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中文摘要：
引入了单体二阶格值逻辑，进而给出了基于格值逻辑的有穷自动机识别语言的逻辑描述，证明了格值逻辑意义下的Buchi—Elgot基本定理。通过引入星自由语言与非周期格值语言，完全刻画了可以用一阶格值逻辑定义的格值语言，得到了格值逻辑意义下的Schtitzenberger分类定理。
英文摘要：
We introduce monadic second-order lattice-valued logic and prove that the behaviors of finite automata based on lattice-valued logic are precisely the lattice-valued languages definable with sentences of our monadic second-order lattice-valued logic. This generalizes Buchi＇s and Elgot＇s fundamental theorems to lattice-valued logic setting. We also consider first-order lattice-valued logic and show that star-free lattice-valued languages and aperiodic lattice-valued languages introduced here coincide with the first-order lattice-valued definable ones. This generalizes Schutzenberger＇ s fundamental theorems to lattice-valued logic setting.
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