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The Semantic Web effort has steadily been gaining traction in the recentyears. In particular,Web search companies are recently realizing that theirproducts need to evolve towards having richer semantic search capabilities.Description logics (DLs) have been adopted as the formal underpinnings forSemantic Web languages used in describing ontologies. Reasoning underuncertainty has recently taken a leading role in this arena, given the natureof data found on theWeb. In this paper, we present a probabilistic extension ofthe DL EL++ (which underlies the OWL2 EL profile) using Markov logic networks(MLNs) as probabilistic semantics. This extension is tightly coupled, meaningthat probabilistic annotations in formulas can refer to objects in theontology. We show that, even though the tightly coupled nature of our languagemeans that many basic operations are data-intractable, we can leverage asublanguage of MLNs that allows to rank the atomic consequences of an ontologyrelative to their probability values (called ranking queries) even when thesevalues are not fully computed. We present an anytime algorithm to answerranking queries, and provide an upper bound on the error that it incurs, aswell as a criterion to decide when results are guaranteed to be correct.

Heuristic Ranking in Tightly Coupled Probabilistic Description Logics