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• W2897847887 abstract "Paraconsistent logics are logical systems that reject the classical principle, usually dubbed Explosion, that a contradiction implies everything. However, the received view about paraconsistency focuses only the inferential version of Explosion, which is concerned with formulae, thereby overlooking other possible accounts. In this paper, we propose to focus, additionally, on a meta-inferential version of Explosion, i.e. which is concerned with inferences or sequents. In doing so, we will offer a new characterization of paraconsistency by means of which a logic is paraconsistent if it invalidates either the inferential or the meta-inferential notion of Explosion. We show the non-triviality of this criterion by discussing a number of logics. On the one hand, logics which validate and invalidate both versions of Explosion, such as classical logic and Asenjo–Priest’s 3-valued logic $$mathbf {LP}$$ . On the other hand, logics which validate one version of Explosion but not the other, such as the substructural logics $$mathbf {TS}$$ and $$mathbf {ST}$$ , introduced by Malinowski and Cobreros, Egré, Ripley and van Rooij, which are obtained via Malinowski’s and Frankowski’s q- and p-matrices, respectively." @default.
• W2897847887 created "2018-10-26" @default.
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• W2897847887 date "2018-01-01" @default.
• W2897847887 modified "2023-10-09" @default.
• W2897847887 title "What is a Paraconsistent Logic?" @default.
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• W2897847887 doi "https://doi.org/10.1007/978-3-319-98797-2_5" @default.
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