Massimiliano Carrara
University of Padua
In this paper, we approach the problem of classical recapture for LP and K3 by using normality operators. These generalize the consistency and determinedness operators from Logics of Formal Inconsistency and Underterminedness, by expressing, in any many-valued logic, that a given formula has a classical truth value (0 or 1). In particular, in the rst part of the paper we introduce the logics LPe and Ke3 , which extends LP and K3 with normality operators, and we establish a classical recapture result based on the two logics. In the second part of the paper, we compare the approach in terms of normality operators with an established approach to classical recapture, namely minimal inconsistency. Finally, we discuss technical issues connecting LPe and Ke3 to the tradition of Logics of Formal Inconsistency and Underterminedness.
Keywords Kleene logics  Classical Recapture  Normality Operators  Logics of Formal Inconsistency
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Saving Truth From Paradox.Hartry Field - 2008 - Oxford University Press.
Outline of a Theory of Truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
The Logic of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
Multiple-Conclusion Lp and Default Classicality.Jc Beall - 2011 - Review of Symbolic Logic 4 (2):326-336.

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