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| Author(s): |
Pietro Kreitlon Carolino
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Filosofia e Ciências Humanas |
| Defense date: | 2009-04-09 |
| Examining board members: |
Walter Alexandre Carnielli;
Marcelo Esteban Coniglio;
Rodrigo de Alvarenga Freire
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| Advisor: | Walter Alexandre Carnielli |
| Abstract | |
The work of George Boole, cornerstone of contemporary logic, does not draw a clear distinction between the methods of mathematical analysis, and those of logic proper. If, on the one hand, this lack of well-de ned borders has earned it harsh criticism, on the other hand it makes Boole's work a true synthesis of formal thought, inherited from Aristotle, Leibniz, Newton and the 17th-century analysts, such as Taylor, MacLaurin and Lagrange. What was called polynomizing in [12] is precisely the attempty to re-evaluate the methods originiating in Boole and Leibniz, which allow one to represent the semantics and syntax of varioius logical systems through algebraic manipulation. Using elementary combinatorial results, it is possible to treat all multivalent truth-functional logics by polynomial manipulation; not only these, but some non-truth-functional logics, and also fragments of first-order logic, which formalize Aristotle's classical theory of syllogisms. The present work intends to throw light upon such questions in a broader way, and to investigate the possibility of extending the method of polynomization to other logics. Some positive results are obtained, such as new proofs of known theorems, but also some negative ones, which show the inherent limitations of the method. We further investigate the relationship between polynomization of logics and other known treatments, such as paraconsistentization, temporalization, algebrization etc. (AU) | |