Algebraic Methods in Philosophical Logic

Klappentext 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. Zusammenfassung 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 a non-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) translate into 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 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. Inhaltsverzeichnis 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 14: References 15: Index ...

Inhalt
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
14: References
15: Index

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