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 \(\mathbf{Grz}\).

中文翻译：

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命题模态逻辑的一致Lyndon插值性质。

我们介绍并研究了统一林登插值属性（ULIP）的概念，该概念加强了统一插值属性和林登插值属性。我们证明了几种命题模态逻辑，包括\（\ mathbf {K} \），\（\ mathbf {KB} \），\（\ mathbf {GL} \）和\（\ mathbf {Grz} \）享受ULIP。我们的证明是使用分层双模拟对Visser的一致插值性质证明进行的修改（Visser，在：Hájek（ed）Gödel'96中，数学，计算机科学和物理学的逻辑基础-库尔特·哥德尔的遗产，施普林格，柏林，1996年）。同样，我们为\（\ mathbf {GL} \）和\（\ mathbf {Grz} \）的统一插值的复杂度给出了新的上限。