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...

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Publicado en:Journal of Symbolic Logic Vol. 91; no. 1; pp. 68 - 105
Autores principales: BEZHANISHVILI, NICK, CLEANI, ANTONIO MARIA
Formato: Artículo
Publicado: Cambridge University Press Mar2026
Materias:
Acceso en línea:Ver este registro en EBSCOhost
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      dt: Mar2026
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      pub: Cambridge University Press
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        193760577
        10.1017/jsl.2025.10126
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        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
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          year: 2026
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