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Author : David M. Clark,Brian A. Davey
Publisher : Cambridge University Press
Page : 372 pages
File Size : 51,5 Mb
Release : 1998-11-12
Category : Mathematics
ISBN : 0521454158
First text in subject; aimed at algebraists, category theorists in mathematics and computer science.
Author : Jane G. Pitkethly,Brian A. Davey
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 52,6 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9780387275703
Natural duality theory is one of the major growth areas within general algebra. This text provides a short path to the forefront of research in duality theory. It presents a coherent approach to new results in the area, as well as exposing open problems. Unary algebras play a special role throughout the text. Individual unary algebras are relatively simple and easy to work with. But as a class they have a rich and complex entanglement with dualisability. This combination of local simplicity and global complexity ensures that, for the study of natural duality theory, unary algebras are an excellent source of examples and counterexamples. A number of results appear here for the first time. In particular, the text ends with an appendix that provides a new and definitive approach to the concept of the rank of a finite algebra and its relationship with strong dualisability.
Author : Aldo Ursini
Publisher : Routledge
Page : 584 pages
File Size : 45,5 Mb
Release : 2017-10-05
Category : Mathematics
ISBN : 9781351434713
""Attempts to unite the fields of mathematical logic and general algebra. Presents a collection of refereed papers inspired by the International Conference on Logic and Algebra held in Siena, Italy, in honor of the late Italian mathematician Roberto Magari, a leading force in the blossoming of research in mathematical logic in Italy since the 1960s.
Author : Mai Gehrke,Sam van Gool
Publisher : Cambridge University Press
Page : 369 pages
File Size : 44,9 Mb
Release : 2024-02-29
Category : Computers
ISBN : 9781009349697
Introducing Stone-Priestley duality theory and its applications to logic and theoretical computer science, this book equips graduate students and researchers with the theoretical background necessary for reading and understanding current research in the area. After giving a thorough introduction to the algebraic, topological, logical, and categorical aspects of the theory, the book covers two advanced applications in computer science, namely in domain theory and automata theory. These topics are at the forefront of active research seeking to unify semantic methods with more algorithmic topics in finite model theory. Frequent exercises punctuate the text, with hints and references provided.
Author : David Yang Gao,Vittorio Latorre,Ning Ruan
Publisher : Springer
Page : 377 pages
File Size : 54,9 Mb
Release : 2017-10-09
Category : Mathematics
ISBN : 9783319580173
This book on canonical duality theory provides a comprehensive review of its philosophical origin, physics foundation, and mathematical statements in both finite- and infinite-dimensional spaces. A ground-breaking methodological theory, canonical duality theory can be used for modeling complex systems within a unified framework and for solving a large class of challenging problems in multidisciplinary fields in engineering, mathematics, and the sciences. This volume places a particular emphasis on canonical duality theory’s role in bridging the gap between non-convex analysis/mechanics and global optimization. With 18 total chapters written by experts in their fields, this volume provides a nonconventional theory for unified understanding of the fundamental difficulties in large deformation mechanics, bifurcation/chaos in nonlinear science, and the NP-hard problems in global optimization. Additionally, readers will find a unified methodology and powerful algorithms for solving challenging problems in complex systems with real-world applications in non-convex analysis, non-monotone variational inequalities, integer programming, topology optimization, post-buckling of large deformed structures, etc. Researchers and graduate students will find explanation and potential applications in multidisciplinary fields.
Author : R. Ramanujam,Sundar Sarukkai
Publisher : Springer
Page : 269 pages
File Size : 49,8 Mb
Release : 2009-01-07
Category : Computers
ISBN : 9783540927013
Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this book constitutes the 5th volume of the FoLLI LNAI subline. It contains the refereed proceedings of the Third Indian Conference on Logic and Its Applications, ICLA 2009, held in Chennai, India, in January 2009. The 12 revised full papers presented together with 7 invited lectures were carefully reviewed and selected from numerous submissions. The papers present current research in all aspects of formal logic. They address in detail: algebraic logic and set theory, combinatorics and philosophical logic, modal logics with applications to computer science and game theory, and connections between ancient logic systems and modern systems.
Author : George Grätzer
Publisher : Springer Science & Business Media
Page : 688 pages
File Size : 47,6 Mb
Release : 2002-11-21
Category : Mathematics
ISBN : 3764369965
"Grätzer’s 'General Lattice Theory' has become the lattice theorist’s bible. Now we have the second edition, in which the old testament is augmented by a new testament. The new testament gospel is provided by leading and acknowledged experts in their fields. This is an excellent and engaging second edition that will long remain a standard reference." --MATHEMATICAL REVIEWS
Author : Hiroakira Ono,Makoto Kanazawa
Publisher : Springer Science & Business Media
Page : 418 pages
File Size : 48,5 Mb
Release : 2009-05-27
Category : Computers
ISBN : 9783642022609
Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this book constitutes the 4th volume of the FoLLI LNAI subline; containing the refereed proceedings of the 16h International Workshop on Logic, Language, Information and Computation, WoLLIC 2009, held in Tokyo, Japan, in June 2009. The 25 revised full papers presented together with six tutorials and invited talks were carefully reviewed and selected from 57 submissions. The papers cover some of the most active areas of research on the frontiers between computation, logic, and linguistics, with particular interest in cross-disciplinary topics. Typical areas of interest are: foundations of computing and programming; novel computation models and paradigms; broad notions of proof and belief; formal methods in software and hardware development; logical approach to natural language and reasoning; logics of programs, actions and resources; foundational aspects of information organization, search, flow, sharing, and protection.
