Dual Erotetic Calculi and the Minimal {mathsf{LFI}}

Studia Logica 103 (6):1245-1278 (2015)

Abstract
An erotetic calculus for a given logic constitutes a sequent-style proof-theoretical formalization of the logic grounded in Inferential Erotetic Logic ). In this paper, a new erotetic calculus for Classical Propositional Logic ), 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 \ and its extensions \ and \. 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 \. Last but not least, as the method is grounded in \, it constitutes an important tool for the so-called question-processing
Keywords Inferential Erotetic Logic  Proof theory of paraconsistent logics   $${\mathsf{mbC}}$$ mbC   $${\mathsf{CLuN}}$$ CLuN   $${\mathsf{CLuNs}}$$ CLuNs  Dual resolution
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DOI 10.1007/s11225-015-9617-0
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References found in this work BETA

First-Order Logic.Raymond M. Smullyan - 1968 - New York [Etc.]Springer-Verlag.
Structural Proof Theory.Sara Negri, Jan von Plato & Aarne Ranta - 2001 - Cambridge University Press.
Socratic Proofs for Quantifiers★.Andrzej Wiśniewski & Vasilyi Shangin - 2006 - Journal of Philosophical Logic 35 (2):147-178.

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