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Positive first-order logic on words
arXiv - CS - Logic in Computer Science Pub Date : 2021-01-06 , DOI: arxiv-2101.01968
Denis Kuperberg

We study FO+, a fragment of first-order logic on finite words, where monadic predicates can only appear positively. We show that there is a 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+.

中文翻译:

单词的正一阶逻辑

我们研究FO +,这是有限词上一阶逻辑的一部分,其中一元谓词只能出现正数。我们表明,有一种FO可定义的语言,该语言在单子谓词中是单调的,但在FO +中是不可定义的。这提供了林登保留定理在有限结构上失败的简单证明。我们还表明,给定一种常规语言,它是否可以在FO +中定义是不确定的。
更新日期:2021-01-07
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