Capturing Homomorphism-Closed Decidable Queries with Existential Rules

TL;DR

This paper characterizes the class of homomorphism-closed decidable queries as exactly those expressible by existential rules with guaranteed chase termination, linking decidability and chase behavior.

Contribution

It proves that every homomorphism-closed decidable query can be represented by an existential rule set with universal chase termination, establishing a precise correspondence.

Findings

Decidable homomorphism-closed queries are expressible with terminating existential rules.

Membership in the fragment of such queries is undecidable.

Chase termination guarantees expressibility of certain query classes.

Abstract

Existential rules are a very popular ontology-mediated query language for which the chase represents a generic computational approach for query answering. It is straightforward that existential rule queries exhibiting chase termination are decidable and can only recognize properties that are preserved under homomorphisms. In this paper, we show the converse: every decidable query that is closed under homomorphism can be expressed by an existential rule set for which the standard chase universally terminates. Membership in this fragment is not decidable, but we show via a diagonalisation argument that this is unavoidable.