Algebraic Methods in Philosophical Logic [Hardcover]

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.

1. Introduction
2. Universal Algebra
3. Order, Lattices and Boolean Algebras
4. Syntax
5. Semantics
6. Logic
7. Matrices and Atlases
8. Representation Theorems
9. Classical Propositional Logic
10. Modal Logic and Closure Algebras
11. Intuitionistic Logic
12. Gaggles: General Galois Logics
13. Representation and Duality
References
Index

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