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 whole framework resorts to concept lattice models from 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.