Pre-filtrations, Pre-stable Canonical Rules, and the Kuznetsov-Muravitsky Isomorphism
Nick Bezhanishvili, Antonio Maria Cleani
TL;DR
This paper introduces pre-filtration and pre-stable canonical rules for intuitionistic modal logic, providing a new proof of the Kuznetsov-Muravitsky isomorphism and exploring algebraic and topological dualities.
Contribution
It presents novel pre-filtration and canonical rules for the Kuznetsov-Muravitsky system, offering a new proof and preservation results in intuitionistic modal logic.
Findings
New proof of Kuznetsov-Muravitsky isomorphism
Establishment of preservation results
Development of duality between modal algebras and topological spaces
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.
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Taxonomy
TopicsLogic, Reasoning, and Knowledge · Advanced Algebra and Logic · Logic, programming, and type systems