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

Bartosz Bednarczyk, Robert Ferens, Piotr Ostropolski-Nalewaja

Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence

Main track. Pages 1719-1725.

Abstract

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.