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Author: N.M. Martin
Publisher: Springer Science & Business Media
ISBN: 147572506X
Category : Mathematics
Languages : en
Pages : 241
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Book Description
This book examines an abstract mathematical theory, placing special emphasis on results applicable to formal logic. If a theory is especially abstract, it may find a natural home within several of the more familiar branches of mathematics. This is the case with the theory of closure spaces. It might be considered part of topology, lattice theory, universal algebra or, no doubt, one of several other branches of mathematics as well. In our development we have treated it, conceptually and methodologically, as part of topology, partly because we first thought ofthe basic structure involved (closure space), as a generalization of Frechet's concept V-space. V-spaces have been used in some developments of general topology as a generalization of topological space. Indeed, when in the early '50s, one of us started thinking about closure spaces, we thought ofit as the generalization of Frechet V space which comes from not requiring the null set to be CLOSURE SPACES ANDLOGIC XlI closed(as it is in V-spaces). This generalization has an extreme advantage in connection with application to logic, since the most important closure notion in logic, deductive closure, in most cases does not generate a V-space, since the closure of the null set typically consists of the "logical truths" of the logic being examined.
Author: N.M. Martin
Publisher: Springer Science & Business Media
ISBN: 147572506X
Category : Mathematics
Languages : en
Pages : 241
Get Book Here
Book Description
This book examines an abstract mathematical theory, placing special emphasis on results applicable to formal logic. If a theory is especially abstract, it may find a natural home within several of the more familiar branches of mathematics. This is the case with the theory of closure spaces. It might be considered part of topology, lattice theory, universal algebra or, no doubt, one of several other branches of mathematics as well. In our development we have treated it, conceptually and methodologically, as part of topology, partly because we first thought ofthe basic structure involved (closure space), as a generalization of Frechet's concept V-space. V-spaces have been used in some developments of general topology as a generalization of topological space. Indeed, when in the early '50s, one of us started thinking about closure spaces, we thought ofit as the generalization of Frechet V space which comes from not requiring the null set to be CLOSURE SPACES ANDLOGIC XlI closed(as it is in V-spaces). This generalization has an extreme advantage in connection with application to logic, since the most important closure notion in logic, deductive closure, in most cases does not generate a V-space, since the closure of the null set typically consists of the "logical truths" of the logic being examined.
Author: Josep Diaz
Publisher: Springer
ISBN: 3662446022
Category : Computers
Languages : en
Pages : 369
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Book Description
This book constitutes the refereed proceedings of the 8th FIP WG 2.2 International Conference, TCS 2014, held in Rome, Italy, in September 2014. The 26 revised full papers presented, together with two invited talks, were carefully reviewed and selected from 73 submissions. [Suggestion--please check and add more if needed] TCS-2014 consisted of two tracks, with separate program committees, which dealt respectively with: - Track A: Algorithms, Complexity and Models of Computation, and - Track B: Logic, Semantics, Specification and Verification
Author: Frdric Mynard
Publisher: American Mathematical Soc.
ISBN: 082184279X
Category : Mathematics
Languages : en
Pages : 395
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Book Description
The purpose of this collection is to guide the non-specialist through the basic theory of various generalizations of topology, starting with clear motivations for their introduction. Structures considered include closure spaces, convergence spaces, proximity spaces, quasi-uniform spaces, merotopic spaces, nearness and filter spaces, semi-uniform convergence spaces, and approach spaces. Each chapter is self-contained and accessible to the graduate student, and focuses on motivations to introduce the generalization of topologies considered, presenting examples where desirable properties are not present in the realm of topologies and the problem is remedied in the more general context. Then, enough material will be covered to prepare the reader for more advanced papers on the topic. While category theory is not the focus of the book, it is a convenient language to study these structures and, while kept as a tool rather than an object of study, will be used throughout the book. For this reason, the book contains an introductory chapter on categorical topology.
Author: Stefan Kramer
Publisher: Springer Science & Business Media
ISBN: 3540281770
Category : Computers
Languages : en
Pages : 437
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Book Description
This book constitutes the refereed proceedings of the 15th International Conference on Inductive Logic Programming, ILP 2005, held in Bonn, Germany, in August 2005. The 24 revised full papers presented together with the abstract of 4 invited lectures were carefully reviewed and selected for inclusion in the book. The papers address all current topics in inductive logic programming, ranging from theoretical and methodological issues to advanced applications in various areas, also including more diverse forms of non-propositional learning.
