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Cylindric Algebras
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Book Synopsis Cylindric Algebras by : Bozzano G Luisa
Download or read book Cylindric Algebras written by Bozzano G Luisa and published by Elsevier. This book was released on 1985-02-01 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Cylindric-like Algebras and Algebraic Logic by : Hajnal Andréka
Download or read book Cylindric-like Algebras and Algebraic Logic written by Hajnal Andréka and published by Springer Science & Business Media. This book was released on 2014-01-27 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Cylindric Algebras written by Leon Henkin and published by North Holland. This book was released on 1971 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Cylindric Algebras written by Leon Henkin and published by . This book was released on 1985 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Cylindric Set Algebras by : L. Henkin
Download or read book Cylindric Set Algebras written by L. Henkin and published by Springer. This book was released on 2006-11-14 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Relation Algebras by Games by : Robin Hirsch
Download or read book Relation Algebras by Games written by Robin Hirsch and published by Elsevier. This book was released on 2002-08-15 with total page 711 pages. Available in PDF, EPUB and Kindle. Book excerpt: Relation algebras are algebras arising from the study of binary relations.They form a part of the field of algebraic logic, and have applications in proof theory, modal logic, and computer science. This research text uses combinatorial games to study the fundamental notion of representations of relation algebras. Games allow an intuitive and appealing approach to the subject, and permit substantial advances to be made. The book contains many new results and proofs not published elsewhere. It should be invaluable to graduate students and researchers interested in relation algebras and games. After an introduction describing the authors' perspective on the material, the text proper has six parts. The lengthy first part is devoted to background material, including the formal definitions of relation algebras, cylindric algebras, their basic properties, and some connections between them. Examples are given. Part 1 ends with a short survey of other work beyond the scope of the book. 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. 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. Chapter 2 introduces the necessary universal algebra and model theory, and more specific model-theoretic ideas are explained as they arise.
Book Synopsis Cylindric-like Algebras and Algebraic Logic by : Hajnal Andréka
Download or read book Cylindric-like Algebras and Algebraic Logic written by Hajnal Andréka and published by . This book was released on 2012 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Cylindric Algebras by : Bozzano G Luisa
Download or read book Cylindric Algebras written by Bozzano G Luisa and published by North Holland. This book was released on 2005-11-22 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Algebraic Logic written by Paul R. Halmos and published by Courier Dover Publications. This book was released on 2016-01-18 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published: New York: Chelsea Publishing Company, 1962.
Book Synopsis Cylindric Set Algebras by : L. Henkin
Download or read book Cylindric Set Algebras written by L. Henkin and published by . This book was released on 2014-01-15 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Cylindric Algebras written by Leon Henkin and published by . This book was released on 1971 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Some Results on Relativized Cylindric Algebras by : Diane Resek
Download or read book Some Results on Relativized Cylindric Algebras written by Diane Resek and published by . This book was released on 1974 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Multi-Dimensional Modal Logic by : Maarten Marx
Download or read book Multi-Dimensional Modal Logic written by Maarten Marx and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modal Logic is a branch of logic with applications in many related disciplines such as computer science, philosophy, linguistics and artificial intelligence. Over the last twenty years, in all of these neighbouring fields, modal systems have been developed that we call multi-dimensional. (Our definition of multi-dimensionality in modal logic is a technical one: we call a modal formalism multi-dimensional if, in its intended semantics, the universe of a model consists of states that are tuples over some more basic set.) This book treats such multi-dimensional modal logics in a uniform way, linking their mathematical theory to the research tradition in algebraic logic. We will define and discuss a number of systems in detail, focusing on such aspects as expressiveness, definability, axiomatics, decidability and interpolation. Although the book will be mathematical in spirit, we take care to give motivations from the disciplines mentioned earlier on.
