Polynomizing: Logic Inference In Polynomial Format And The Legacy Of Boole

Abstract

Polynomizing is a term that intends to describe the uses of polynomiallike representations as a reasoning strategy and as a tool for scientific heuristics. I show how proof-theory and semantics for classical and several non-classical logics can be approached from this perspective, and discuss the assessment of this prospect, in particular to recover certain ideas of George Boole in unifying logic, algebra and the differential calculus. © 2007 Springer-Verlag Berlin Heidelberg.64349364Agudelo, J.C., Carnielli, W.A.: Quantum algorithms, paraconsistent computation and Deutsch's problem. In Bhanu Prasad et al., eds.: Proceedings of the 2nd Indian International Conference on Artificial Intelligence, Pune, India, December 20-22 (2005) IICAI 2005, 1609-1628. Pre-print available from CLE e-Prints 5(10) (2005) ftp://logica.cle.unicamp.br/pub/e-prints/ MTPs-CompQuant%28Ing%29.pdfAhmed, T.S., Algebraic logic, where does it stand today? (2005) Bull. 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