Bounded Treewidth and the Infinite Core Chase – Complications and Workarounds toward Decidable Querying

Vortrag von Sebastian Rudolph

Veranstaltungsort: APB room 3027
Beginn: 2. November 2023 um 11:00
Ende: 2. November 2023 um 12:00
Event series: Research Seminar Logic and AI
iCal

Abstract: The core chase, a popular algorithm for answering conjunctive queries (CQs) over existential rules, is guaranteed to terminate and compute a finite universal model whenever one exists, leading to the equivalence of the universal-model-based and the chase-based definitions of finite expansion sets (fes) – a class of rulesets featuring decidable CQ entailment. In case of non-termination, however, it is non-trivial to define a "result" of the core chase, due to its non-monotonicity. This causes complications when dealing with advanced decidability criteria based on the existence of (universal) models of finite treewidth. For these, sufficient chase-based conditions have only been established for weaker, monotonic chase variants.

This paper starts out from the – desirable and prima facie plausible – conjecture that the existence of a treewidth-bounded universal model and the existence of a treewidth-bounded core-chase sequence coincide – which would conveniently entail decidable CQ entailment whenever the latter holds. Perhaps surprisingly, carefully crafted examples show that both directions of this conjectured correspondence fail. On a positive note, we are still able to define an aggregation scheme for the infinite core chase that preserves treewidth bounds and produces a finitely universal model, i.e., one that satisfies exactly the entailed CQs. This allows us to prove that the existence of a treewidth-bounded core-chase sequence *does* warrant decidability of CQ entailment (yet, on other grounds than expected). Hence, for the first time, we are able to define a chase-based notion of bounded treewidth sets of rules that subsumes fes.

The talk will take place in a hybrid fashion, physically in the APB room 3027, and online through the link:

https://bbb.tu-dresden.de/b/pio-zwt-smp-aus