All-Instances Oblivious Chase Termination is Undecidable for Single-Head Binary TGDs

Bartosz BednarczykBartosz Bednarczyk, Piotr Ostropolski-NalewajaPiotr Ostropolski-Nalewaja, Robert FerensRobert Ferens

Bartosz Bednarczyk, Piotr Ostropolski-Nalewaja, Robert Ferens
All-Instances Oblivious Chase Termination is Undecidable for Single-Head Binary TGDs
Proceedings of the 29th International Joint Conference on Artificial Intelligence and the 17th Pacific Rim International Conference on Artificial Intelligence (IJCAI 2020), to appear. International Joint Conferences on Artificial Intelligence

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KurzfassungAbstract
The chase is a famous algorithmic procedure in database theory with numerous applications in ontology-mediated query answering. We consider static analysis of the chase termination problem, which asks, given set of TGDs, whether the chase terminates on all input databases. The problem was recently shown to be undecidable by Gogacz et al. for sets of rules containing only ternary predicates. In this work, we show that undecidability occurs already for sets of single-head TGD over binary vocabularies. This question is relevant since many real-world ontologies, e.g., those from the Horn fragment of the popular OWL, are of this shape.
Projekt:Project: DeciGUT
Forschungsgruppe:Research Group: Computational LogicComputational Logic

@inproceedings{BOF2020,
  author    = {Bartosz Bednarczyk and Piotr Ostropolski-Nalewaja and Robert
               Ferens},
  title     = {All-Instances Oblivious Chase Termination is Undecidable for
               Single-Head Binary {TGDs}},
  booktitle = {Proceedings of the 29th International Joint Conference on
               Artificial Intelligence and the 17th Pacific Rim International
               Conference on Artificial Intelligence (IJCAI 2020)},
  publisher = {International Joint Conferences on Artificial Intelligence},
  year      = {2020},
  month     = {July}
}