Информационная система "Конференции"

Abstracts

Non-classical logics, proof theory and universal algebra

Given a logic, how to obtain its paraconsistent counterpart? Given a paraconsistent logic, how to obtain the non-paraconsistent counterpart of this logic? Many systems of paraconsistent logics were already proposed using different methods and techniques. Although this fact, there is not a singular way to generate paraconsistent logics. I propose a method called "paraconsistentization of logics" which is able to give, at least, a partial answer to the above questions.
I examine the plurality of ways which can be used to create a paraconsistent logic: defining paraconsistent negations in the language (Beziau's argument showing how to generate paraconsistent logics from modal logics and vice-versa), by restrictions in the axioms (the example of some modal paraconsistent logics) and changing valuations (many-valued logics). I apply my methodology to some modal logics and many-valued logics in order to justify the paraconsistentization and, jumping into abstraction, the creation of a general theory of the combination of logics.

References

[1] Carnielli,W. A.; Marcos,J. A taxonomy of C-systems. Paraconsistency: The logical way to the inconsistent.
Papers from the 2nd World Congress (WCP’2000) held in So Sebastio, May 12–19, 2000. Edited by Walter A. Carnielli, Marcelo E. Coniglio and Itala M. Loffredo D’Ottaviano. Lecture Notes in Pure and Appl. Math., 228, Dekker, New York, 2002

[2] Carnielli,W. A.; Coniglio,M. E.; Marcos,J. Logics of formal inconsistency.
In D. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic, volume 12. Kluwer Academic Publishers, in print.

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