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dc.contributor.authorYin, Hongkai
dc.contributor.authorBen-Yami, Hanoch
dc.date.accessioned2023-06-16T14:43:35Z
dc.date.available2023-06-16T14:43:35Z
dc.date.issued2023
dc.identifier.issn0039-3215, 1572-8730
dc.identifier.doi10.1007/s11225-022-10022-5
dc.identifier.urihttp://hdl.handle.net/20.500.14018/14013
dc.description.abstractWe introduce a two-valued and a three-valued truth-valuational substitutional semantics for the Quantified Argument Calculus (Quarc). We then prove that the 2-valid arguments are identical to the 3-valid ones with strict-to-tolerant validity. Next, we introduce a Lemmon-style Natural Deduction system and prove the completeness of Quarc on both two- and three-valued versions, adapting Lindenbaum’s Lemma to truth-valuational semantics. We proceed to investigate the relations of three-valued Quarc and the Predicate Calculus (PC). Adding a logical predicate T to Quarc, true of all singular arguments, allows us to represent PC quantification in Quarc and translate PC into Quarc, preserving validity. Introducing a weak existential quantifier into PC allows us to translate Quarc into PC, also preserving validity. However, unlike the translated systems, neither extended system can have a sound and complete proof system with Cut, supporting the claim that these are basically different calculi.
dc.language.isoeng
dc.publisherSpringer
dc.rightsCC BY 4.0
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.titleThe Quantified Argument Calculus with Two- and Three-valued Truth-valuational Semantics
dc.typeJournal article
dc.source.journaltitleStudia Logica
dc.source.volume111
dc.source.issue2
dc.source.spage281
dc.source.epage320
dc.description.versionPublished version
refterms.dateFOA2023-06-16T14:43:35Z
dc.contributor.unitDepartment of Philosophy
dc.source.journalabbrevStud Logica
dc.identifier.urlhttps://link.springer.com/10.1007/s11225-022-10022-5


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