A semantics for conditionals with default negation

Abstract

Ranking functions constitute a powerful formalism for nonmonotonic reasoning based on qualitative conditional knowledge. Conditionals are formalized defeasible rules and thus allow one to express that certain individuals or subclasses of some broader concept behave differently. More precisely, in order to model these exceptions by means of ranking functions, it is necessary to state that they behave contrarily with respect to the considered property. This paper proposes conditionals with default negation which instead enable a knowledge engineer to formalize exceptions without giving more specific information. This is useful when a subclass behaves indifferent towards a certain property, or the knowledge engineer wants to exclude a certain subclass because she is not aware of its behavior. Based on this novel type of conditionals, we further present and discuss a nonmonotonic inference formalism.