Finite-Cliquewidth Sets of Existential Rules: Toward a General Criterion for Decidable yet Highly Expressive Querying

TL;DR

This paper introduces finite-cliquewidth sets (FCS) of existential rules, a new class ensuring decidable query answering in ontology-based systems, generalizing previous classes and exploring their properties and limitations.

Contribution

It defines FCS based on graph-theoretic measures, proves its decidability guarantees, and compares it with existing classes like FES, BTS, and FUS, highlighting its advantages and boundaries.

Findings

FCS guarantees decidability of entailment for a broad class of queries.

FCS generalizes finite-expansion sets and bounded-treewidth sets.

FCS is incomparable with finite-unification sets, but subsumes FUS under certain restrictions.

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.