格值有穷自动机和单体二阶格值逻辑  

Finite Automata with Membership Values in Lattices and Monadic Second-order Lattice-valued Logic

作　　者：范艳焕[1] 李永明[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《模糊系统与数学》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)

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.

关 键 词：格值逻辑 有穷自动机 单体二阶逻辑 格值语言 

分 类 号：O141[理学—数学]