We present Circle, a classification algorithm based on the priciples of boolean function minimization. This classification process uses a recursive method to generate a set of implicants (or rules). The novelty of this algorithm is in the fact that the rules generated contain information about not only presence of features, but also their absence in determining class values. Although function minimization is inherently exponential on the number of attributes, we introduce several optimization techniques to reduce the complexity to the extent that we are able to scale the algorithm to 1000 columns, the limit in most commercial database systems. Circle is levelwise algorithm that iteratively produces implicants. For portions of the training set that are misclassified, Circle recurs producing additional implicants that will be logically conjoined to the previous implicants. Several optimization techniques were applied to the base Circle algorithm, as well as numerous ways it can be configured for specifc data mining tasks. Circle is completely implemented in Java with a JDBC-compliant database backend. One of the primary applications of Circle is mining bioinformatics data, and particularly genomic data. We present results of our experiments running circle on several well-known data sets for machine learning, as well as special large genomic data sets.