Query answering under probabilistic uncertainty in Datalog+ / − ontologies

The recently introduced Datalog+ / − family of ontology languages is especially useful for representing and reasoning over lightweight ontologies, and is set to play a central role in the context of query answering and information extraction for the Semantic Web. Recently, it has become apparent that it is necessary to develop a principled way to handle uncertainty in this domain. In addition to uncertainty as an inherent aspect of the Web, one must also deal with forms of uncertainty due to inconsistency and incompleteness, uncertainty resulting from automatically processing Web data, as well as uncertainty stemming from the integration of multiple heterogeneous data sources. In this paper, we take an important step in this direction by developing a probabilistic extension of Datalog+ / −. This extension uses Markov logic networks as the underlying probabilistic semantics. Here, we focus especially on scalable algorithms for answering threshold queries, which correspond to the question “what is the set of all ground atoms that are inferred from a given probabilistic ontology with a probability of at least p ?”. These queries are especially relevant to Web information extraction, since uncertain rules lead to uncertain facts, and only information with a certain minimum confidence is desired. We present several algorithms, namely a basic approach, an anytime one, and one based on heuristics, which is guaranteed to return sound results. Furthermore, we also study inconsistency in probabilistic Datalog+ / − ontologies. We propose two approaches for computing preferred repairs based on two different notions of distance between repairs, namely symmetric and score-based distance. We also study the complexity of the decision problems corresponding to computing such repairs, which turn out to be polynomial and NP-complete in the data complexity, respectively.