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dc.contributor.authorJacinto, Bruno Miguel
dc.contributor.authorRead, Stephen Louis
dc.identifier.citationJacinto , B M & Read , S L 2017 , ' General-elimination stability ' Studia Logica , vol. 105 , no. 2 , pp. 361-405 .
dc.identifier.otherPURE: 246332985
dc.identifier.otherPURE UUID: f23594b3-90a8-4bd4-a799-12edda778cc6
dc.identifier.otherScopus: 84991670403
dc.description.abstractGeneral-elimination harmony articulates Gentzen's idea that the elimination-rules are justified if they infer from an assertion no more than can already be inferred from the grounds for making it. Dummett described the rules as not only harmonious but stable if the E-rules allow one to infer no more and no less than the I-rules justify. Pfenning and Davies call the rules locally complete if the E-rules are strong enough to allow one to infer the original judgement. A method is given of generating harmonious general-elimination rules from a collection of I-rules. We show that the general-elimination rules satisfy Pfenning and Davies' test for local completeness, but question whether that is enough to show that they are stable. Alternative conditions for stability are considered, including equivalence between the introduction- and elimination-meanings of a connective, and recovery of the grounds for assertion, finally generalizing the notion of local completeness to capture Dummett's notion of stability satisfactorily. We show that the general-elimination rules meet the last of these conditions, and so are indeed not only harmonious but also stable.en
dc.relation.ispartofStudia Logicaen
dc.rightsCopyright © The Author(s) 2016 Open Access: This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, 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. The published version is available at DOI: 10.1007/s11225-016-9692-xen
dc.subjectGeneral-elimination rulesen
dc.subjectLocal completenessen
dc.subjectBC Logicen
dc.titleGeneral-elimination stabilityen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. Philosophyen
dc.contributor.institutionUniversity of St Andrews. Arché Philosophical Research Centre for Logic, Language, Metaphysics and Epistemologyen
dc.contributor.institutionUniversity of St Andrews. St Andrews Institute of Mediaeval Studiesen
dc.description.statusPeer revieweden

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