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- W4309968400 abstract "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 lift this example language to finite graphs, thereby providing a new result of independent interest for FO-definable graph classes: negation might be needed even when the class is closed under addition of edges. We finally show that the problem of whether a given regular language of finite words is definable in FO+ is undecidable." @default.
- W4309968400 created "2022-11-30" @default.
- W4309968400 creator A5017960584 @default.
- W4309968400 date "2023-07-25" @default.
- W4309968400 modified "2023-09-30" @default.
- W4309968400 title "Positive First-order Logic on Words and Graphs" @default.
- W4309968400 doi "https://doi.org/10.46298/lmcs-19(3:7)2023" @default.
- W4309968400 hasPublicationYear "2023" @default.
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