We introduce McCarthy-Kleene fuzzy automata (MK-fuzzy automata) over a bimonoid K which is related to the fuzzification of the McCarthy-Kleene logic. Our automata are inspired by, and intend to contribute to, practical applications being in development in a project on runtime network monitoring based on predicate logic. We investigate closure properties of the class of recognizable MK-fuzzy languages accepted by MK-fuzzy automata as well as of deterministically recognizable MK-fuzzy languages accepted by their deterministic counterparts. Moreover, we establish a Nivat-like result for recognizable MK-fuzzy languages. We introduce an MK-fuzzy MSO logic and show the expressive equivalence of a fragment of this logic with MK-fuzzy automata, i.e., a Büchi type theorem.

我们介绍了一个二元类K上的McCarthy-Kleene模糊自动机（MK-fuzzy自动机），它与McCarthy-Kleene逻辑的模糊化有关。我们的自动机受到基于谓词逻辑的运行时网络监视项目中正在开发的实际应用程序的启发，并打算为这些应用程序做出贡献。我们研究了MK模糊自动机接受的可识别MK模糊语言以及其确定性对应语言接受的可确定性识别的MK模糊语言的闭包特性。此外，我们为可识别的MK模糊语言建立了类似于Nivat的结果。我们介绍了MK模糊MSO逻辑，并用MK模糊自动机（即Büchi型定理）展示了该逻辑的片段的表达等价形式。