Database records can be often interpreted as state descriptions of some world, system or generic object, states of which occur independently and are described by binary properties. If records do not contain missing values, then there exists close relationship between association rules and propositions about state properties. In data mining we usually get a lot of association rules with large confidence and large support. Since their interpretation is often cumbersome, some quantitative measure of their informativeness would be very helpful. The main aim of the paper is to define a measure of the amount of information contained in an association rule. For this purpose we make use of the tight correspondence between association rules and logical implications. At first a quantitative measure of information content of logical formulas is introduced and studied. Information content of an association rule is then defined as information content of the corresponding logical implication in the situation when no knowledge about dependence among properties of world states is at our disposal. The intuitive meaning of the defined measure is that the association rule that allows more appropriate correction of the distribution of world states, acquired under unfair assumption of independence of state properties, contains also larger amount of information. The more appropriate correction here means a correction of the current probability distribution of states that leads to the distribution that is closer to the true distribution in the sense of Kullback-Leibler divergence measure.
In the paper, we focus on reasoning with IF-THEN rules in propositional fragment of predicate calculus and on its modeling with neural networks. At first, IF-THEN deduction from facts is defined. Then it is proved that for any non-contradictory set of IF-THEN rules and literals (representing facts) there exists a layered recurrent network with 2 hidden layers that can specify all IF-THEN deducible literals. If we denote the set of all literal IF-THEN consequences as D_0 and the set of all literal logical consequences as D, then obviously D_0 \subset D. Thus, D_0 can be considered to be an approximation of D. Using the designed network for simulation of contradiction proof, the approximation D_0 may be easily refined. Furthermore, the network may also be used for determination of D. However, the algorithm that realizes necessary network computations has exponential complexity.