Knocking Down Boxes: The FMP for K ⊕ \Box^m+k p → \Box^m p

2025/10/01 by Søren Brinck Knudstorp, Knudstorp, Søren Brinck
Computer Science · #03B25 #03B45 #06E25 #F.4.1 #FOS: Mathematics #Logic (math.LO) #Numerical Methods and Algorithms

paper · pdf · doi:10.48550/arxiv.2510.00864

openalex publication_date 2025/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is a long-standing open problem whether modal logics of the form K ⊕ \Boxⁿ p → \Box^m p for n>m>1 have the finite model property (FMP). We solve this by showing that any modal logic axiomatized by formulas of the form \Boxⁿ p → \Box^m p where n>m>1 has the FMP.

Citations

• Tho Modal Logic of Minimal Upper Bounds
• Decidability of Quasi-Dense Modal Logics

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