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Tightly Integrated Probabilistic Description Logic Programs for Representing Ontology Mappings

Thomas Lukasiewicz‚ Livia Predoiu and Heiner Stuckenschmidt


Creating mappings between ontologies is a common way of approaching the semantic heterogeneity problem on the Semantic Web. To fit into the landscape of Semantic Web languages, a suitable, logic-based representation formalism for mappings is needed. We argue that such a formalism has to be able to deal with uncertainty and inconsistencies in automatically created mappings. We analyze the requirements for such a formalism, and we propose a novel approach to probabilistic description logic programs as such a formalism, which tightly combines normal logic programs under the well-founded semantics with both tractable ontology languages and Bayesian probabilities. We define the language, and we show that it can be used to resolve inconsistencies and merge mappings from different matchers based on the level of confidence assigned to different rules. Furthermore, we explore the semantic and computational aspects of probabilistic description logic programs under the well-founded semantics. In particular, we show that the well-founded semantics approximates the answer set semantics. We also describe algorithms for consistency checking and tight query processing, and we analyze the data and general complexity of these two central computational problems. As a crucial property, the novel tightly integrated probabilistic description logic programs under the well-founded semantics allow for tractable consistency checking and for tractable tight query processing in the data complexity, and they have even a first-order rewritable (and thus LogSpace data complexity) special case, which is especially interesting for representing ontology mappings.

Annals of Mathematics and Artificial Intelligence