Normality operators and Classical Recapture in Extensions of Kleene Logics


Authors
Massimiliano Carrara
University of Padua
Abstract
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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References found in this work BETA

Saving Truth From Paradox.Hartry Field - 2008 - Oxford University Press.
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Sorting Out the Sorites.David Ripley - 2013 - In Francesco Berto, Edwin Mares & Koji Tanaka (eds.), Paraconsistency: Logic and Applications. pp. 329-348.

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