We extend different Description Logics by concrete domains (such as integers and reals) and by aggregation functions over these domains (such as min,max,count,sum), which are usually available in database systems. We present decision procedures for the inference problems satisfiability for these Logics-provided that the concrete domain is not too expressive. An example of such a concrete domain is the set of (nonnegative) integers with comparisons (=,≤, ≤n, ...) and the aggregation functions min, max, count. / This is a new, extended version of a report with the same number. An abridged version has appeared in the Proceedings of the European Conference on Artificial Intelligence, Brighton, UK, 1998.

Integrating sophisticated statistical methods into database management systems is gaining more and more attention in research and industry. One important statistical method is time series forecasting, which is crucial for decision management in many domains. In this context, previous work addressed the processing of ad-hoc and recurring forecast queries. In contrast, we focus on subscription-based forecast queries that arise when an application (subscriber) continuously requires forecast values for further processing. Forecast queries exhibit the unique characteristic that the underlying forecast model is updated with each new actual value and better forecast values might be available. However, (re-)sending new forecast values to the subscriber for every new value is infeasible because this can cause significant overhead at the subscriber side. The subscriber therefore wishes to be notified only when forecast values have changed relevant to the application. In this paper, we reduce the costs of the subscriber by optimizing the notifications sent to the subscriber, i.e., by balancing the number of notifications and the notification length. We introduce a generic cost model to capture arbitrary subscriber cost functions and discuss different optimization approaches that reduce the subscriber costs while ensuring constrained forecast values deviations. Our experimental evaluation on real datasets shows the validity of our approach with low computational costs.

A common optimization technique in data warehouse environments is the use of materialized aggregates. Aggregate processing becomes complex, if partitions of aggregates or queries are materialized and reused later. Most problematic are the implication problems regarding the restriction predicates. We show that in the presence of hierarchies in a multidimensional environment an efficient algorithm can be given to construct - or to derive - an aggregate from one or more overlapping materialized aggregate partitions (set-derivability).