A Hypersequent Calculus with Clusters for Data Logic over Ordinals

Anthony Lick (1)

1 LSV - Laboratoire Spécification et Vérification [Cachan]

We study freeze tense logic over well-founded data streams. The logic features past-and future-navigating modalities along with freeze quantifiers, which store the datum of the current position and test data (in)equality later in the formula. We introduce a decidable fragment of that logic, and present a proof system that is sound for the whole logic, and complete for this fragment. Technically, this is a hy-persequent system enriched with an ordering, clusters, and annotations. The proof system is tailored for proof search, and yields an optimal coNP complexity for validity and a small model property for our fragment.

Domaines: Logique en informatique [cs.LO]

Anthony Lick. A Hypersequent Calculus with Clusters for Data Logic over Ordinals. 2019. ⟨hal-02165359⟩