Intuitionistic Logic and Elementary Rules.
The interplay of introduction and elimination rules for propositional connectives is often seen as suggesting a distinguished role for intuitionistic logic. We prove three formal results concerning intuitionistic propositional logic that bear on that perspective, and discuss their significance. Firs...
| Publicado en: | Mind (0026-4423) Vol. 120; no. 480; pp. 1035 - 1052 |
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| Autores principales: | , |
| Formato: | Artículo |
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Oxford University Press / USA
Oct2011
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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=88989101&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 88989101 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00264423 MND jtl: Mind (0026-4423) issn: 00264423 maglogo: N pubinfo: dt: Oct2011 vid: 120 iid: 480 pid: 622 pub: Oxford University Press / USA artinfo: ui: 88989101 10.1093/mind/fzr076 ppf: 1035 ppct: 17 formats: fmt: @attributes: type: P size: 122KB tig: atl: Intuitionistic Logic and Elementary Rules. aug: au: Humberstone, Lloyd Makinson, David affil: Monash University lloyd.humberstone@monash.edu London School of Economics david.makinson@gmail.com su: Logic Philosophy Critical thinking Reasoning Intellect sug: subj: Logic Philosophy Critical thinking Reasoning Intellect ab: The interplay of introduction and elimination rules for propositional connectives is often seen as suggesting a distinguished role for intuitionistic logic. We prove three formal results concerning intuitionistic propositional logic that bear on that perspective, and discuss their significance. First, for a range of connectives including both negation and the falsum, there are no classically or intuitionistically correct introduction rules. Second, irrespective of the choice of negation or the falsum as a primitive connective, classical and intuitionistic consequence satisfy exactly the same structural, introduction, and elimination (briefly, elementary) rules. Third, for falsum as primitive only, intuitionistic consequence is the least consequence relation that satisfies all classically correct elementary rules. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: © 2019 Mind Association. item: Mind (0026-4423) holder: Oxford University Press / USA dt: @attributes: year: 2011 holdings: @attributes: islocal: N |
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