaces and other algebraic vari eties, and conversely. Moreover, restriction to the "Galois-closed" or "Galois-open" objects (the fixed points of the composite maps) leads to a precise "duality between two maximal subworlds".
Posted in Mathematics

Computational Intelligence, Theory and Applications

International Conference 8th Fuzzy Days in Dortmund, Germany, Sept. 29-Oct. 01, 2004 Proceedings

Author: Bernd Reusch

Publisher: Springer Science & Business Media

ISBN: 9783540311829

Category: Computers

Page: 814

View: 1259

This book constitutes the refereed proceedings of the 8th Dortmund Fuzzy Days, held in Dortmund, Germany, 2004. The Fuzzy-Days conference has established itself as an international forum for the discussion of new results in the field of Computational Intelligence. All the papers had to undergo a thorough review guaranteeing a solid quality of the programme. The papers are devoted to foundational and practical issues in fuzzy systems, neural networks, evolutionary algorithms, and machine learning and thus cover the whole range of computational intelligence.
Posted in Computers

Formale Begriffsanalyse

Mathematische Grundlagen

Author: Bernhard Ganter,Rudolf Wille

Publisher: Springer-Verlag

ISBN: 3642614507

Category: Computers

Page: 286

View: 9606

Dieses erste Lehrbuch zur Formalen Begriffsanalyse gibt eine systematische Darstellung der mathematischen Grundlagen und ihrer Verbindung zu Anwendungen in der Informatik, insbesondere in der Datenanalyse und Wissensverarbeitung. Das Buch vermittelt vor allem Methoden der graphischen Darstellung von Begriffssystemen, die sich in der Wissenskommunikation bestens bewährt haben. Theorie und graphische Darstellung werden dabei eng miteinander verknüpft. Die mathematischen Grundlagen werden vollständig abgehandelt und durch zahlreiche Beispiele anschaulich gemacht. Da zur Wissensverarbeitung immer stärker der Computer genutzt wird, gewinnen formale Methoden begrifflicher Analyse überall an Bedeutung. Das Buch macht die dafür grundlegende Theorie in kompakter Form zugänglich.
Posted in Computers

Categorical Structures and Their Applications

Author: W Gähler,G Preuss

Publisher: World Scientific

ISBN: 981448170X

Category: Mathematics

Page: 356

View: 3302

The book collects original research papers on applied categorical structures, most of which have been presented at the North-West European Category Seminar 2003 in Berlin. The spectrum of these mathematical results reflects the varied interests of Horst Herrlich — one of the leading category theorists of the world — to whom this volume is dedicated in view of his 65th birthday. The book contains applications of categorical methods in various branches of mathematics such as algebra, analysis, logic and topology, as well as fuzzy structures and computer science. At the end of the book the reader will find a complete list of Horst Herrlich's publications. The proceedings have been selected for coverage in: • Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings) • Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings) • CC Proceedings — Engineering & Physical Sciences Contents:On Boole's Booleanness (B Banaschewski)Homeomorphically Closed Nearness Spaces (H L Bentley & J W Carlson)The Tensor Product of Orthomodular Posets (R Börger)Saturated Collections of Metrics (E Colebunders et al.)Topological Structures in Logics (W Gähler)The Structure of Affine Algebraic Sets (E Giuli)A Characterization of Co-Retracts of Functional Structures (R Kaschek)Introducing Lagois Correspondences (A Melton)On Coalgebras which are Algebras (H-E Porst & C Dzierzon)Fibrewise Sobriety (G Richter & A Vauth)and other papers Readership: Graduate students, researchers, academics and lecturers in mathematics and computer science. Keywords:Category Theory;Algebra;Logic;Topology;Fuzzy Structures;Computer Science
Posted in Mathematics

Formal Concept Analysis

12th International Conference, ICFCA 2014, Cluj-Napoca, Romania , June 10-13, 2014. Proceedings

Author: Cynthia Vera Glodeanu,Mehdi Kaytoue,Christian Sacarea

Publisher: Springer

ISBN: 331907248X

Category: Computers

Page: 297

View: 4247

This book constitutes the refereed proceedings of the 12th International Conference on Formal Concept Analysis, ICFCA 2014, held in Cluj-Napoca, Romania, in June 2014. The 16 regular papers presented together with 3 invited talks were carefully reviewed and selected from 39 submissions. The papers in this volume cover a rich range of FCA aspects, such as theory, enhanced FCA. Knowledge discovery and knowledge spaces, as well as methods and applications. In addition the book contains a reprint of the first publication "Sub direct decomposition of concept lattices" by Rudolf Wille.
Posted in Computers

