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Uniform Lyndon interpolation property in propositional modal logics

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Abstract

We introduce and investigate the notion of uniform Lyndon interpolation property (ULIP) which is a strengthening of both uniform interpolation property and Lyndon interpolation property. We prove several propositional modal logics including \(\mathbf{K}\), \(\mathbf{KB}\), \(\mathbf{GL}\) and \(\mathbf{Grz}\) enjoy ULIP. Our proofs are modifications of Visser’s proofs of uniform interpolation property using layered bisimulations (Visser, in: Hájek (ed) Gödel’96, logical foundations of mathematics, computer science and physics—Kurt Gödel’s legacy, Springer, Berlin, 1996). Also we give a new upper bound on the complexity of uniform interpolants for \(\mathbf{GL}\) and \(\mathbf{Grz}\).

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Notes

  1. Essential parts of the modification of our proof from Visser’s are the use of the relation \(\prec _\varphi ^s\) and this definition of witnesses.

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  1. National Institute of Technology, Kisarazu College, Chiba, Japan

    Taishi Kurahashi

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Correspondence to Taishi Kurahashi.

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This work was supported by JSPS KAKENHI Grant No. 16K17653.

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Kurahashi, T. Uniform Lyndon interpolation property in propositional modal logics. Arch. Math. Logic 59, 659–678 (2020). https://doi.org/10.1007/s00153-020-00713-y

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