Please use this identifier to cite or link to this item: https://doi.org/10.1093/jigpal/jzy059
Title: Truth in a Logic of Formal Inconsistency: How classical can it get?
Authors: LAVINIA MARIA PICOLLO 
Keywords: Kripke fixed points
LFIs
sequent-calculus truth theories
proof-theoretic strength
Issue Date: 1-Oct-2020
Publisher: Oxford University Press (OUP)
Citation: LAVINIA MARIA PICOLLO (2020-10-01). Truth in a Logic of Formal Inconsistency: How classical can it get?. Logic Journal of the IGPL 28 (5) : 771-806. ScholarBank@NUS Repository. https://doi.org/10.1093/jigpal/jzy059
Abstract: AbstractWeakening classical logic is one of the most popular ways of dealing with semantic paradoxes. Their advocates often claim that such weakening does not affect non-semantic reasoning. Recently, however, Halbach and Horsten (2006) have shown that this is actually not the case for Kripke’s fixed-point theory based on the Strong Kleene evaluation scheme. Feferman’s axiomatization $\textsf{KF}$ in classical logic is much stronger than its paracomplete counterpart $\textsf{PKF}$, not only in terms of semantic but also in arithmetical content. This paper compares the proof-theoretic strength of an axiomatization of Kripke’s construction based on the paraconsistent evaluation scheme of $\textsf{LP}$, formulated in classical logic with that of an axiomatization directly formulated in $\textsf{LP}$, extended with a consistency operator. The ultimate goal is to find out whether paraconsistent solutions to the paradoxes that employ consistency operators fare better in this respect than paracomplete ones.
Source Title: Logic Journal of the IGPL
URI: https://scholarbank.nus.edu.sg/handle/10635/194760
ISSN: 1367-0751
1368-9894
DOI: 10.1093/jigpal/jzy059
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Picollo (2020) Corrigendum for "Truth in a Logic of Formal Inconsistency-How Classical Can It Get?".pdfPublished version86.03 kBAdobe PDF

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Picollo (2018) Truth in a Logic of Formal Inconsistency-How classical can it get?.pdfPublished version548.49 kBAdobe PDF

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