On Horn Axiomatizations for Sequential Data

We propose a notion of deterministic association rules for ordered data. We prove that our proposed rules can be formally justified by a purely logical characterization, namely, a natural notion of empirical Horn approximation for ordered data which involves background Horn conditions; these ensure the consistency of the propositional theory obtained with the ordered context. The main proof resorts to a concept lattice model in the framework of Formal Concept Analysis, but adapted to ordered contexts. We also discuss a general method to mine these rules that can be easily incorporated into any algorithm for mining closed sequences, of which there are already some in the literature.

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