# Adding Circumscription to Decidable Fragments of First-Order Logic: A Complexity Rollercoaster

From International Center for Computational Logic

# Adding Circumscription to Decidable Fragments of First-Order Logic: A Complexity Rollercoaster

*Talk by Quentin Maniere*

- Location: Video conference
- Start: 10. October 2024 at 11:00 am
- End: 10. October 2024 at 12:00 pm
- Event series: Research Seminar Logic and AI
- iCal

We study extensions of expressive decidable fragments of first-order logic with circumscription, in particular the two-variable fragment FO2, its extension C2 with counting quantifiers, and the guarded fragment GF. We prove that if only unary predicates are minimized (or fixed) during circumscription, then decidability of logical consequence is preserved. For FO2 the complexity increases from coNExp to coNExp^NP-complete, for GF it (remarkably!) increases from 2Exp to Tower-complete, and for C2 the complexity remains open. We also consider querying circumscribed knowledge bases whose ontology is a GF sentence, showing that the problem is decidable for unions of conjunctive queries, Tower-complete in combined complexity, and Elementary in data complexity. Already for atomic queries and ontologies that are sets of guarded existential rules, however, for every k ≥ 0 there is an ontology and query that are k-Exp-hard in data complexity.