David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Cambridge University Press (1996)
Classical logic has proved inadequate in various areas of computer science, artificial intelligence, mathematics, philosopy and linguistics. This is an introduction to extensions of first-order logic, based on the principle that many-sorted logic (MSL) provides a unifying framework in which to place, for example, second-order logic, type theory, modal and dynamic logics and MSL itself. The aim is two fold: only one theorem-prover is needed; proofs of the metaproperties of the different existing calculi can be avoided by borrowing them from MSL. To make the book accessible to readers from different disciplines, whilst maintaining precision, the author has supplied detailed step-by-step proofs, avoiding difficult arguments, and continually motivating the material with examples. Consequently this can be used as a reference, for self-teaching or for first-year graduate courses.
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Jeffrey Ketland (2006). Structuralism and the Identity of Indiscernibles. Analysis 66 (292):303–315.
Guillermo E. Rosado Haddock (2010). Some Uses of Logic in Rigorous Philosophy. Axiomathes 20 (2-3):385-398.
Carlos Areces, Patrick Blackburn, Antonia Huertas & María Manzano (2013). Completeness in Hybrid Type Theory. Journal of Philosophical Logic (2-3):1-30.
Jeffrey Ketland (2011). Identity and Indiscernibility. Review of Symbolic Logic 4 (2):171-185.
Robert M. Solovay, R. D. Arthan & John Harrison (2012). Some New Results on Decidability for Elementary Algebra and Geometry. Annals of Pure and Applied Logic 163 (12):1765-1802.
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