Algebraic Methods in Philosophical Logic

by J. Michael Dunn, Gary Hardegree

Overview

This comprehensive text demonstrates how various notions of logic can be viewed as notions of universal algebra. It is aimed primarily at logisticians in mathematics, philosophy, computer science and linguistics with an interest in algebraic logic, but is also accessible to those from a non-logistics background. The premise of the text is that standard algebraic results (representations) translate into standard logical results (completeness) and it identifies classes of algebras appropriate for classical and non-classical logic studies, including: gaggles, distributoids, partial- gaggles, and tonoids. Also discused is the idea that logic is fundamentally information based, with its main elements being propositions, that can be understood as sets of information states. Logics are considered in various senses such as systems of theorems, consequence relations and, symmetric consequence relations.

Product Details

ISBN-13:	9780198531920
Publisher:	Oxford University Press
Publication date:	08/30/2001
Series:	Oxford Logic Guides , #41
Pages:	486
Product dimensions:	9.42(w) x 6.34(h) x 1.23(d)

About the Author

Indiana University

University of Massachusetts

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 DualityReferencesIndex

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

From the Publisher

A textbook for a graduate or advanced undergraduate course exploring some of the intersection between algebraic and philosophical logic. A major theme is that standard algebraic-type results, such as representation theorems, translate into standard logic-type results, such as completeness theorems. Computer and information scientists are the target readers. Annotation c. Book News, Inc., Portland, OR (booknews.com)