Positive first-order logic on words
Formal Languages and Automata Theory
2021-10-12 v6 Logic in Computer Science
Logic
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 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+.
Cite
@article{arxiv.2101.01968,
title = {Positive first-order logic on words},
author = {Denis Kuperberg},
journal= {arXiv preprint arXiv:2101.01968},
year = {2021}
}