BLOK–ESAKIA THEOREMS VIA STABLE CANONICAL RULES.
We present a new uniform method for studying modal companions of superintuitionistic rule systems and related notions, based on the machinery of stable canonical rules. Using this method, we obtain alternative proofs of the Blok–Esakia theorem and of the Dummett–Lemmon conjecture for rule systems. S...
| Publicado en: | Journal of Symbolic Logic Vol. 91; no. 1; pp. 68 - 105 |
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| Autores principales: | , |
| Formato: | Artículo |
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Cambridge University Press
Mar2026
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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=193760577&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 193760577 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00224812 3TY jtl: Journal of Symbolic Logic issn: 00224812 maglogo: N pubinfo: dt: Mar2026 vid: 91 iid: 1 pid: 15979 pub: Cambridge University Press artinfo: ui: 193760577 10.1017/jsl.2025.10126 ppf: 68 ppct: 37 formats: tig: atl: BLOK–ESAKIA THEOREMS VIA STABLE CANONICAL RULES. aug: au: BEZHANISHVILI, NICK CLEANI, ANTONIO MARIA affil: INSTITUTE FOR LOGIC, LANGUAGE AND COMPUTATION UNIVERSITY OF AMSTERDAM 1012 WP AMSTERDAM, THE NETHERLANDS E-mail SCHOOL OF PHILOSOPHY UNIVERSITY OF SOUTHERN CALIFORNIA LOS ANGELES, CA 90007, USA su: Modal logic Nonclassical mathematical logic Logic Rule-based programming Isomorphism (Mathematics) sug: subj: Modal logic Nonclassical mathematical logic Logic Rule-based programming Isomorphism (Mathematics) keyword: bi-intuitionistic logic Gödel translation intuitionistic logic modal companion modal logic provability logic rule system stable canonical rule tense logic ab: We present a new uniform method for studying modal companions of superintuitionistic rule systems and related notions, based on the machinery of stable canonical rules. Using this method, we obtain alternative proofs of the Blok–Esakia theorem and of the Dummett–Lemmon conjecture for rule systems. Since stable canonical rules may be developed for any rule system admitting filtration, our method generalizes smoothly to richer signatures. Using essentially the same argument, we obtain a proof of an analogue of the Blok–Esakia theorem for bi-superintuitionistic and tense rule systems, and of the Kuznetsov–Muravitsky isomorphism between rule systems extending the modal intuitionistic logic $\mathtt {KM}$ and modal rule systems extending the provability logic $\mathtt {GL}$. In addition, our proof of the Dummett–Lemmon conjecture also generalizes to the bi-superintuitionistic and tense cases. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y dt: @attributes: year: 2026 holdings: @attributes: islocal: N |
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