GNNQ: a neuro-symbolic approach to query answering over incomplete knowledge graphs

Real-world knowledge graphs (KGs) are usually incomplete—that is, miss some facts representing valid information. So, when applied to such KGs, standard symbolic query engines fail to produce answers that are expected but not logically entailed by the KGs. To overcome this issue, state-of-the-art ML-based approaches first embed KGs and queries into a low-dimensional vector space, and then produce query answers based on the proximity of the candidate entity and the query embeddings in the embedding space. This allows embedding-based approaches to obtain expected answers that are not logically entailed. However, embedding-based approaches are not applicable in the inductive setting, where KG entities (i.e., constants) seen at runtime may differ from those seen during training. In this paper, we propose a novel neuro-symbolic approach to query answering over incomplete KGs applicable in the inductive setting. Our approach first symbolically augments the input KG with facts representing parts of the KG that match query fragments, and then applies a generalisation of the Relational Graph Convolutional Networks (RGCNs) to the augmented KG to produce the predicted query answers. We formally prove that, under reasonable assumptions, our approach can capture an approach based on vanilla RGCNs (and no KG augmentation) using a (often substantially) smaller number of layers. Finally, we empirically validate our theoretical findings by evaluating an implementation of our approach against the RGCN baseline on several dedicated benchmarks

Faithful rule extraction for differentiable rule learning models

There is increasing interest in methods for extracting interpretable rules from ML models trained to solve a wide range of tasks over knowledge graphs (KGs), such as KG completion, node classification, question answering and recommendation. Many such approaches, however, lack formal guarantees establishing the precise relationship between the model and the extracted rules, and this lack of assurance becomes especially problematic when the extracted rules are applied in safety-critical contexts or to ensure compliance with legal requirements. Recent research has examined whether the rules derived from the influential Neural-LP model exhibit soundness (or completeness), which means that the results obtained by applying the model to any dataset always contain (or are contained in) the results obtained by applying the rules to the same dataset. In this paper, we extend this analysis to the context of DRUM, an approach that has demonstrated superior practical performance. After observing that the rules currently extracted from a DRUM model can be unsound and/or incomplete, we propose a novel algorithm where the output rules, expressed in an extension of Datalog, ensure both soundness and completeness. This algorithm, however, can be inefficient in practice and hence we propose additional constraints to DRUM models facilitating rule extraction, albeit at the expense of reduced expressive power

The Stable Model Semantics of Datalog with Metric Temporal Operators

We introduce negation under the stable model semantics in DatalogMTL - a temporal extension of Datalog with metric temporal operators. As a result, we obtain a rule language which combines the power of answer set programming with the temporal dimension provided by metric operators. We show that, in this setting, reasoning becomes undecidable over the rational timeline, and decidable in EXPSPACE in data complexity over the integer timeline. We also show that, if we restrict our attention to forward-propagating programs, reasoning over the integer timeline becomes PSPACE-complete in data complexity, and hence, no harder than over positive programs; however, reasoning over the rational timeline in this fragment remains undecidable. Under consideration in Theory and Practice of Logic Programming (TPLP).Comment: Under consideration in Theory and Practice of Logic Programming (TPLP