Information Algebras

Author : Juerg Kohlas
Publisher : Springer Science & Business Media
Page : 274 pages
File Size : 49,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447100096

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Information Algebras by Juerg Kohlas Pdf

Information usually comes in pieces, from different sources. It refers to different, but related questions. Therefore information needs to be aggregated and focused onto the relevant questions. Considering combination and focusing of information as the relevant operations leads to a generic algebraic structure for information. This book introduces and studies information from this algebraic point of view. Algebras of information provide the necessary abstract framework for generic inference procedures. They allow the application of these procedures to a large variety of different formalisms for representing information. At the same time they permit a generic study of conditional independence, a property considered as fundamental for knowledge presentation. Information algebras provide a natural framework to define and study uncertain information. Uncertain information is represented by random variables that naturally form information algebras. This theory also relates to probabilistic assumption-based reasoning in information systems and is the basis for the belief functions in the Dempster-Shafer theory of evidence.

Author : Giovanni Sommaruga
Publisher : Springer Science & Business Media
Page : 275 pages
File Size : 44,6 Mb
Release : 2009-04-22
Category : Computers
ISBN : 9783642006586

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Formal Theories of Information by Giovanni Sommaruga Pdf

This book presents the scientific outcome of a joint effort of the computer science departments of the universities of Berne, Fribourg and Neuchâtel. Within an initiative devoted to "Information and Knowledge", these research groups collaborated over several years on issues of logic, probability, inference, and deduction. The goal of this volume is to examine whether there is any common ground between the different approaches to the concept of information. The structure of this book could be represented by a circular model, with an innermost syntactical circle, comprising statistical and algorithmic approaches; a second, larger circle, the semantical one, in which "meaning" enters the stage; and finally an outermost circle, the pragmatic one, casting light on real-life logical reasoning. These articles are complemented by two philosophical contributions exploring the wide conceptual field as well as taking stock of the articles on the various formal theories of information.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 48,5 Mb
Release : 2024-07-03
Category : Electronic
ISBN : 9789814469722

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Theory of Information by Anonim Pdf

Author : Jonathan S. Golan
Publisher : Springer Science & Business Media
Page : 207 pages
File Size : 42,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401592413

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Power Algebras over Semirings by Jonathan S. Golan Pdf

This monograph is a continuation of several themes presented in my previous books [146, 149]. In those volumes, I was concerned primarily with the properties of semirings. Here, the objects of investigation are sets of the form RA, where R is a semiring and A is a set having a certain structure. The problem is one of translating that structure to RA in some "natural" way. As such, it tries to find a unified way of dealing with diverse topics in mathematics and theoretical com puter science as formal language theory, the theory of fuzzy algebraic structures, models of optimal control, and many others. Another special case is the creation of "idempotent analysis" and similar work in optimization theory. Unlike the case of the previous work, which rested on a fairly established mathematical foundation, the approach here is much more tentative and docimastic. This is an introduction to, not a definitative presentation of, an area of mathematics still very much in the making. The basic philosphical problem lurking in the background is one stated suc cinctly by Hahle and Sostak [185]: ". . . to what extent basic fields of mathematics like algebra and topology are dependent on the underlying set theory?" The conflicting definitions proposed by various researchers in search of a resolution to this conundrum show just how difficult this problem is to see in a proper light.

Author : Wendy MacCaull,Michael Winter,Ivo Düntsch
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 50,9 Mb
Release : 2006-04-18
Category : Computers
ISBN : 9783540333395

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Relational Methods in Computer Science by Wendy MacCaull,Michael Winter,Ivo Düntsch Pdf

This volume is the post conference proceedings of the 8th International Seminar on Relational Methods in Computer Science (RelMiCS 8), held in conjunction with the 3rd International Workshop on Applications of Kleene Algebra and a COST Action 274 (TARSKI) Workshop. This combined meeting took place in St. Catharines, Ontario, Canada, from February 22 to February 26, 2005.

