Studia Logica

, Volume 103, Issue 6, pp 1245–1278 | Cite as

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

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Article

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.

Keywords

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

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© The Author(s) 2015

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Logic and Cognitive ScienceInstitute of Psychology, Adam Mickiewicz UniversityPoznańPoland

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