In this paper we study the distinct count aggregation function used in queries into expressive ontologies. The main differences in this settings opposed to aggregation in relational database systems are the Open World Assumption and incomplete knowledge. We propose different interpretations useful in different practical use-cases of the distinct count function, i.e. basic count, semantic count, epistemic count and semantic tuple count some of which use knowledge derived from the ontology in order to obtain results in accordance with the Open World Assumption. We use interval semantics to model the uncertainty of the distinct count function's result induced by incomplete knowledge in the ontology. We show that interval semantics are particularly useful in aggregate queries with filtering clause and when we need the retrieval of the boundaries of the uncertainty of the distinct count function's result. We study and present relationships among the different interpretations and decidability of the semantic tuple count. We also propose a theoretical approximation of the semantic tuple count. Our results are applicable to a wide range of description logic formalisms allowing to express equality/inequality between individuals, concepts and relations, e.g. Web Ontology Language.
['Bogdan Kostov', 'Petr Křemen']
Count aggregation in semantic queries