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A major task of traditional temporal event sequence mining is to find all frequent event patterns from a long temporal sequence. In many real applications, however, events are often grouped into different types, and not all types are of equal importance. In this paper, we consider the problem of efficient mining of temporal event sequences which lead to an instance of a specific type of event. Temporal constraints are used to ensure sensibility of the mining results. We will first generalise and formalise the problem of event-oriented temporal sequence data mining. After discussing some unique issues in this new problem, we give a set of criteria, which are adapted from traditional data mining techniques, to measure the quality of patterns to be discovered. Finally we present an algorithm to discover potentially interesting patterns.