arXiv subjects

Lucas Larroque

Publications and source records attributed to Lucas Larroque.

5 recordsLinked to original sources

arXiv2026

Will My Favorite Chases Terminate if Evaluating Conjunctive Queries Does? One Does Not Simply Decide This

Existential rules are a prominent formalism to enrich a database with knowledge from the domain of interest, but make even basic reasoning tasks on the resulting knowledge base undecidable. To circumvent this, several classes of rules offering various useful properties have been identified. One such class, for instance, contains all sets of rules on which the chase algorithm always terminates, which guarantees the existence of a finite universal model. However, these classes are often abstract rather than concrete: it may be undecidable to check whether a given set of rules belongs to them. Given that the most studied classes of existential rules are designed for reasoning on databases, thus ensuring decidable conjunctive query entailment, we ask: Within a class that supports decidable query entailment, do the usual abstract classes become concrete? We answer in the negative for classes based upon the termination of all classical chase variants and for the bounded treewidth set (BTS) class.

cs.DB↗

arXiv2026

No Cliques Allowed: The Next Step Towards BDD/FC Conjecture

This paper addresses one of the fundamental open questions in the realm of existential rules: the conjecture on the finite controllability of bounded derivation depth rule sets (bdd $\Rightarrow$ fc). We take a step toward a positive resolution of this conjecture by demonstrating that universal models generated by bdd rule sets cannot contain arbitrarily large tournaments (arbitrarily directed cliques) without entailing a loop query, $\exists{x} E(x, x)$. This simple yet elegant result narrows the space of potential counterexamples to the (bdd $\Rightarrow$ fc) conjecture.

cs.DB↗

arXiv2025

About the Multi-Head Linear Restricted Chase Termination

The chase is a ubiquitous algorithm in database theory. However, for existential rules (aka tuple-generating dependencies), its termination is not guaranteed, and even undecidable in general. The problem of termination becomes particularly difficult for the restricted (or standard) chase, for which the order of rule application matters. Thus, decidability of restricted chase termination is still open for many well-behaved classes such as linear or guarded multi-headed rules. We make a step forward by showing that all-instances restricted chase termination is decidable in the linear multi-headed case.

cs.DB↗

arXiv2025

Restricted Chase Termination: You Want More than Fairness

The chase is a fundamental algorithm with ubiquitous uses in database theory. Given a database and a set of existential rules (aka tuple-generating dependencies), it iteratively extends the database to ensure that the rules are satisfied in a most general way. This process may not terminate, and a major problem is to decide whether it does. This problem has been studied for a large number of chase variants, which differ by the conditions under which a rule is applied to extend the database. Surprisingly, the complexity of the universal termination of the restricted (aka standard) chase is not fully understood. We close this gap by placing universal restricted chase termination in the analytical hierarchy. This higher hardness is due to the fairness condition, and we propose an alternative condition to reduce the hardness of universal termination.

cs.LO↗

arXiv2022

Normalisations of Existential Rules: Not so Innocuous!

Existential rules are an expressive knowledge representation language mainly developed to query data. In the literature, they are often supposed to be in some normal form that simplifies technical developments. For instance, a common assumption is that rule heads are atomic, i.e., restricted to a single atom. Such assumptions are considered to be made without loss of generality as long as all sets of rules can be normalised while preserving entailment. However, an important question is whether the properties that ensure the decidability of reasoning are preserved as well. We provide a systematic study of the impact of these procedures on the different chase variants with respect to chase (non-)termination and FO-rewritability. This also leads us to study open problems related to chase termination of independent interest.

cs.AI↗