It might have been classical logic

Logique Et Analyse 55 (218):241-279 (2012)
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Abstract

In this paper, a prepositional logic Q is presented. This logic is more attractive than classical propositional logic P for explicating actual proofs. Moreover, while Q and P assign the same consequence set to consistent premise sets, Q assigns a sensible and non-trivial consequence set to inconsistent premise sets. © 2012 Elsevier B.V., All rights reserved.

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Diderik Batens
University of Ghent

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