Author: Bozzano G Luisa
Publisher: Elsevier
ISBN: 0080887589
Category : Science
Languages : en
Pages : 313
Book Description
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.
Cylindric Algebras
Author: Bozzano G Luisa
Publisher: Elsevier
ISBN: 0080887589
Category : Science
Languages : en
Pages : 313
Book Description
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.
Publisher: Elsevier
ISBN: 0080887589
Category : Science
Languages : en
Pages : 313
Book Description
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.
Cylindric-like Algebras and Algebraic Logic
Author: Hajnal Andréka
Publisher: Springer Science & Business Media
ISBN: 3642350259
Category : Mathematics
Languages : en
Pages : 457
Book Description
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.
Publisher: Springer Science & Business Media
ISBN: 3642350259
Category : Mathematics
Languages : en
Pages : 457
Book Description
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.
Cylindric Set Algebras
Author: L. Henkin
Publisher: Springer
ISBN: 3540387900
Category : Mathematics
Languages : en
Pages : 328
Book Description
Publisher: Springer
ISBN: 3540387900
Category : Mathematics
Languages : en
Pages : 328
Book Description
Cylindric Algebras
Author: Leon Henkin
Publisher: North Holland
ISBN:
Category : Computers
Languages : en
Pages : 524
Book Description
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.
Publisher: North Holland
ISBN:
Category : Computers
Languages : en
Pages : 524
Book Description
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.
Cylindric Algebras
Author: Leon Henkin
Publisher:
ISBN:
Category : Cylindric algebras
Languages : en
Pages : 322
Book Description
Publisher:
ISBN:
Category : Cylindric algebras
Languages : en
Pages : 322
Book Description
Cylindric-like Algebras and Algebraic Logic
Author: Hajnal Andréka
Publisher:
ISBN: 9789639453159
Category : Algebraic logic
Languages : en
Pages : 478
Book Description
Publisher:
ISBN: 9789639453159
Category : Algebraic logic
Languages : en
Pages : 478
Book Description
Relation Algebras by Games
Author: Robin Hirsch
Publisher: Elsevier
ISBN: 0080540457
Category : Mathematics
Languages : en
Pages : 711
Book Description
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.
Publisher: Elsevier
ISBN: 0080540457
Category : Mathematics
Languages : en
Pages : 711
Book Description
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.
Algebraic Logic
Author: Paul R. Halmos
Publisher: Courier Dover Publications
ISBN: 0486801454
Category : Mathematics
Languages : en
Pages : 276
Book Description
Originally published: New York: Chelsea Publishing Company, 1962.
Publisher: Courier Dover Publications
ISBN: 0486801454
Category : Mathematics
Languages : en
Pages : 276
Book Description
Originally published: New York: Chelsea Publishing Company, 1962.
Cylindric Algebras
Author: Bozzano G Luisa
Publisher: North Holland
ISBN: 9780720420432
Category : Mathematics
Languages : en
Pages : 508
Book Description
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.
Publisher: North Holland
ISBN: 9780720420432
Category : Mathematics
Languages : en
Pages : 508
Book Description
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.
Cylindric Set Algebras
Author: L. Henkin
Publisher:
ISBN: 9783662179758
Category :
Languages : en
Pages : 336
Book Description
Publisher:
ISBN: 9783662179758
Category :
Languages : en
Pages : 336
Book Description