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Algebraic methods in philosophical logic. (English) Zbl 1014.03002

Oxford Logic Guides. 41. Oxford: Oxford University Press. xvi, 470 p. (2001).
Publisher’s description: This comprehensive text demonstrates how various notions of logic can be viewed as notions of universal algebra. It is aimed primarily at logicians in mathematics, philosophy, computer science and linguistics with an interest in algebraic logic, but is also accessible to those from a non-logic 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 nonclassical logic studies, including: gaggles, distributoids, partial gaggles, and tonoids. Also discussed 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.

MSC:

03-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematical logic and foundations
03Gxx Algebraic logic
03-02 Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations
03A05 Philosophical and critical aspects of logic and foundations