Universal Algebra and Applications in Theoretical Computer Science

Author: Klaus Denecke,Shelly L. Wismath

Publisher: CRC Press

ISBN: 9781584882541

Category: Mathematics

Page: 383

View: 8387

Over the past 20 years, the emergence of clone theory, hyperequational theory, commutator theory and tame congruence theory has led to a growth of universal algebra both in richness and in applications, especially in computer science. Yet most of the classic books on the subject are long out of print and, to date, no other book has integrated these theories with the long-established work that supports them. Universal Algebra and Applications in Theoretical Computer Science introduces the basic concepts of universal algebra and surveys some of the newer developments in the field. The first half of the book provides a solid grounding in the core material. A leisurely pace, careful exposition, numerous examples, and exercises combine to form an introduction to the subject ideal for beginning graduate students or researchers from other areas. The second half of the book focuses on applications in theoretical computer science and advanced topics, including Mal'cev conditions, tame congruence theory, clones, and commutators. The impact of the advances in universal algebra on computer science is just beginning to be realized, and the field will undoubtedly continue to grow and mature. Universal Algebra and Applications in Theoretical Computer Science forms an outstanding text and offers a unique opportunity to build the foundation needed for further developments in its theory and in its computer science applications.
Posted in Mathematics

Recent developments of general topology and its applications

International Conference in Memory of Felix Hausdorff (1868-1942), Berlin, March 22-28, 1992

Author: Werner Gähler,Horst Herrlich

Publisher: Vch Pub

ISBN: 9783055014239

Category: Mathematics

Page: 319

View: 3120

This volume contains the main part of the lectures contributed to the conference. They reflect the new trends of development in general topology.
Posted in Mathematics

Galois Theories

Author: Francis Borceux,George Janelidze

Publisher: Cambridge University Press

ISBN: 9780521803090

Category: Mathematics

Page: 341

View: 6230

Develops Galois theory in a more general context, emphasizing category theory.
Posted in Mathematics

Domains and Processes

Proceedings of the 1st International Symposium on Domain Theory, Shanghai, China, October 1999

Author: Klaus Keimel,Guo-Qiang Zhang,Ying Ming Liu,Yixiang Chen

Publisher: Springer Science & Business Media

ISBN: 9780792371434

Category: Computers

Page: 273

View: 6320

Proceedings of the 1st International Symposium on Domain Theory
Posted in Computers

Category Theory and Computer Programming

Tutorial and Workshop, Guildford, U.K., September 16 - 20, 1985. Proceedings

Author: David Pitt,Samson Abramsky,Axel Poigne,David Rydeheard

Publisher: Springer

ISBN: 9783540171621

Category: Computers

Page: 519

View: 1284

Posted in Computers

Generalized Galois logics

relational semantics of nonclassical logical calculi

Author: Katalin Bimbó,J. Michael Dunn

Publisher: Center for the Study of Language and Inf

ISBN: 9781575865737

Category: Language Arts & Disciplines

Page: 382

View: 6624

Nonclassical logics have played an increasing role in recent years in disciplines ranging from mathematics and computer science to linguistics and philosophy. Generalized Galois Logics develops a uniform framework of relational semantics to mediate between logical calculi and their semantics through algebra. This volume addresses normal modal logics such as K and S5, and substructural logics, including relevance logics, linear logic, and Lambek calculi. The authors also treat less-familiar and new logical systems with equal deftness.
Posted in Language Arts & Disciplines

Mathematical Reviews

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 7434

Posted in Mathematics

Galois Groups and Fundamental Groups

Author: Tamás Szamuely

Publisher: Cambridge University Press

ISBN: 0521888506

Category: Mathematics

Page: 270

View: 9371

Assuming little technical background, the author presents the strong analogies between these two concepts starting at an elementary level.
Posted in Mathematics

Abstract Algebra

Applications to Galois Theory, Algebraic Geometry, and Cryptography

Author: Celine Carstensen,Benjamin Fine,Gerhard Rosenberger

Publisher: Walter de Gruyter

ISBN: 311025008X

Category: Mathematics

Page: 366

View: 2038

A new approach to conveying abstract algebra, the area that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras, that is essential to various scientific disciplines such as particle physics and cryptology. It provides a well written account of the theoretical foundations; also contains topics that cannot be found elsewhere, and also offers a chapter on cryptography. End of chapter problems help readers with accessing the subjects. This work is co-published with the Heldermann Verlag, and within Heldermann's Sigma Series in Mathematics."
Posted in Mathematics

Valuation Theory and Its Applications

Author: Franz-Viktor Kuhlmann,Salma Kuhlmann,Murray Marshall

Publisher: American Mathematical Soc.

ISBN: 9780821871393

Category: Mathematics

Page: 449

View: 4899

This book is the first of two proceedings volumes stemming from the International Conference and Workshop on Valuation Theory held at the University of Saskatchewan (Saskatoon, SK, Canada). Valuation theory arose in the early part of the twentieth century in connection with number theory and has many important applications to geometry and analysis: the classical application to the study of algebraic curves and to Dedekind and Prufer domains; the close connection to the famousresolution of the singularities problem; the study of the absolute Galois group of a field; the connection between ordering, valuations, and quadratic forms over a formally real field; the application to real algebraic geometry; the study of noncommutative rings; etc. The special feature of this book isits focus on current applications of valuation theory to this broad range of topics. Also included is a paper on the history of valuation theory. The book is suitable for graduate students and research mathematicians working in algebra, algebraic geometry, number theory, and mathematical logic.
Posted in Mathematics