Author: Peter Bruza
Publisher: Springer
ISBN: 3642008348
Category : Science
Languages : en
Pages : 324
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Book Description
This book constitutes the refereed proceedings of the Third International Symposium on Quantum Interaction, QI 2009, held in Saarbrücken, Germany, in March 2009. The 21 revised full papers presented together with the 3 position papers were carefully reviewed and selected from numerous submissions. The papers show the cross-disciplinary nature of quantum interaction covering topics such as computation, cognition, decision theory, information retrieval, information systems, social interaction, computational linguistics and finance.
Author: K. Kuratowski
Publisher: Elsevier
ISBN: 1483272567
Category : Mathematics
Languages : en
Pages : 581
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Book Description
Topology, Volume I deals with topology and covers topics ranging from operations in logic and set theory to Cartesian products, mappings, and orderings. Cardinal and ordinal numbers are also discussed, along with topological, metric, and complete spaces. Great use is made of closure algebra. Comprised of three chapters, this volume begins with a discussion on general topological spaces as well as their specialized aspects, including regular, completely regular, and normal spaces. Fundamental notions such as base, subbase, cover, and continuous mapping, are considered, together with operations such as the exponential topology and quotient topology. The next chapter is devoted to the study of metric spaces, starting with more general spaces, having the limit as its primitive notion. The space is assumed to be metric separable, and this includes problems of cardinality and dimension. Dimension theory and the theory of Borei sets, Baire functions, and related topics are also discussed. The final chapter is about complete spaces and includes problems of general function theory which can be expressed in topological terms. The book includes two appendices, one on applications of topology to mathematical logics and another to functional analysis. This monograph will be helpful to students and practitioners of algebra and mathematics.
Author: Plamen L. Simeonov
Publisher: Springer Science & Business Media
ISBN: 3642281117
Category : Technology & Engineering
Languages : en
Pages : 424
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Book Description
Perhaps the most distinct question in science throughout the ages has been the one of perceivable reality, treated both in physics and philosophy. Reality is acting upon us, and we, and life in general, are acting upon reality. Potentiality, found both in quantum reality and in the activity of life, plays a key role. In quantum reality observation turns potentiality into reality. Again, life computes possibilities in various ways based on past actions, and acts on the basis of these computations. This book is about a new approach to biology (and physics, of course!). Its subtitle suggests a perpetual movement and interplay between two elusive aspects of modern science — reality/matter and potentiality/mind, between physics and biology — both captured and triggered by mathematics — to understand and explain emergence, development and life all the way up to consciousness. But what is the real/potential difference between living and non-living matter? How does time in potentiality differ from time in reality? What we need to understand these differences is an integrative approach. This book contemplates how to encircle life to obtain a formal system, equivalent to the ones in physics. Integral Biomathics attempts to explore the interplay between reality and potentiality.
Author: Marco Bernardo
Publisher: Springer
ISBN: 3319340964
Category : Computers
Languages : en
Pages : 269
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Book Description
This book presents 8 tutorial lectures given by leading researchers at the 16th edition of the International School on Formal Methods for the Design of Computer, Communication and Software Systems, SFM 2016, held in Bertinoro, Italy, in June 2016. SFM 2016 was devoted to the Quantitative Evaluation of Collective Adaptive Systems and covered topics such as self-organization in distributed systems, scalable quantitative analysis, spatio-temporal models, and aggregate programming.
Author: Fabio Gadducci
Publisher: Springer Nature
ISBN: 3030513726
Category : Computers
Languages : en
Pages : 346
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Book Description
This book constitutes the refereed proceedings of the 13th International Conference on Graph Transformation, ICGT 2020, in Bergen, Norway, in June 2020.* The 16 research papers and 4 tool paper presented in this book were carefully reviewed and selected from 40 submissions. One invited paper is also included. The papers deal with the following topics: theoretical advances; application domains; and tool presentations. *The conference was held virtually due to the COVID-19 pandemic.
Author: Reiko Heckel
Publisher: Springer
ISBN: 3642402062
Category : Computers
Languages : en
Pages : 370
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Book Description
This book constitutes the refereed proceedings of the 5th International Conference on Algebra and Coalgebra in Computer Science, CALCO 2013, held in Warsaw, Poland, in September 2013. The 18 full papers presented together with 4 invited talks were carefully reviewed and selected from 33 submissions. The papers cover topics in the fields of abstract models and logics, specialized models and calculi, algebraic and coalgebraic semantics, system specification and verification, as well as corecursion in programming languages, and algebra and coalgebra in quantum computing. The book also includes 6 papers from the CALCO Tools Workshop, co-located with CALCO 2013 and dedicated to tools based on algebraic and/or coalgebraic principles.
