Pré-Publication, Document De Travail Année : 2024

Positive and monotone fragments of FO and LTL

Résumé

We study the positive logic FO+ on finite words, and its fragments, pursuing and refining the work initiated in [Kuperberg 2023]. First, we transpose notorious logic equivalences into positive first-order logic: FO+ is equivalent to LTL+ , and its two-variable fragment FO2+ with (resp. without) successor available is equivalent to UTL+ with (resp. without) the "next" operator X available. This shows that despite previous negative results, the class of FO+-definable languages exhibits some form of robustness. We then exhibit an example of an FO-definable monotone language on one predicate, that is not FO+-definable, refining the example from [Kuperberg 2023] with 3 predicates. Moreover, we show that such a counter-example cannot be FO2-definable.
Fichier principal
Vignette du fichier
2406.17693v1.pdf (919) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04774430 , version 1 (08-11-2024)

Identifiants

Citer

Denis Kuperberg, Quentin Moreau. Positive and monotone fragments of FO and LTL. 2024. ⟨hal-04774430⟩
3 Consultations
9 Téléchargements

Altmetric

Partager

More