Logic, Reasoning, and Knowledge
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Abstract
Abstract
Abstract It is a long-standing open problem whether modal logics of the form K ⊕ ◻ n p → ◻ m p $\mathbf {K}\oplus \Box ^np\to \Box ^mp$ bold upper K circled plus white medium square Superscript n Baseline p right arrow white medium square Superscript m Baseline p for n > m > 1 $n>m>1$ n greater than m greater than 1 have the finite model property (FMP). We solve this by showing that any modal logic axiomatized by formulas of the form ◻ n p → ◻ m p $\Box ^np\to \Box ^mp$ white medium square Superscript n Baseline p right arrow white medium square Superscript m Baseline p where n > m > 1 $n>m>1$ n greater than m greater than 1 has the FMP.
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@article{Knudstorp2026KNOCKING,
title = {KNOCKING DOWN BOXES: THE FMP FOR K ⊕ ◻ m + k p → ◻ m p $\\mathbf \{K\}\\oplus \\Box ^\{m+k\} p\\to \\Box ^m p$ bold upper K circled plus white medium square Superscript m plus k Baseline p right arrow white medium square Superscript m Baseline p},
author = {Søren Brinck Knudstorp},
journal = {Journal of Symbolic Logic},
year = {2026},
doi = {10.1017/jsl.2026.10248},
url = {https://doi.org/10.1017/jsl.2026.10248}
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