An Adaptive Logic Based on Jaśkowskiˈs Approach to Paraconsistency

Journal of Philosophical Logic 35 (6):539-567 (2006)
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Abstract

In this paper, I present the modal adaptive logic $AJ^{r}$ (based on S5) as well as the discussive logic $D_{2}^{r}$ that is defined from it. $D_{2}^{r}$ is a (nonmonotonic) alternative for Jaśkowski's paraconsistent system D₂. Like D₂, $D_{2}^{r}$ validates all single-premise rules of Classical Logic. However, for formulas that behave consistently, $D_{2}^{r}$ moreover validates all multiple-premise rules of Classical Logic. Importantly, and unlike in the case of D₂, this does not require the introduction of discussive connectives. It is argued that this has clear advantages with respect to one of the main application contexts of discussive logics, namely the interpretation of discussions

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References found in this work

A New Introduction to Modal Logic.M. J. Cresswell & G. E. Hughes - 1996 - New York: Routledge. Edited by M. J. Cresswell.
A New Introduction to Modal Logic.G. E. Hughes - 1996 - New York: Psychology Press. Edited by M. J. Cresswell.
On Inferences from Inconsistent Premises.Nicholas Rescher & Ruth Manor - 1970 - Theory and Decision 1 (2):179-217, 1970-1971.
Minimally inconsistent LP.Graham Priest - 1991 - Studia Logica 50 (2):321 - 331.

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