Blok–esakia Theorems Via Stable Canonical Rules
Year: 2025
Type: article
Abstract: 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.
Source: Journal of Symbolic Logic
Authors: NICK BEZHANISHVILI, ANTONIO MARIA CLEANI
Institutions: University of Amsterdam, University of Southern California
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W4413697230