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What is a Paraconsistent Logic?

  • Eduardo Barrio
  • Federico Pailos
  • Damian Szmuc
Chapter
Part of the Trends in Logic book series (TREN, volume 47)

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.

Notes

Acknowledgements

The ideas contained in this paper were presented at the Work In Progress seminar of the Buenos Aires Logic Group, the XVI Trends in Logic conference, and the Kyoto Philosophical Logic Workshop II at Kyoto University. We are thankful to the members of those audiences for the discussion provided. We would also like to thank Rohan French, Andreas Fjellstad, Hitoshi Omori, Francesco Paoli, Graham Priest, Dave Ripley, Zach Weber and two anonymous reviewers for their helpful suggestions and comments on previous versions of this article. Finally, we are thankful to the editors of this volume, Walter Carnielli, and Jacek Malinowski, for their assistance through the editorial process.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.IIF-SADAF, National Scientific and Technical Research Council (CONICET)Buenos AiresArgentina

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