Pre-filtrations, Pre-stable Canonical Rules, and the Kuznetsov-Muravitsky Isomorphism

2025/11/13 by Nick Bezhanishvili, Bezhanishvili, Nick, Antonio Maria Cleani +1
Computer Science · #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems

paper · pdf · doi:10.48550/arxiv.2511.09824

openalex publication_date 2025/11/13 · openalex created_date 2025/11/15 · openalex updated_date 2026/07/30

Abstract

We introduce pre-filtration and pre-stable canonical rules for the Kuznetsov-Muravitsky system of intuitionistic modal logic and provide a new proof of the Kuznetsov-Muravitsky isomorphism, along with several preservation results. The proofs employ these rules and a duality between modal (Heyting) algebras and their corresponding order-topological spaces.

Citations

• An explicit Kuznetsov-Muravitsky enrichment
• Blok-Esakia Theorems via Stable Canonical Rules
• On the Blok-Esakia theorem for universal classes

Related

• Stable Canonical Rules and Formulas for Pre-transitive Logics via Definable Filtration
• Intuitionistic logic, dual intuitionistic logic, and modality
• Blok-Esakia Theorems via Stable Canonical Rules
• On the Equipollence of the Calculi Int and KM
• First-order logic in the Medvedev lattice