Outlier Detection Using Default Logic

Default logic is used to describe regular behavior and normal properties. We suggest to exploit the framework of default logic for detecting outliers - individuals who behave in an unexpected way or feature abnormal properties. The ability to locate outliers can help to maintain knowledgebase integrity and to single out irregular individuals. We first formally define the notion of an outlier and an outlier witness. We then show that finding outliers is quite complex. Indeed, we show that several versions of the outlier detection problem lie over the second level of the polynomial hierarchy. For example, the question of establishing if at least one outlier can be detected in a given propositional default theory is ∑₃^P -complete. Although outlier detection involves heavy computation, the queries involved can frequently be executed off-line, thus somewhat alleviating the difficulty of the problem. In addition, we show that outlier detection can be done in polynomial time for both the class of acyclic normal unary defaults and the class of acyclic dual normal unary defaults.