Author : George Grätzer
Publisher : Springer Science & Business Media
Page : 601 pages
File Size : 48,5 Mb
Release : 2008-12-15
Category : Mathematics
ISBN : 9780387774879
Universal Algebra has become the most authoritative, consistently relied on text in a field with applications in other branches of algebra and other fields such as combinatorics, geometry, and computer science. Each chapter is followed by an extensive list of exercises and problems. The "state of the art" account also includes new appendices (with contributions from B. Jónsson, R. Quackenbush, W. Taylor, and G. Wenzel) and a well selected additional bibliography of over 1250 papers and books which makes this an indispensable new edition for students, faculty, and workers in the field.
Author : Valery B. Kudryavtsev,Ivo G. Rosenberg
Publisher : Springer Science & Business Media
Page : 448 pages
File Size : 52,7 Mb
Release : 2006-01-18
Category : Mathematics
ISBN : 9781402038174
Semigroups, Automata, Universal Algebra, Varieties
Author : George M. Bergman
Publisher : Springer
Page : 572 pages
File Size : 47,7 Mb
Release : 2015-02-05
Category : Mathematics
ISBN : 9783319114781
Rich in examples and intuitive discussions, this book presents General Algebra using the unifying viewpoint of categories and functors. Starting with a survey, in non-category-theoretic terms, of many familiar and not-so-familiar constructions in algebra (plus two from topology for perspective), the reader is guided to an understanding and appreciation of the general concepts and tools unifying these constructions. Topics include: set theory, lattices, category theory, the formulation of universal constructions in category-theoretic terms, varieties of algebras, and adjunctions. A large number of exercises, from the routine to the challenging, interspersed through the text, develop the reader's grasp of the material, exhibit applications of the general theory to diverse areas of algebra, and in some cases point to outstanding open questions. Graduate students and researchers wishing to gain fluency in important mathematical constructions will welcome this carefully motivated book.
Author : Uli Fahrenberg,Peter Jipsen,Michael Winter
Publisher : Springer Nature
Page : 352 pages
File Size : 49,9 Mb
Release : 2020-04-01
Category : Mathematics
ISBN : 9783030435202
This book constitutes the proceedings of the 18th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2020, which was due to be held in Palaiseau, France, in April 2020. The conference was cancelled due to the COVID-19 pandemic. The 20 full papers presented together with 3 invited abstracts were carefully selected from 29 submissions. Topics covered range from mathematical foundations to applications as conceptual and methodological tools in computer science and beyond.
Author : Petr Vojtěchovský,Murray R. Bremner,J. Scott Carter,Anthony B. Evans,John Huerta,Michael K. Kinyon,G. Eric Moorhouse,Jonathan D. H. Smith
Publisher : American Mathematical Soc.
Page : 297 pages
File Size : 53,5 Mb
Release : 2019-01-14
Category : Nonassociative algebras
ISBN : 9781470442453
Nonassociative mathematics is a broad research area that studies mathematical structures violating the associative law x(yz)=(xy)z. The topics covered by nonassociative mathematics include quasigroups, loops, Latin squares, Lie algebras, Jordan algebras, octonions, racks, quandles, and their applications. This volume contains the proceedings of the Fourth Mile High Conference on Nonassociative Mathematics, held from July 29–August 5, 2017, at the University of Denver, Denver, Colorado. Included are research papers covering active areas of investigation, survey papers covering Leibniz algebras, self-distributive structures, and rack homology, and a sampling of applications ranging from Yang-Mills theory to the Yang-Baxter equation and Laver tables. An important aspect of nonassociative mathematics is the wide range of methods employed, from purely algebraic to geometric, topological, and computational, including automated deduction, all of which play an important role in this book.
Author : Zoran Majkic
Publisher : Walter de Gruyter GmbH & Co KG
Page : 425 pages
File Size : 45,6 Mb
Release : 2022-09-06
Category : Computers
ISBN : 9783110981469
This book introduces the properties of conservative extensions of First Order Logic (FOL) to new Intensional First Order Logic (IFOL). This extension allows for intensional semantics to be used for concepts, thus affording new and more intelligent IT systems. Insofar as it is conservative, it preserves software applications and constitutes a fundamental advance relative to the current RDB databases, Big Data with NewSQL, Constraint databases, P2P systems, and Semantic Web applications. Moreover, the many-valued version of IFOL can support the AI applications based on many-valued logics.
Author : Peter Höfner,Damien Pous,Georg Struth
Publisher : Springer
Page : 323 pages
File Size : 49,9 Mb
Release : 2017-05-08
Category : Mathematics
ISBN : 9783319574189
This book constitutes the proceedings of the 16th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2017, held in Lyon, France, in May 2017. The 17 revised full papers and 2 invited papers presented together with 1 invited abstract were carefully selected from 28 submissions. Topics covered range from mathematical foundations to applications as conceptual and methodological tools in computer science and beyond.
