On Modal μ-Calculus and Non-Well-Founded Set Theory
On Modal μ-Calculus and Non-Well-Founded Set Theory
复制标题
模态 μ 微积分与非良基集合论
DOI：
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发表时间：
2004
影响因子：
1.5
通讯作者：
Vincenzo Salipante
中科院分区：
文献类型：
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作者：
L. Alberucci;Vincenzo Salipante
利用模态μ微积分的最大不动点公式，建立了具有有限传递闭包的非良建立集的有限刻划。这推广了文献中的标准结果，其中有限模态表征只提供了有限传递闭包的成立良好集。该证明依赖于自动机的概念，从而导致自动机理论与非良根据集之间的新联系。
A finitary characterization for non-well-founded sets with finite transitive closure is established in terms of a greatest fixpoint formula of the modal μ-calculus. This generalizes the standard result in the literature where a finitary modal characterization is provided only for wellfounded sets with finite transitive closure. The proof relies on the concept of automaton, leading then to new interlinks between automata theory and non-well-founded sets.