Interpreting a contingency table by rules

Abstract

Joint distributions of discrete random variables, for instance, in the form of contingency tables, are a well-known means for representing knowledge. Their mathematical exactness and easy computability seem to be ideal preconditions for use as a knowledge base. The complexity of information they embody, however, makes it difficult to assign correct probabilities to events or—on the other hand—to understand the meanings of such probabilities and realize dependencies and independences. In this article, we introduce a method to detect automatically dependencies between random variables, extracting and aggregating the information given only by the probability values of the underlying distribution. No further presuppositions are imposed on the random variables; the method works by intensional reasoning. We use probabilistic logic to derive and describe our results, and the interpretation of the joint distribution is presented as a set of probabilistic rules. Most of the rules have the character of default rules, and hints on possible exceptions may be found as well. Moreover, classifications and hierarchical structures may also be taken into account. Thus, the rules are intended to reflect important features of the objects under consideration. © 1996 John Wiley & Sons, Inc.