eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-02-01
23:1
23:19
10.4230/LIPIcs.CSL.2023.23
article
Order-Invariance in the Two-Variable Fragment of First-Order Logic
Grange, Julien
1
LACL, Université Paris-Est Créteil, France
We study the expressive power of the two-variable fragment of order-invariant first-order logic. This logic departs from first-order logic in two ways: first, formulas are only allowed to quantify over two variables. Second, formulas can use an additional binary relation, which is interpreted in the structures under scrutiny as a linear order, provided that the truth value of a sentence over a finite structure never depends on which linear order is chosen on its domain.
We prove that on classes of structures of bounded degree, any property expressible in this logic is definable in first-order logic. We then show that the situation remains the same when we add counting quantifiers to this logic.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol252-csl2023/LIPIcs.CSL.2023.23/LIPIcs.CSL.2023.23.pdf
Finite model theory
Two-variable logic
Order-invariance