Denis Kuperberg - Positive First-order Logic on Words and Graphs

lmcs:9081 - Logical Methods in Computer Science, July 25, 2023, Volume 19, Issue 3 -
Positive First-order Logic on Words and GraphsArticle

Authors: 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 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.

    Volume: Volume 19, Issue 3
    Published on: July 25, 2023
    Accepted on: June 13, 2023
    Submitted on: February 15, 2022
    Keywords: Computer Science - Formal Languages and Automata Theory,Computer Science - Logic in Computer Science,Mathematics - Logic


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