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Bubchi-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Schubtzenberger分类定理。
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.
出处
《模糊系统与数学》
CSCD
北大核心
2013年第2期23-29,共7页
Fuzzy Systems and Mathematics
基金
国家自然科学基金资助项目(60873119)
关键词
格值逻辑
有穷自动机
单体二阶逻辑
格值语言
Lattice-valued Logic
Finite Automata
Monadic Second Lattice-valued Logic
Lattice-valuedLanguage
