Learning Logic Formulas and Related Error Distributions

This chapter describes a method for learning logic formulas that correctly classify the records of a given data set consisting of two classes. The method derives from given training data certain minimum cost satisfiability problems, solves these problems, and deduces from the solutions the desired logic formulas. There are at least two ways in which the results may be employed. First, one may use the logic formulas directly as rules in application programs. Second, one may construct vote-based rules, where the formulas produce votes and where the votes are combined to a vote-total. The latter approach allows for assessment and even control of prediction errors, as follows: Once the method has produced the logic formulas, it computes from the training data estimated distributions for the vote-totals without use of any additional data. From these distributions the method estimates probabilities for prediction errors. That information supports assessment and control of errors. Uses of the method include datamining, knowledge acquisition in expert systems, and identification of critical characteristics for recognition systems. Computational tests indicate that the method is fast and effective.