词的正一阶逻辑

2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2021-01-06 DOI:10.1109/LICS52264.2021.9470602

Denis Kuperberg

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引用次数: 4

摘要

我们研究了有限词上的一阶逻辑片段FO+，其中一元谓词只能正数出现。我们证明了存在一种FO可定义语言，它在一元谓词中是单调的，但在FO+中是不可定义的。这提供了林登保存定理在有限结构上失效的一个简单证明。我们还表明，给定一种正则语言，它在FO+中是否可定义是不可确定的。

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Positive First-order Logic on Words

We study FO+, a fragment of first-order logic on finite words, where monadic predicates can only appear positively. We show that there is an FO-definable language that is monotone in monadic predicates but not definable in FO+. This provides a simple proof that Lyndon’s preservation theorem fails on finite structures. We additionally show that given a regular language, it is undecidable whether it is definable in FO+.

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来源期刊

2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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