Author : Ewa Orlowska,Andrzej Szalas
Publisher : Physica
Page : 293 pages
File Size : 45,7 Mb
Release : 2013-11-11
Category : Computers
ISBN : 9783790818284

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Relational Methods for Computer Science Applications by Ewa Orlowska,Andrzej Szalas Pdf

This volume addresses all current aspects of relational methods and their applications in computer science. It presents a broad variety of fields and issues in which theories of relations provide conceptual or technical tools. The contributions address such subjects as relational methods in programming, relational constraints, relational methods in linguistics and spatial reasoning, relational modelling of uncertainty. All contributions provide the readers with new and original developments in the respective fields. The reader thus gets an interdisciplinary spectrum of the state of the art of relational methods and implementation-oriented solutions of problems related to these areas.

Author : Anastasios Mallios,Marina Haralampidou
Publisher : American Mathematical Soc.
Page : 466 pages
File Size : 47,6 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821838686

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Topological Algebras and Applications by Anastasios Mallios,Marina Haralampidou Pdf

The Fifth International Conference on Topological Algebras and Applications was held in Athens, Greece, from June 27th to July 1st of 2005. The main topic of the Conference was general theory of topological algebras and its various applications, with emphasis on the ``non-normed'' case. in addition to the study of the internal structure of non-normed, and even non-locally convex topological algebras, there are applications to other branches of mathematics, such as differential geometry of smooth manifolds, and mathematical physics, such as quantum relativity and quantum cosmology. Operator theory of unbounded operators and related non-normed topological algebras are intensively studied here. Other topics presented in this volume are topological homological algebra, topological algebraic geometry, sheaf theory and $K$-theory.

Author : Roland Glück,Luigi Santocanale,Michael Winter
Publisher : Springer Nature
Page : 309 pages
File Size : 52,9 Mb
Release : 2023-03-07
Category : Computers
ISBN : 9783031280832

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Relational and Algebraic Methods in Computer Science by Roland Glück,Luigi Santocanale,Michael Winter Pdf

This book constitutes the proceedings of the 20th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2023, which took place in Augsburg, Germany, during April 3–6, 2023. The 17 papers presented in this book were carefully reviewed and selected from 26 submissions. They deal with the development and dissemination of relation algebras, Kleene algebras, and similar algebraic formalisms. Topics covered range from mathematical foundations to applications as conceptual and methodological tools in computer science and beyond. Apart from the submitted articles, this volume features the abstracts of the presentations of the three invited speakers.

Author : N. Jacobson
Publisher : Springer
Page : 120 pages
File Size : 49,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540374275

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PI-Algebras by N. Jacobson Pdf

Author : Victor W. Marek,Ewa Orlowska,Roman Slowiński,Wojciech Ziarko
Publisher : Springer Science & Business Media
Page : 389 pages
File Size : 41,8 Mb
Release : 2007-04-17
Category : Computers
ISBN : 9783540716624

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Transactions on Rough Sets VII by Victor W. Marek,Ewa Orlowska,Roman Slowiński,Wojciech Ziarko Pdf

Together with volume VI of the Transactions on Rough Sets series, this book commemorates the life and work of Zdzislaw Pawlak (1926-2006). It presents papers that reflect the profound influence of a number of research initiatives by Professor Pawlak, introducing a number of advances in the foundations and applications of AI, engineering, logic, mathematics, and science, which have had significant implications in a number of research areas.

Author : Masamichi Takesaki
Publisher : Springer Science & Business Media
Page : 424 pages
File Size : 43,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461261889

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Theory of Operator Algebras I by Masamichi Takesaki Pdf

