We formulate and prove logical characterizations of fuzzy simulations for fuzzy labeled transition systems under the Gödel semantics. Apart from the usual setting, we consider also the setting that allows graded modal operators, which are used to talk about the number of successors with a certain property of the current state. Our characterizations are formulated w.r.t. the existential fragment of fuzzy propositional dynamic logic and its extension with graded modal operators. The results concern fuzzy preservation of existential modal formulas under fuzzy simulations as well as the Hennessy-Milner property of fuzzy simulations.

中文翻译：

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在模糊命题动态逻辑中表征模糊标记过渡系统的模糊仿真

我们在Gödel语义下为模糊标记的过渡系统制定并证明了模糊仿真的逻辑特征。除了通常的设置外，我们还要考虑允许使用分级模态运算符的设置，该运算符用于讨论具有当前状态的某些属性的后继者的数量。我们的表征是用模糊命题动态逻辑的存在性片段及其在分级模态算子上的扩展来表示的。结果涉及在模糊模拟下对现有模态公式的模糊保存以及模糊模拟的Hennessy-Milner属性。