Book Synopsis Set Theoretical Logic-The Algebra of Models by : W Felscher
Download or read book Set Theoretical Logic-The Algebra of Models written by W Felscher and published by CRC Press. This book was released on 2000-05-30 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to mathematical logic in which all the usual topics are presented: compactness and axiomatizability of semantical consequence, Löwenheim-Skolem-Tarski theorems, prenex and other normal forms, and characterizations of elementary classes with the help of ultraproducts. Logic is based exclusively on semantics: truth and satisfiability of formulas in structures are the basic notions. The methods are algebraic in the sense that notions such as homomorphisms and congruence relations are applied throughout in order to gain new insights. These concepts are developed and can be viewed as a first course on universal algebra. The approach to algorithms generating semantical consequences is algebraic as well: for equations in algebras, for propositional formulas, for open formulas of predicate logic, and for the formulas of quantifier logic. The structural description of logical consequence is a straightforward extension of that of equational consequence, as long as Boolean valued propositions and Boolean valued structures are considered; the reduction of the classical 2-valued case then depends on the Boolean prime ideal theorem.
Book Synopsis The Life and Work of Leon Henkin by : María Manzano
Download or read book The Life and Work of Leon Henkin written by María Manzano and published by Springer. This book was released on 2014-10-23 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive book on the life and works of Leon Henkin (1921–2006), an extraordinary scientist and excellent teacher whose writings became influential right from the beginning of his career with his doctoral thesis on “The completeness of formal systems” under the direction of Alonzo Church. Upon the invitation of Alfred Tarski, Henkin joined the Group in Logic and the Methodology of Science in the Department of Mathematics at the University of California Berkeley in 1953. He stayed with the group until his retirement in 1991. This edited volume includes both foundational material and a logic perspective. Algebraic logic, model theory, type theory, completeness theorems, philosophical and foundational studies are among the topics covered, as well as mathematical education. The work discusses Henkin’s intellectual development, his relation to his predecessors and contemporaries and his impact on the recent development of mathematical logic. It offers a valuable reference work for researchers and students in the fields of philosophy, mathematics and computer science.
Book Synopsis Universal Algebraic Logic by : Hajnal Andréka
Download or read book Universal Algebraic Logic written by Hajnal Andréka and published by Springer Nature. This book was released on 2022-11-01 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a comprehensive introduction to Universal Algebraic Logic. The three main themes are (i) universal logic and the question of what logic is, (ii) duality theories between the world of logics and the world of algebra, and (iii) Tarskian algebraic logic proper including algebras of relations of various ranks, cylindric algebras, relation algebras, polyadic algebras and other kinds of algebras of logic. One of the strengths of our approach is that it is directly applicable to a wide range of logics including not only propositional logics but also e.g. classical first order logic and other quantifier logics. Following the Tarskian tradition, besides the connections between logic and algebra, related logical connections with geometry and eventually spacetime geometry leading up to relativity are also part of the perspective of the book. Besides Tarskian algebraizations of logics, category theoretical perspectives are also touched upon. This book, apart from being a monograph containing state of the art results in algebraic logic, can be used as the basis for a number of different courses intended for both novices and more experienced students of logic, mathematics, or philosophy. For instance, the first two chapters can be used in their own right as a crash course in Universal Algebra.
Book Synopsis Handbook of Philosophical Logic by : Dov M. Gabbay
Download or read book Handbook of Philosophical Logic written by Dov M. Gabbay and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is with great pleasure that we are presenting to the community the second edition of this extraordinary handbook. It has been over 15 years since the publication of the first edition and there have been great changes in the landscape of philosophical logic since then. The first edition has proved invaluable to generations of students and researchers in formal philosophy and language, as weIl as to consumers of logic in many applied areas. The main logic artiele in the Encyelopaedia Britannica 1999 has described the first edition as 'the best starting point for exploring any of the topics in logic'. We are confident that the second edition will prove to be just as good. ! The first edition was the second handbook published for the logic commu nity. It followed the North Holland one volume Handbook 0/ Mathematical Logic, published in 1977, edited by the late Jon Barwise. The four volume Handbook 0/ Philosophical Logic, published 1983-1989 came at a fortunate at the evolution of logic. This was the time when logic temporal junction was gaining ground in computer science and artificial intelligence cireles. These areas were under increasing commercial pressure to provide devices which help andjor replace the human in his daily activity. This pressure required the use of logic in the modelling of human activity and organisa tion on the one hand and to provide the theoretical basis for the computer program constructs on the other.
