Nonmonotonic reasoning under uncertain evidence

Abstract

Representation of uncertain evidence is a recurrent need in the reasoning process, for example to decide among multiple extensions, to detect possible inconsistencies among sources of information, to rank alternatives or goals, and to propagate the information through a reasoning network. Management of uncertain, incomplete and contradictory knowledge has usually been left to ad hoc representation and combination rules, lacking either a sound theory or clear semantics. This consideration is specially relevant in nonmonotonic reasoning, since representation of uncertain evidence has been usually left out of these systems' possibilities. We present a logic that aims to solve formally and pragmatically these representation and reasoning issues. The logic regards incomplete or uncertain evidence about a given situation as information provided by more or less trustable sources. A semantic characterization of the set of conclusions is given, and a derivation procedure is proven sound and complete with respect to this semantics. The system overcomes some common problems arising in nonmonotonic reasoning, such as multiple extensions, inconsistent contexts or reasoning deadlocks.