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Top1. Introduction
Ontologies are applied in a wide range of application fields such as knowledge management, natural language processing, e-commerce, intelligent information integration, information retrieval, Semantic Web, and so on. Another emerging application area is data warehousing, in particular, in the construction of Multidimensional information systems, also known as OLAP (On-Line Analytical Processing) systems (Thomsen, 2002). In such a context, ontologies may be used for several purposes, as to address semantic heterogeneity (Priebe & Pernul, 2003; Niemi et al., 2007). But in this paper, the two applications of ontologies in OLAP systems we are interested in are the use of ontologies to enrich cube dimensions (Mazón, Trujillo, Serrano & Piattini, 2006; Mazón & Trujillo, 2006; Pardillo & Mazón, 2011; Neumayr, Schütz, & Schrefl, 2013), and the definition of ontology based-dimensions (Romero & Abelló, 2007a, 2007b, 2010).
With respect to the first use, dimension enrichment may be carried out obtaining from existing ontologies new relationships (adding new aggregation levels), or obtaining another semantic relationships (e.g. the whole-part relationship), so that new hierarchies may be added to the dimensions. In (Mazón, Trujillo, Serrano & Piattini, 2006; Mazón & Trujillo, 2006), the use of WordNet (Miller et al, 1990) for enriching data warehouse dimensions is proposed, based on the semantic relationships defined between WordNet concepts. Therefore, if a Product dimension is used in our OLAP system, using the semantic relationships defined on WordNet, the subtype, type, and class of a product can be obtained. (For example, if we have a product named as Chardonnay, we can obtain that it is White wine, Wine, and an Alcoholic beverage.) But, if dimensions are enriched with every semantic relationship available in WordNet, details that are beyond the scope of the dimension may be added to it. Even, dimensions may be obscured because of the massive incorporation of related attributes.
With respect to the other use of ontologies in data warehousing, the definition of dimensions using existing ontologies, it makes easier dealing with integration and interoperability issues when data warehouses share some dimensions. However, it is possible that these ontologies we are using to define the dimensions include concepts that are not needed for the dimensions.
Therefore, on the one hand, dimension enrichment using existing ontologies may lead to obtain dimensions that include attributes that have not to be included in the dimension; on the other hand, the definition of dimensions using ontologies may force that an OLAP tool has dimensions that that incorporate concepts that are not needed. One way or another, these problems may be solved using one of the existing mechanisms to define ontology views (Magkanaraki et al., 2004; Rajugan et al, 2005; Uceda-Sosa et al., 2004; Volz et al., 2003; Noy et al., 2004; Seidenberg & Rector, 2006) Therefore, concepts that are not needed for the domain ontology are kept out of the view. However, this view must be closed. The closure property is a well-known property of schemas in object databases, so that no class of a schema has references to classes that are not included in the schema (Rundensteiner, 1992; Lacroix & Delobel, 1998; Torres & Samos, 2001). Analogously, an ontology will be closed if every component of the ontology does not have references to components that are not included in the ontology.