Discovering Anomalies in Evidential Knowledge by Logic Programming

Abstract

The development of effective knowledge discovery techniques has become in the recent few years a very active research area due to the important impact it has in several relevant application areas. One interesting task thereof is that of singling out anomalous individuals from a given population, e.g., to detect rare events in time-series analysis settings, or to identify objects whose behavior is deviant w.r.t. a codified standard set of “social” rules. Such exceptional individuals are usually referred to as outliers in the literature.

Recently, outlier detection has also emerged as a relevant KR&R problem in the context of default logic [2]. For instance, detection algorithms can be used by rational agents to single out those observations that are anomalous to some extent w.r.t. their own, trustable knowledge about the world encoded in the form of a suitable logic theory.

In this paper, we formally state the concept of outliers in the context of logic programming. Besides the novel formalization we propose which helps in shedding some lights on the real nature of outliers, a major contribution of the work lies in the exploitation of a minimality criteria in their detection. Moreover, the computational complexity of outlier detection problems arising in this novel setting is thoroughly investigated and accounted for in the paper as well. Finally, we also propose a rewriting algorithm that transforms any outlier problem into an equivalent answer set computation problem, thereby making outlier computation effective and realizable on top of any answer set engine.