Algebraic Methods in Philosophical Logic

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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 e.g. systems of theorems, consequence relations and, symmetric consequence relations.
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Editorial Reviews

From The Critics
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)
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Product Details

  • ISBN-13: 9780198531920
  • Publisher: Oxford University Press, USA
  • Publication date: 8/28/2001
  • Series: Oxford Logic Guides Series , #41
  • Pages: 488
  • Product dimensions: 9.10 (w) x 6.00 (h) x 1.20 (d)

Meet the Author

Indiana University

University of Massachusetts

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Table of Contents

1 Introduction 1
2 Universal Algebra 10
3 Order, Lattices, and Boolean Algebras 55
4 Syntax 125
5 Semantics 141
6 Logic 184
7 Matrices and Atlases 226
8 Representation Theorems 277
9 Classical Propositional Logic 321
10 Modal Logic and Closure Algebras 356
11 Intuitionistic Logic and Heyting Algebras 380
12 Gaggles: General Galois Logics 394
13 Representations and Duality 431
References 445
Index 455
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