Time Granularity in Temporal Data Mining

In this chapter, a formalism for a specific temporal data mining task (the discovery of rules, inferred from databases of events having a temporal dimension), is defined. The proposed theoretical framework, based on first-order temporal logic, allows the definition of the main notions (event, temporal rule, confidence) in a formal way. This formalism is then extended to include the notion of temporal granularity and a detailed study is made to investigate the formal relationships between the support measures of the same event in linear time structures with different granularities. Finally, based on the concept of consistency, a strong result concerning the independence of the confidence measure for a temporal rule, over the worlds with different granularities, is proved.