Universal Algebra, Algebraic Logic, and Databases

Author: B. Plotkin

Publisher: Springer Science & Business Media

ISBN: 940110820X

Category: Mathematics

Page: 438

View: 3967

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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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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: 8397

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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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Algebraic Structures in Automata and Databases Theory

Author: Boris Isaakovich Plotkin,L. Ja Greenglaz,A. A. Gvaramija

Publisher: World Scientific

ISBN: 9789810209360

Category: Mathematics

Page: 280

View: 9502

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The book is devoted to the investigation of algebraic structure. The emphasis is on the algebraic nature of real automation, which appears as a natural three-sorted algebraic structure, that allows for a rich algebraic theory. Based on a general category position, fuzzy and stochastic automata are defined. The final chapter is devoted to a database automata model. Database is defined as an algebraic structure and this allows us to consider theoretical problems of databases.
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Algebraic Structures in Automata and Database Theory

Author: B I Plotkin,L Ja Greenglaz,A A Gvaramija

Publisher: World Scientific

ISBN: 9814505668

Category: Mathematics

Page: 296

View: 4853

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The book is devoted to the investigation of algebraic structure. The emphasis is on the algebraic nature of real automation, which appears as a natural three-sorted algebraic structure, that allows for a rich algebraic theory. Based on a general category position, fuzzy and stochastic automata are defined. The final chapter is devoted to a database automata model. Database is defined as an algebraic structure and this allows us to consider theoretical problems of databases. Contents:PrefacePreliminariesPure AutomataConstructions and Decomposition of Pure AutomataLinear AutomataVarieties of AutomataAutomata Model of DatabaseBibliographyIndex Readership: Graduate students in mathematics and mathematicians. keywords:Automata;Database Theory;Fuzzy Automata;Stochastic Automata;Linear Automata
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Logic for Programming, Artificial Intelligence, and Reasoning

8th International Conference, LPAR 2001, Havana, Cuba, December 3-7, 2001, Proceedings

Author: Robert Nieuwenhuis,Andrei Voronkov

Publisher: Springer

ISBN: N.A

Category: Logic programming

Page: 738

View: 4500

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This book constitutes the refereed proceedings of the 8th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, LPAR 2001, held in Havana, Cuba, in December 2001. The 40 revised full papers presented together with an invited paper were carefully reviewed and selected from 112 submissions. The book offers topical sections on verification, guarded logic, agents, automated theorem proving, non-classical logics, types, experimental aspects, foundations of logic, CSP and SAT, nonmonotonic reasoning, semantics, termination, knowledge-based systems, analysis of logic programs, databases and knowledge bases, and program analysis and proof planning.
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