发表机构
Institute of Informatics, University of Warsaw; Faculty of Information Technology, Nguyen Tat Thanh University（华沙大学信息学研究所; 胡志明市阮tat成大学信息技术学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究剩余格上模糊模态逻辑的模糊定向模拟，证明模糊模态逻辑\(fPDL\)正公式在此模拟下不变并建立相关定理，提出计算两个有限模糊克里普克模型间最大模糊定向模拟的方法并实现及评估性能。
AI 中文摘要
我们引入了任意线性和完全剩余格上模糊克里普克模型之间的模糊定向模拟概念，并研究其基本性质。特别地，我们证明了模糊模态逻辑\(fPDL\)的所有正公式在模糊定向模拟下保持不变，并为此概念建立了亨尼西 - 米尔纳定理。此外，我们提出了一种计算两个有限模糊克里普克模型之间最大模糊定向模拟的方法，并针对底层剩余格为哥德尔、乘积或卢卡西维茨结构的情况进行了实现。最后，我们对实现的性能进行了实验评估并展示了结果。
英文摘要
We introduce the notion of fuzzy directed simulation between fuzzy Kripke models over linear and complete residuated lattices and investigate its fundamental properties. In particular, we prove that all positive formulas of a fuzzy extension of propositional dynamic logic are preserved under fuzzy directed simulations and establish a Hennessy-Milner theorem for this notion. Furthermore, we present a method for computing the greatest fuzzy directed simulation between two finite fuzzy Kripke models and implement it for the case where the underlying residuated lattice is the Gödel, product, or Lukasiewicz structure. Finally, we experimentally evaluate the performance of the implementation and present the obtained results.
