ABSTRACT
This chapter briefly outlines the scope of automated reasoning in the absence of complete knowledge about the world. The incompleteness of facts or knowledge may appear in a reasoning system in different forms. There is no general notion to treat the different types of incompleteness of data and knowledge (clauses) by a unified approach. In this chapter, we cover 4 distinct techniques, all of which, however, may not be applicable to a common problem. The techniques are popularly known as default logic, non-monotonic logic, circumscription and auto-epistemic logic. Informally, default logic infers a consequent, when its pre-conditions are consistent with the world knowledge. The non-monotonic logic works with two modal operators and can continue reasoning in the presence of contradictory evidences. Circumscription is an alternative form of non-monotonic reasoning, which attempts to minimize the interpretations of some predicates and thus continues reasoning even in the presence of contradictions. The auto-epistemic logic that works on the belief of the reasoning system, occasionally changes inferences, as new evidences refute the existing belief.
