Motivations and ChallengesAccessing the relevant data in Big Data scenarios is increasingly difficult both for end-user and IT-experts, due to the volume, variety, and velocity dimensions of Big Data.This brings a hight cost overhead in data access for large enterprises. For instance, in the oil and gas industry, IT-experts spend 30-70% of their time gathering and assessing the quality of data [1]. The Optique project (http://www.optique-project. eu/) advocates a next generation of the well known Ontology-Based Data Access (OBDA) approach to address the Big Data dimensions and in particular the data access problem. The project aims at solutions that reduce the cost of data access dramatically.OBDA systems address the data access problem by presenting a general ontologybased and end-user oriented query interface over heterogeneous data sources. The core elements in a classical OBDA systems are an ontology describing the application domain and a set of mappings, relating the ontological terms with the schemata of the underlying data source. OBDA is natural for addressing the 3V of Big Data: the ontology covers the variety of data sources, on the fly data access for query evaluation allows to obtain fresh data regardless the velocity of its changes, and the virtual nature of data integration allows to manage large volumes of data.The important limitations of the state of the art OBDA systems are as follows: -The usability of OBDA systems is hampered by the need to use a formal query language which is difficult for end-users even if they know the ontological vocabulary. -The prerequisites of OBDA, i.e., ontology and mappings, are in practice expensive to obtain. Additionally, they are not static artefacts and should evolve according to the new end-users' information requirements. In current OBDA systems bootstrapping of ontologies and mappings are in a premature stage at the best. -The scope of existing systems is too narrow. The chosen expressiveness of the ontology and mapping language are focused on very concrete solutions. Management of streaming data is essentially ignored despite their importance for industry. -The efficiency of the translation process and the execution of the queries is too low. Some of these items were addressed by the Semantic Web community, but the solutions are limited and there is no unified approach to deal with all these aspects in one system.

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A new logic of belief (in the "only knowing" family) with confidence levels is presented. The logic allows a natural distinction between explicit and implicit belief representations, where the explicit form directly expresses its models. The explicit form can be found by applying a set of equivalence preserving rewriting rules to the implicit form. The rewriting process is performed entirely within the logic, on the object level, provided we supply an explicit formalization of the logical space. We prove that the problem of deciding whether there exists a consistent explicit form is p 2 -complete, a complexity class to which many problems of nonmonotonic reasoning belong. The article also contains a conceptual analysis of basic notions like belief, co-belief and degrees of confidence.