Logic of Association Rules

Association rules corresponding to general relation of two Boolean attributes are introduced. Association rules based on statistical hypotheses test are also included. Several classes of association rules are defined e.g. classes of implicational and of equivalence rules. Special logical calculi such that their formulae correspond to association rules are defined and studied. Practically important deduction rules of these calculi are introduced. It is shown that the question if the given association rule logically follows from an other given association rule can be converted into the question if suitable formulae of propositional calculus are tautologies. Several further theoretical results and research directions are mentioned.

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