Walter Carnielli (CLE and IFCH–Unicamp): “Possible-Translations Semantics: A tool to combine logics, and to give them meaning”
It is a demanding challenge to find semantics for non-standard logics which can be simultaneously strongly adequate and intuitively acceptable. The idea of Possible-Translations Semantics (PTS’s) is to serve as a unifying framework, not only in giving meaning to such logics, but also as a handy tool to combine them (cf., ). Contrary to some traditional philosophical views, contradictions are precious in informal reasoning. It is a task of logic to offer a suitable formal model for the perfectly licit act of reasoning under contradictions, and paraconsistent logic accomplishes this. In particular, the wide family of Logics of Formal Inconsistency (LFI’s) (cf. ) achieves this in a remarkably natural and elegant way. The PTS’s were devised in 1990 (cf. ) in order to offer a palatable interpretation for some non-classical logics, and are well adapted to LFI’s. Improved recent expositions appear in ,  and . This tutorial intends to be an introduction to the PTS’s, its methods and its relevant literature.
- W. A. Carnielli, M. E. Coniglio , D. Gabbay, P. Gouveia, and C. Sernadas. Analysis and Synthesis of Logics: How to Cut and Paste Reasoning Systems,. Applied Logic Series volume 35, Springer-Verlag, 2008.
- W. A. Carnielli and M. E. Coniglio. Combining Logics. Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/logic-combining/
-W. A. Carnielli, M. E. Coniglio and J. Marcos. Logics of Formal Inconsistency. In: D. Gabbay; F. Guenthner. (Org.). Handbook of Philosophical Logic. 2 ed. Springer, 2007, v. 14, pp. 15-107.
- W. A. Carnielli. Possible-translations semantics for paraconsistent logics. In: D. Batens et al. (Org.). Frontiers in Paraconsistent Logic: Proceedings of the I World Congress on Paraconsistency. Kings College Publications, London, 2000, pp. 159-172.
 – W. A. Carnielli, Many-valued logics and plausible reasoning. Proceedings of the XX International Congress on Many-Valued Logics, IEEE Computer Society, (1990) pp. 328-35.
- J. Marcos. Possible-translations semantics for some weak classically-based paraconsistent logics. Journal of Applied Non-Classical Logics 18(1): 7-28, 2008.