Cylindric Algebras

Author: Leon Henkin,James Donald Monk,Alfred Tarski

Publisher: North Holland

ISBN: N.A

Category: Computers

Page: 508

View: 1355

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Volume I provides a detailed analysis of cylindric algebras, starting with a formulation of their axioms and a development of their elementary properties, and proceeding to a deeper study of their interrelationships by means of general algebraic notions such as subalgebras, homomorphisms, direct products, free algebras, reducts and relativized algebras.
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Universal Algebra, Algebraic Logic, and Databases

Author: B. Plotkin

Publisher: Springer Science & Business Media

ISBN: 940110820X

Category: Mathematics

Page: 438

View: 4832

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Modern algebra, which not long ago seemed to be a science divorced from real life, now has numerous applications. Many fine algebraic structures are endowed with meaningful contents. Now and then practice suggests new and unexpected structures enriching algebra. This does not mean that algebra has become merely a tool for applications. Quite the contrary, it significantly benefits from the new connections. The present book is devoted to some algebraic aspects of the theory of databases. It consists of three parts. The first part contains information about universal algebra, algebraic logic is the subject of the second part, and the third one deals with databases. The algebraic material of the flI'St two parts serves the common purpose of applying algebra to databases. The book is intended for use by mathematicians, and mainly by algebraists, who realize the necessity to unite theory and practice. It is also addressed to programmers, engineers and all potential users of mathematics who want to construct their models with the help of algebra and logic. Nowadays, the majority of professional mathematicians work in close cooperation with representatives of applied sciences and even industrial technology. It is neces sary to develop an ability to see mathematics in different particular situations. One of the tasks of this book is to promote the acquisition of such skills.
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Ordered Sets and Lattices II

Author: N.A

Publisher: American Mathematical Soc.

ISBN: 9780821895887

Category: Lattice theory

Page: 246

View: 2653

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This indispensable reference source contains a wealth of information on lattice theory. The book presents a survey of virtually everything published in the fields of partially ordered sets, semilattices, lattices, and Boolean algebras that was reviewed in Referativnyi Zhurnal Matematika from mid-1982 to the end of 1985. A continuation of a previous volume (the English translation of which was published by the AMS in 1989, as volume 141 in Translations - Series 2), this comprehensive work contains more than 2200 references. Many of the papers covered here were originally published in virtually inaccessible places. The compilation of the volume was directed by Milan Kolibiar of Comenius University at Bratislava and Lev A. Skornyakov of Moscow University. Of interest to mathematicians, as well as to philosophers and computer scientists in certain areas, this unique compendium is a must for any mathematical library.
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Computational Collective Intelligence. Semantic Web, Social Networks and Multiagent Systems

First International Conference, ICCCI 2009, Wroclaw, Poland, October 5-7, 2009, Proceedings

Author: Ryszard Kowalczyk

Publisher: Springer Science & Business Media

ISBN: 3642044409

Category: Computers

Page: 860

View: 3614

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Computational collective intelligence (CCI) is most often understood as a subfield of artificial intelligence (AI) dealing with soft computing methods that enable group decisions to be made or knowledge to be processed among autonomous units acting in distributed environments. The needs for CCI techniques and tools have grown signi- cantly recently as many information systems work in distributed environments and use distributed resources. Web-based systems, social networks and multi-agent systems very often need these tools for working out consistent knowledge states, resolving conflicts and making decisions. Therefore, CCI is of great importance for today’s and future distributed systems. Methodological, theoretical and practical aspects of computational collective int- ligence, such as group decision making, collective action coordination, and knowledge integration, are considered as the form of intelligence that emerges from the collabo- tion and competition of many individuals (artificial and/or natural). The application of multiple computational intelligence technologies such as fuzzy systems, evolutionary computation, neural systems, consensus theory, etc. , can support human and other collective intelligence and create new forms of CCI in natural and/or artificial s- tems.
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Proceedings of the International Conference on Algebra Dedicated to the Memory of A.I. Malcev

Author: Leonid A. Bokut',Anatoliĭ Ivanovich Malʹt︠s︡ev,I͡Uriĭ Leonidovich Ershov,A. I. Kostrikin

Publisher: American Mathematical Soc.

ISBN: 0821851381

Category: Mathematics

Page: 666

View: 655

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In August 1989, more than 700 Soviet algebraists and more than 200 foreign mathematicians convened in Novosibirsk in what was then the Soviet Union for the International Conference on Algebra. Dedicated to the memory of A.I. Mal'cev, the Russian algebraist and logician, the conference marked the first time since the International Congress of Mathematicians was held in Moscow in 1966 that Soviet algebraists could meet with a large number of their foreign colleagues. This volume contains the proceedings from this historic conference. Some of the Soviet contributors to this volume are not easily available from other sources. Some of the major figures in the field, including P.M. Cohn, P. Gabriel, N. Jacobson, E.R. Kolchin, and V. Platonov, contributed to this volume. The papers span a broad range of areas including groups, Lie algebras, associative and nonassociative rings, fields and skew fields, differential algebra, universal algebra, categories, combinatorics, logic, algebraic geometry, topology, and mathematical physics.
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Cylindric Algebras

Author: Bozzano G Luisa

Publisher: Elsevier

ISBN: 9780080887586

Category: Mathematics

Page: 301

View: 4349

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Volume II completes the description of the main aspects of the theory, covering representation questions, model theory and decision problems for them, translations from logic to algebra and vice-versa, and relationships with other algebraic versions of logic.
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Cylindric-like Algebras and Algebraic Logic

Author: Hajnal Andréka,Miklós Ferenczi,István Németi

Publisher: Springer Science & Business Media

ISBN: 3642350259

Category: Mathematics

Page: 474

View: 5754

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Algebraic logic is a subject in the interface between logic, algebra and geometry, it has strong connections with category theory and combinatorics. Tarski’s quest for finding structure in logic leads to cylindric-like algebras as studied in this book, they are among the main players in Tarskian algebraic logic. Cylindric algebra theory can be viewed in many ways: as an algebraic form of definability theory, as a study of higher-dimensional relations, as an enrichment of Boolean Algebra theory, or, as logic in geometric form (“cylindric” in the name refers to geometric aspects). Cylindric-like algebras have a wide range of applications, in, e.g., natural language theory, data-base theory, stochastics, and even in relativity theory. The present volume, consisting of 18 survey papers, intends to give an overview of the main achievements and new research directions in the past 30 years, since the publication of the Henkin-Monk-Tarski monographs. It is dedicated to the memory of Leon Henkin.​
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Relation Algebras by Games

Author: Robin Hirsch,Ian Hodkinson

Publisher: Gulf Professional Publishing

ISBN: 9780444509321

Category: Mathematics

Page: 691

View: 8310

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In part 2, games are introduced, and used to axiomatise various classes of algebras. Part 3 discusses approximations to representability, using bases, relation algebra reducts, and relativised representations. Part 4 presents some constructions of relation algebras, including Monk algebras and the 'rainbow construction', and uses them to show that various classes of representable algebras are non-finitely axiomatisable or even non-elementary. Part 5 shows that the representability problem for finite relation algebras is undecidable, and then in contrast proves some finite base property results. Part 6 contains a condensed summary of the book, and a list of problems. There are more than 400 exercises. P The book is generally self-contained on relation algebras and on games, and introductory text is scattered throughout. Some familiarity with elementary aspects of first-order logic and set theory is assumed, though many of the definitions are given.-
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