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Understandability, reuse, and maintainability of analytical queries belong to the key challenges of Data Warehousing, especially in settings where a large number of business analysts work together and need to share knowledge. To tackle these challenges we propose Ontology-based OLAP where an ontology acts as superimposed conceptual layer between business analysts and multidimensional data. In Ontologybased OLAP, dimensions and facts are enriched by concept definitions capturing the semantics of relevant business terms used to define measures and to formulate analytical queries. Using traditional ontology languages, it is, however, very difficult to capture the hierarchical and multidimensional conceptualizations of business analysts. In this paper, we propose hierarchical and multidimensional ontologies to better capture these structural specificities. We define and implement the abstract structure and semantics of multidimensional ontologies as rules and constraints in Datalog with negation and represent multidimensional ontologies as Datalog facts. In addition to reasoning over multidimensional ontologies (open-world) we discuss their grounding in Data Warehouses (closed-world) as the fundament of Ontologybased OLAP.

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