Deduction Schemes for Association Rules

Several notions of redundancy exist for Association Rules. Often, these notions take the form "any dataset in which this first rule holds must obey also that second rule, therefore the second is redundant'"; if we see datasets as interpretations (or models) in the logical sense; this is a form of logical entailment. In many logics, entailment has a syntactic counterpart in the form of a deduction calculus. We provide such a deduction calculus for existing notions of redundancy; then; we consider a very general notion of entailment; where a confidence threshold is fixed and several rules can act as simultaneous premises; and identify exactly the cases where a partial rule follows from two partial rules; we also give a deduction calculus for this setting.