Algebraic Methods in Philosophical Logic

Hardcover | June 1, 2001

byJ. Michael Dunn, Gary Hardegree

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This comprehensive text demonstrates how various notions of logic can be viewed as notions of universal algebra. It is aimed primarily for logisticians in mathematics, philosophy, computer science and linguistics with an interest in algebraic logic, but is also accessible to those from anon-logistics background. It is suitable for researchers, graduates and advanced undergraduates who have an introductory knowledge of algebraic logic providing more advanced concepts, as well as more theoretical aspects. The main theme is that standard algebraic results (representations) translateinto standard logical results (completeness). Other themes involve identification of a class of algebras appropriate for classical and non-classical logic studies, including: gaggles, distributoids, partial- gaggles, and tonoids. An imporatant sub title is that logic is fundamentally informationbased, with its main elements being propositions, that can be understood as sets of information states. Logics are considered in various senses e.g. systems of theorems, consequence relations and, symmetric consequence relations.

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This comprehensive text demonstrates how various notions of logic can be viewed as notions of universal algebra. It is aimed primarily for logisticians in mathematics, philosophy, computer science and linguistics with an interest in algebraic logic, but is also accessible to those from anon-logistics background. It is suitable for rese...

J. Michael Dunn is at Indiana University. Gary Hardegree is at University of Massachusetts.

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Format:HardcoverDimensions:486 pages, 9.21 × 6.14 × 1.14 inPublished:June 1, 2001Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198531923

ISBN - 13:9780198531920

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Table of Contents

1. Introduction2. Universal Algebra3. Order, Lattices and Boolean Algebras4. Syntax5. Semantics6. Logic7. Matrices and Atlases8. Representation Theorems9. Classical Propositional Logic10. Modal Logic and Closure Algebras11. Intuitionistic Logic12. Gaggles: General Galois Logics13. Representation and Duality14. References15. Index

Editorial Reviews

"This book provides an introduction tot he algebraic study of classical and non-classical propositional logics. . . . The general theme of the text is to show how standard logical results, such as completeness, are obtained from standard algebraic results, such as representation theorems. . . .Overall, the book is a rich source of information and the authors' style of presentation makes it enjoyable to read." -- Mathematical Reviews