A Note on Contradictions in Francez-Weiss Logics.
It is an unusual property for a logic to prove a formula and its negation without ending up in triviality. Some systems have nonetheless been observed to satisfy this property: one group of such non-trivial negation inconsistent logics has its archetype in H. Wansing’s constructive connexive logic,...
| Publicado en: | Logic & Logical Philosophy Vol. 34; no. 3; pp. 387 - 417 |
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| Formato: | Artículo |
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Logic & Logical Philosophy
Sep2025
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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=190216898&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 190216898 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 14253305 DS9 jtl: Logic & Logical Philosophy issn: 14253305 maglogo: N pubinfo: dt: Sep2025 vid: 34 iid: 3 pid: 42904 pub: Logic & Logical Philosophy artinfo: ui: 190216898 10.12775/LLP.2024.031 ppf: 387 ppct: 30 formats: fmt: @attributes: type: P size: 1.6MB tig: atl: A Note on Contradictions in Francez-Weiss Logics. aug: au: Niki, Satoru affil: Department of Philosophy I Ruhr University Bochum Bochum, Germany. su: Contradiction Negation (Logic) Paradox Conditionals (Logic) Nonclassical mathematical logic sug: subj: Contradiction Negation (Logic) Paradox Conditionals (Logic) Nonclassical mathematical logic keyword: connexive logic contradictory logic relevant logic sequent calculus strong negation ab: It is an unusual property for a logic to prove a formula and its negation without ending up in triviality. Some systems have nonetheless been observed to satisfy this property: one group of such non-trivial negation inconsistent logics has its archetype in H. Wansing’s constructive connexive logic, whose negation-implication fragment already proves contradictions. N. Francez and Y. Weiss subsequently investigated relevant subsystems of this fragment, and Weiss in particular showed that they remain negation inconsistent. In this note, we take a closer look at this phenomenon in the systems of Francez and Weiss, and point out two types of necessary conditions, one proof-theoretic and one relevant, which any contradictory formula must satisfy. As a consequence, we propose a ninefold classification of provable contradictions for the logics. 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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