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Dual Erotetic Calculi and the Minimal \({\mathsf{LFI}}\)

Abstract

An erotetic calculus for a given logic constitutes a sequent-style proof-theoretical formalization of the logic grounded in Inferential Erotetic Logic (\({\mathsf{IEL}}\)). In this paper, a new erotetic calculus for Classical Propositional Logic (\({\mathsf{CPL}}\)), dual with respect to the existing ones, is given. We modify the calculus to obtain complete proof systems for the propositional part of paraconsistent logic \({\mathsf{CLuN}}\) and its extensions \({\mathsf{CLuNs}}\) and \({\mathsf{mbC}}\). The method is based on dual resolution. Moreover, the resolution rule is non-clausal. According to the authors knowledge, this is the first account of resolution for \({\mathsf{mbC}}\). Last but not least, as the method is grounded in \({\mathsf{IEL}}\), it constitutes an important tool for the so-called question-processing.

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Correspondence to Szymon Chlebowski.

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Chlebowski, S., Leszczyńska-Jasion, D. Dual Erotetic Calculi and the Minimal \({\mathsf{LFI}}\) . Stud Logica 103, 1245–1278 (2015). https://doi.org/10.1007/s11225-015-9617-0

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Keywords

  • Inferential Erotetic Logic
  • Proof theory of paraconsistent logics
  • \({\mathsf{mbC}}\)
  • \({\mathsf{CLuN}}\)
  • \({\mathsf{CLuNs}}\)
  • Dual resolution