Finite-Cliquewidth Sets of Existential Rules: Toward a General Criterion for Decidable yet Highly Expressive Querying
Abstract
In our pursuit of generic criteria for decidable ontology-based querying, we introduce 'finite-cliquewidth sets' (FCS) of existential rules, a model-theoretically defined class of rule sets, inspired by the cliquewidth measure from graph theory. By a generic argument, we show that FCS ensures decidability of entailment for a sizable class of queries (dubbed 'DaMSOQs') subsuming conjunctive queries (CQs). The FCS class properly generalizes the class of finite-expansion sets (FES), and for signatures of arity at most 2, the class of bounded-treewidth sets (BTS). For higher arities, BTS is only indirectly subsumed by FCS by means of reification. Despite the generality of FCS, we provide a rule set with decidable CQ entailment (by virtue of first-order-rewritability) that falls outside FCS, thus demonstrating the incomparability of FCS and the class of finite-unification sets (FUS). In spite of this, we show that if we restrict ourselves to single-headed rule sets over signatures of arity at most 2, then FCS subsumes FUS.
Cite
@article{arxiv.2209.02464,
title = {Finite-Cliquewidth Sets of Existential Rules: Toward a General Criterion for Decidable yet Highly Expressive Querying},
author = {Thomas Feller and Tim S. Lyon and Piotr Ostropolski-Nalewaja and Sebastian Rudolph},
journal= {arXiv preprint arXiv:2209.02464},
year = {2022}
}
Comments
Accepted to the 26th International Conference on Database Theory (ICDT) 2023