Enhancing multidimensional database models with aggregation hierarchies allows viewing data at different levels of aggregation. Usually, hierarchy instances are represented by means of so-called rollup functions. Rollup between adjacent levels in the hierarchy are given extensionally, while rollups between connected nonadjacent levels are obtained by means of function composition. In many real-life cases, this model cannot capture accurately the meaning of common situations, particularly when exceptions arise. Exceptions may appear due to corporate policies, unreliable data or uncertainty, and their presence may turn the notion of rollup composition unsuitable for representing real relationships in the aggregation hierarchies. In this paper we present a language allowing augmenting traditional extensional rollup functions with intensional knowledge. We denote this language IRAH (Intensional Redefinition for Aggregation Hierarchies). Programs in IRAH consist of intensional rules, which can be regarded as patterns for: (a) overriding natural composition between rollup functions on adjacent levels in the concept hierarchy, (b) canceling the effect of rollup functions for specific values. Our proposal is presented as a stratified default theory. We show that a unique model for the underlying theory always exists, and can be computed in a bottom-up fashion. Finally, we present an algorithm that computes the revised dimension in polynomial time, although under more realistic assumptions, complexity becomes linear on the number of paths in the hierarchy of the dimension instance.

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A peer-to-peer (P2P) data management system consists essentially of a network of peer systems, each maintaining full autonomy over its own data resources. Data exchange between peers occurs when one of them, in the role of a local peer, needs data available in other nodes, denoted the acquaintances of the local peer. No global schema is assumed to exist for any data under this computing paradigm. Henceforth, data provided by an acquaintance of a local peer must be adapted, in a manner that answers to queries posed by local peer users conform the view those users have of their data. Because a multidimensional database normally consists in a collection of views of aggregated data, a careful translation process is needed in this case, in order to transform any summary concept that appears in a peer acquaintance into a summary concept meaningful to the requesting peer. We present a model for multidimensional data distributed in a P2P network, and a query rewriting technique, that allows a local peer to propagate OLAP queries among its acquaintances, obtaining a meaningful and correct answer.