A van Benthem Theorem for Fuzzy Modal Logic
A van Benthem Theorem for Fuzzy Modal Logic
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DOI：
10.1145/3209108.3209180
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发表时间：
2018-02
期刊：
影响因子：
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通讯作者：
P. Wild;Lutz Schröder;D. Pattinson;B. König
中科院分区：
文献类型：
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作者：
P. Wild;Lutz Schröder;D. Pattinson;B. König
我们提出了一个模糊（或定量）版本的货车Benthem定理，它的特点命题模态逻辑作为一阶逻辑的互模拟不变片段。具体地说，我们考虑一阶模糊谓词逻辑沿着其模态片段，并表明，模糊一阶公式是非扩张的w.r.t.互模拟距离的自然概念正好是那些可以通过模糊模态公式来近似的概念。
We present a fuzzy (or quantitative) version of the van Benthem theorem, which characterizes propositional modal logic as the bisimulation-invariant fragment of first-order logic. Specifically, we consider a first-order fuzzy predicate logic along with its modal fragment, and show that the fuzzy first-order formulas that are non-expansive w.r.t. the natural notion of bisimulation distance are exactly those that can be approximated by fuzzy modal formulas.