On Logical Interpretation of Association Rules

A. Vesely (Czech Republic)


knowledge acquisition, data mining, association rules, logical formulas


In the paper the relationship between Agrawal’s association rules and logical formulas is systematically studied. In order to be possible to interpret association rules as logical formulas and to estimate the probability of their validity, the set of transactions has to be restricted to the set of so called complete transactions. Then it is possible to prove that an association rule with confidence conf ≅ 1 and support sup can be interpreted as logical implication and the probability of its validity can be estimated as 1+sup −sup/cf ≅ 1. Moreover, the probability of its possible use in deduction is sup/cf ≅ sup. Thus the time consuming task of finding logical implications in large complete transaction data sets can be solved with effective Agrawal’s algorithms for mining association rules. On the other hand, any association rule with parameters conf and sup can be interpreted in natural way as logical implication that is valid with probability depending only on parameters conf and sup.

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