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In this paper, 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, constraint) 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 semantics for the same event in linear time structures with different granularities.
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