First-Order Logic Based Formalism for Temporal Data Mining

In this article we define a formalism for a methodology that has as purpose the discovery of knowledge, represented in the form of general Horn clauses, inferred from databases with a temporal dimension. To obtain what we called temporal rules, a discretisation phase that extracts events from raw data is applied first, followed by an induction phase, which constructs classification trees from these events. The theoretical framework we proposed, based on first-order temporal logic, permits us to define the main notions (event, temporal rule, constraint) in a formal way. The concept of consistent linear time structure allows us to introduce the notions of general interpretation and of confidence. These notions open the possibility to use statistical approaches in the design of algorithms for inferring higher order temporal rules, denoted temporal meta-rules.