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In this paper we survey our recent results characterizing various graph neural network (GNN) architectures in terms of their ability to classify nodes over graphs, for classifiers based on unary logical formulas- or queries. We focus on the language FOC2, a well-studied fragment of FO. This choice is motivated by the fact that FOC2 is related to theWeisfeiler-Lehman (WL) test for checking graph isomorphism, which has the same ability as GNNs for distinguishing nodes on graphs. We unveil the exact relationship between FOC2 and GNNs in terms of node classification. To tackle this problem, we start by studying a popular basic class of GNNs, which we call AC-GNNs, in which the features of each node in a graph are updated, in successive layers, according only to the features of its neighbors. We prove that the unary FOC2 formulas that can be captured by an AC-GNN are exactly those that can be expressed in its guarded fragment, which in turn corresponds to graded modal logic. This result implies in particular that ACGNNs are too weak to capture all FOC2 formulas. We then seek for what needs to be added to AC-GNNs for capturing all FOC2. We show that it suffices to add readouts layers, which allow updating the node features not only in terms of its neighbors, but also in terms of a global attribute vector. We call GNNs with readouts ACR-GNNs. We also describe experiments that validate our findings by showing that, on synthetic data conforming to FOC2 but not to graded modal logic, AC-GNNs struggle to fit in while ACR-GNNs can generalise even to graphs of sizes not seen during training.

The original SPARQL proposal was often criticized for its inability to navigate through the structure of RDF documents. For this reason property paths were introduced in SPARQL 1.1, but up to date there are no theoretical studies examining how their addition to the language affects main computational tasks such as query evaluation, query containment, and query subsumption. In this paper we tackle all of these problems and show that although the addition of property paths has no impact on query evaluation, they do make the containment and subsumption problems substantially more difficult.

Semantic Web systems provide open interfaces for end-users to access data via a powerful high-level query language, SPARQL. But users unfamiliar with either the details of SPARQL or properties of the target dataset may find it easier to query by example-give examples of the information they want (or examples of both what they want and what they do not want) and let the system reverse engineer the desired query from the examples. This approach has been heavily used in the setting of relational databases. We provide here an investigation of the reverse engineering problem in the context of SPARQL. We first provide a theoretical study, formalising variants of the reverse engineering problem and giving tight bounds on its complexity. We next explain an implementation of a reverse engineering tool for positive examples. An experimental analysis of the tool shows that it scales well in the data size, number of examples, and in the size of the smallest query that fits the data. We also give evidence that reverse engineering tools can provide benefits on real-life datasets. * The authors would like to thank Michael Benedikt for many fruitful discussions about the results presented in this paper. M. Arenas was funded by Millennium Nucleus Center for Semantic Web Research under Grant NC120004, and G. I. Diaz by Becas Chile of CONICYT Chile. Copyright is held by the International World Wide Web Conference Committee (IW3C2). IW3C2 reserves the right to provide a hyperlink to the author's site if the Material is used in electronic media.

While the problem of answering positive existential queries, in particular, conjunctive queries (CQs) and unions of CQs, over description logic ontologies has been studied extensively, there have been few attempts to analyse queries with negated atoms. Our aim is to sharpen the complexity landscape of the problem of answering CQs with negation and inequalities in lightweight description logics of the DL-Lite and EL families. We begin by considering queries with safe negation and show that there is a surprisingly significant increase in the complexity from AC 0 to undecidability (even if the ontology and query are fixed and only the data is regarded as input). We also investigate the problem of answering queries with inequalities and show that answering a single CQ with one inequality over DL-Lite with role inclusions is undecidable. In the light of our undecidability results, we explore syntactic restrictions to attain efficient query answering with negated atoms. In particular, we identify a novel class of local CQs with inequalities, for which query answering over DL-Lite is decidable.