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In this paper, we discuss methods to assess the interestingness of a query in an environment of data cubes. We assume a hierarchical multidimensional database, storing data cubes and level hierarchies. We start with a comprehensive review of related work in the fields of human behavior studies and computer science. We define the interestingness of a query as a vector of scores along different aspects, like novelty, relevance, surprise and peculiarity and complement this definition with a taxonomy of the information that can be used to assess each of these aspects of interestingness. We provide both syntactic (result-independent) and extensional (result-dependent) checks, measures and algorithms for assessing the different aspects of interestingness in a quantitative fashion. We also report our findings from a user study that we conducted, analyzing the significance of each aspect, its evolution over time and the behavior of the study's participants. [ABSTRACT FROM AUTHOR]