Paradoxes versus Contradictions in Logic of Sentential Operators.
Classical logic, of first or higher order, is extended with sentential operators and quantifiers, interpreted substitutionally over unrestricted substitution class. Operators mark a single layered, consistent metalanguage. Self-reference, arising from substitutional quantification over sentences, al...
| Publicado en: | Logic & Logical Philosophy Vol. 34; no. 4; pp. 631 - 675 |
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| Formato: | Artículo |
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Logic & Logical Philosophy
Dec2025
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=194269720&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 194269720 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 14253305 DS9 jtl: Logic & Logical Philosophy issn: 14253305 maglogo: N pubinfo: dt: Dec2025 vid: 34 iid: 4 pid: 42904 pub: Logic & Logical Philosophy artinfo: ui: 194269720 10.12775/LLP.2024.002 ppf: 631 ppct: 44 formats: fmt: @attributes: type: P size: 3.1MB tig: atl: Paradoxes versus Contradictions in Logic of Sentential Operators. aug: au: Walicki, Michał affil: Department of Informatics, University of Bergen, Norway su: Paradox Contradiction Semantics (Philosophy) Predicate calculus Propositional calculus Nonclassical mathematical logic sug: subj: Paradox Contradiction Semantics (Philosophy) Predicate calculus Propositional calculus Nonclassical mathematical logic keyword: (semi)kernels of digraphs classical logic paraconsistent semantics semantic and intensional paradoxes sentential operators ab: Classical logic, of first or higher order, is extended with sentential operators and quantifiers, interpreted substitutionally over unrestricted substitution class. Operators mark a single layered, consistent metalanguage. Self-reference, arising from substitutional quantification over sentences, allows to express paradoxes which, unlike contradictions, do not lead to explosion. Semantics of the resulting language, using semi-kernels of digraphs, is non-explosive yet two-valued and has classical semantics as a special case for clasically consistent theories. A complete reasoning is obtained by extending LK with two rules for sentential quantifiers. Adding (cut) yields a complete system for the explosive semantics. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Copyright of Logic & Logical Philosophy is the property of Logic & Logical Philosophy and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. item: Logic & Logical Philosophy holder: Logic & Logical Philosophy dt: @attributes: year: 2025 holdings: @attributes: islocal: N |
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