Computing Specificity in Default Reasoning

Abstract

One of the most important problem encountered in knowledge based systems is the handling of exceptions in generic knowledge. A rule having exceptions (called also a default rule or a conditional assertion) is a piece of information of the following form “generally, if α is believed then β is also believed”, where a and, β are assumed here to be propositional logical formulas. A typical example of a conditional assertion is “generally, birds fly”. In the presence of incomplete information, one may jump to conclusions which are just plausible and can be revised in the light of new and complete information. For instance, given the default rules “generally, birds fly”, “generally, penguins do not fly”, and “all penguins are birds”, then from the incomplete information Tweety is a bird (but we do not know if Tweety is a penguin or not), we want to conclude that it flies. However, If we later learn that it is a penguin we should withdraw this conclusion. Classical logic is not appropriate for dealing with default information since we get inconsistency each time that an exceptional situation is observed. In the presence of inconsistency, classical logic infers trivial results. However, when there is no exceptions in our generic knowledge, classical logic is an efficient tool for correct reasoning.