Abstract
The authors introduce monadic second-order(MSO-) Lukasiewicz logic and prove that the behaviors of fuzzy finite automata are precisely the fuzzy languages definable with sentences of the MSO Lukasiewicz logic.This generalizes Buchi's and Elgot's fundamental theorems to fuzzy logic setting.The authors also consider first-order Lukasiewicz logic and show that star-free fuzzy languages and aperiodic fuzzy languages introduced here coincide with the first-order definable ones.
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