Mathematics for infinite dimensional objects is becoming more and more important today both in theory and application. Rings of operators, renamed von Neumann algebras by J. Dixmier, were first introduced by J. von Neumann fifty years ago, 1929, in [254] with his grand aim of giving a sound founda tion to mathematical sciences of infinite nature. J. von Neumann and his collaborator F. J. Murray laid down the foundation for this new field of mathematics, operator algebras, in a series of papers, [240], [241], [242], [257] and [259], during the period of the 1930s and early in the 1940s. In the introduction to this series of investigations, they stated Their solution 1 {to the problems of understanding rings of operators) seems to be essential for the further advance of abstract operator theory in Hilbert space under several aspects. First, the formal calculus with operator-rings leads to them. Second, our attempts to generalize the theory of unitary group-representations essentially beyond their classical frame have always been blocked by the unsolved questions connected with these problems. Third, various aspects of the quantum mechanical formalism suggest strongly the elucidation of this subject. Fourth, the knowledge obtained in these investigations gives an approach to a class of abstract algebras without a finite basis, which seems to differ essentially from all types hitherto investigated. Since then there has appeared a large volume of literature, and a great deal of progress has been achieved by many mathematicians.

Author : Shoichiro Sakai
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 43,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642619939

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C*-Algebras and W*-Algebras by Shoichiro Sakai Pdf

From the reviews: "This book is an excellent and comprehensive survey of the theory of von Neumann algebras. It includes all the fundamental results of the subject, and is a valuable reference for both the beginner and the expert." Mathematical Reviews

Author : M. Hazewinkel
Publisher : Elsevier
Page : 542 pages
File Size : 42,6 Mb
Release : 2006-05-30
Category : Mathematics
ISBN : 0080462499

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Handbook of Algebra by M. Hazewinkel Pdf

Algebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these have been named and many more could (and perhaps should) have a name or a convenient designation. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. If this happens, one should be able to find enough information in this Handbook to judge if it is worthwhile to pursue the quest. In addition to the primary information given in the Handbook, there are references to relevant articles, books or lecture notes to help the reader. An excellent index has been included which is extensive and not limited to definitions, theorems etc. The Handbook of Algebra will publish articles as they are received and thus the reader will find in this third volume articles from twelve different sections. The advantages of this scheme are two-fold: accepted articles will be published quickly and the outline of the Handbook can be allowed to evolve as the various volumes are published. A particularly important function of the Handbook is to provide professional mathematicians working in an area other than their own with sufficient information on the topic in question if and when it is needed. - Thorough and practical source for information - Provides in-depth coverage of new topics in algebra - Includes references to relevant articles, books and lecture notes

Author : Mark Burgin
Publisher : World Scientific
Page : 964 pages
File Size : 50,5 Mb
Release : 2016-10-27
Category : Business & Economics
ISBN : 9789814522694

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Theory of Knowledge by Mark Burgin Pdf

This book aims to synthesize different directions in knowledge studies into a unified theory of knowledge and knowledge processes. It explicates important relations between knowledge and information. It provides the readers with understanding of the essence and structure of knowledge, explicating operations and process that are based on knowledge and vital for society. The book also highlights how the theory of knowledge paves the way for more advanced design and utilization of computers and networks. Contents:IntroductionKnowledge Characteristics and TypologyKnowledge Evaluation and Validation in the Context of Epistemic StructuresKnowledge Structure and Functioning: Microlevel or Quantum Theory of KnowledgeKnowledge Structure and Functioning: Macrolevel or Theory of Average KnowledgeKnowledge Structure and Functioning: Megalevel or Global Theory of KnowledgeKnowledge Production, Acquisition, Engineering, and ApplicationKnowledge, Data, and InformationConclusion Readership: Graduate students and researchers in artificial intelligence and knowledge management.

Author : Lech Polkowski,Andrzej Skowron
Publisher : Physica
Page : 600 pages
File Size : 47,8 Mb
Release : 1998-07-20
Category : Business & Economics
ISBN : UOM:39015046474899

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Rough Sets in Knowledge Discovery 1 by Lech Polkowski,Andrzej Skowron Pdf

The ideas and techniques worked out in Rough Set Theory allow for knowledge reduction and to finding near - to - functional dependencies in data. This fact determines the importance of these techniques for the rapidly growing field of knowledge discovery. Volume 1 and 2 will bring together articles covering the present state of the methods developed in this field of research. Among the topics covered we may mention: rough mereology and rough mereological approach to knowledge discovery in distributed systems; discretization and quantization of attributes; morphological aspects of rough set theory; analysis of default rules in the framework of rough set theory.