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Harmless but Useful: Beyond Separable Equality Constraints in Datalog+/-

Bellomarini, Luigi, Sallinger, Emanuel

arXiv.org Artificial Intelligence

Ontological query answering is the problem of answering queries in the presence of schema constraints representing the domain of interest. Datalog+/- is a common family of languages for schema constraints, including tuple-generating dependencies (TGDs) and equality-generating dependencies (EGDs). The interplay of TGDs and EGDs leads to undecidability or intractability of query answering when adding EGDs to tractable Datalog+/- fragments, like Warded Datalog+/-, for which, in the sole presence of TGDs, query answering is PTIME in data complexity. There have been attempts to limit the interaction of TGDs and EGDs and guarantee tractability, in particular with the introduction of separable EGDs, to make EGDs irrelevant for query answering as long as the set of constraints is satisfied. While being tractable, separable EGDs have limited expressive power. We propose a more general class of EGDs, which we call ``harmless'', that subsume separable EGDs and allow to model a much broader class of problems. Unlike separable EGDs, harmless EGDs, besides enforcing ground equality constraints, specialize the query answer by grounding or renaming the labelled nulls introduced by existential quantification in the TGDs. Harmless EGDs capture the cases when the answer obtained in the presence of EGDs is less general than the one obtained with TGDs only. We conclude that the theoretical problem of deciding whether a set of constraints contains harmless EGDs is undecidable. We contribute a sufficient syntactic condition characterizing harmless EGDs, broad and useful in practice. We focus on Warded Datalog+/- with harmless EGDs and argue that, in such fragment, query answering is decidable and PTIME in data complexity. We study chase-based techniques for query answering in Warded Datalog+/- with harmless EGDs, conducive to an efficient algorithm to be implemented in state-of-the-art reasoners.


iWarded: A System for Benchmarking Datalog+/- Reasoning (technical report)

Baldazzi, Teodoro, Bellomarini, Luigi, Sallinger, Emanuel, Atzeni, Paolo

arXiv.org Artificial Intelligence

Recent years have seen increasing popularity of logic-based reasoning systems, with research and industrial interest as well as many flourishing applications in the area of Knowledge Graphs. Despite that, one can observe a substantial lack of specific tools able to generate nontrivial reasoning settings and benchmark scenarios. As a consequence, evaluating, analysing and comparing reasoning systems is a complex task, especially when they embody sophisticated optimizations and execution techniques that leverage the theoretical underpinnings of the adopted logic fragment. In this paper, we aim at filling this gap by introducing iWarded, a system that can generate very large, complex, realistic reasoning settings to be used for the benchmarking of logic-based reasoning systems adopting Datalog+/-, a family of extensions of Datalog that has seen a resurgence in the last few years. In particular, iWarded generates reasoning settings for Warded Datalog+/-, a language with a very good tradeoff between computational complexity and expressive power. In the paper, we present the iWarded system and a set of novel theoretical results adopted to generate effective scenarios. As Datalog-based languages are of general interest and see increasing adoption, we believe that iWarded is a step forward in the empirical evaluation of current and future systems.