Algebraic methods in philosophical logic

J. Michael Dunn and Gary M. Hardegree

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.

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[目次]

  • 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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この本の情報

書名 Algebraic methods in philosophical logic
著作者等 Dunn, Jon Michael
Hardegree, Gary M.
Hardegree Gary
Dunn J. Michael
シリーズ名 Oxford logic guides
出版元 Clarendon Press;Oxford University Press
刊行年月 2001
ページ数 xv, 470 p.
大きさ 24 cm
ISBN 0198531923
NCID BA52890254
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言語 英語
出版国 イギリス
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