E-Book 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.
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OXFORD LOGIC GUIDES 0 41 Algebraic Methods in Philosophical Logic J. MICHAEL DUNN and GARY M. HARDEGREE OXFORD SCIENCE PUBLICATIONS OXFORD LOGIC GUIDES: 41 General Editors DOV M. GABBAY ANGUS MACINTYRE DANA SCOTT OXFORD LOGIC GUIDES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. Jane Bridge: Beginning model theory: the completeness theorem and sorne consequences Michael Dummett: Elements of intuitionnism (1st edition) A. S. Troelstra: Choice sequences: a chapter of intuitionistic mathematics J. L. Bell: Boolean-valued models and independence proofs in set theory (1st edition) Krister Seberberg: Classical propositional operators: an exercise in the foundation of logic G. C. Smith: The Boole-De Morgan correspondence 1842-1864 Alec Fisher: Formal number theory and computability: a work book Anand Pillay: An introduction to stability theory H. E. Rose: Subrecursion: functions and hierarchies Michael Hallett: Cantorian set theory and limitation of size R. Mansfield and G. Weitkamp: Recursive aspects of descriptive set theory J. L. Bell: Boolean-valued models and independence proofs in set theory (2nd edition) Melvin Fitting: Computability theory: semantics and logic progranrning J. L. Bell: Toposes and local set theories: an introduction R. Kaye: Models of Peano arithmetic J. Chapman and F. Rowbottom: Relative category theory and geometric morphisms: a logical approach Stewart Shapiro: Foundations without foundationalisnn John P. Cleave: A study of logics R. M. Smullyan: Godel's incompleteness theorems T. E. Forster: Set theory with a universal set: exploring an untyped universe C. McLarty: Elementary categories, elementary toposes R. M. Smullyan: Recursion theory for metamathematics Peter Clote and Jan Krajiacek:Arithmetic, proof theory, and computational complexity A. Tarski: Introduction to logic and to the methodology of deductive sciences G. Malinowski: Many valued logics Alexandre Borovik and Ali Nesin: Groups of finite Morley rank R. M. Smullyan: Diagonalization and self-reference Dov M. Gabbay, Ian Hodkinson, and Mark Reynolds: Temporal logic: mathematical foundations and computational aspects: Volume I Saharon Shelah: Cardinal arithmetic Erik Sandewall: Features and fiuents: Volume I: a systematic approach to the representation of knowledge about dynamical systems T. E. Forster: Set theory with a universal set: exploring an untyped universe (2nd edition) Anand Pillay: Geometric stability theory Dov. M. Gabbay: Labelled deductive systems Raymond M. Smullyan and Melvin Fitting: Set theory and the continuum problem Alexander Chagrov and Michael Zakharyaschev: Modal logic G. Sambin and J. Smith: Twenty-five years of Ma tin-Lof constructive type theory Maria Manzano: Model theory Dov M. Gabbay: Fibring logics Micha