FULL NONMONOTONICITY : A NEW PERSPECTIVE IN DEFEASIBLE REASONING

The capability of drawing defeasible conclusions in presence of partial information is a crucial factor of intelligent behavior. To achieve this capability, human beings resort to a particular kind of knowledge, called default knowledge. The most significant property of default knowledge is that it can be exploited in the reasoning process even if there is only partial information about the satisfaction of the preconditions which allow its application, on condition that there is no reason to believe that such preconditions are not satisfied. If new information becomes available from which the falsity of such preconditions can be deduced, the conclusions derived from the application of default knowledge have to be retracted. This particular form of reasoning, involving the use of default knowledge, may be called defeasible reasoning. In order to build automated reasoning systems including defeasible reasoning capabilities, many extensions of classical logic have been proposed as models of defeasible reasoning. These proposals, even if differing in many important technical details, share a common conceptual ground, since they all rely substantially on the same conceptual model of defeasible reasoning activity. Among the most notable and classic proposals in this field we mention default logic [7] and nonmonotonic logic [5]. However, this conceptual model suffers from some important limitations, which severely restrict its applicability scope and prevent it (as well as the approaches grounded on it) to correctly capture and represent some very general and common cases of practical defeasible reasoning. In order to overcome these limitations, both a more general conceptual model of defeasible reasoning activity and a formalism capturing the new concepts introduced are needed. Following the track of some previous investigations in this area [1] [2], this paper points out a further limitation of most known models of defeasible reasoning which (as to our knowledge) has never been highlighted before. The paper is organized as follows. In section 2 we briefly review some approaches to defeasible reasoning and identify the conceptual model underlying them. In section 3 we define a property for defeasible reasoning formalisms, called full nonmonotonicity: we point out that this property has received a very limited attention in the past and that most approaches to defeasible reasoning fail to satisfy this property. In section 4, we present a common sense example of defeasible reasoning (let’s call it the "ill secretary" example) that requires the full nonmonotonicity property and that, therefore, can not be adequately represented in most classical defeasible reasoning models. Finally, in section 5, we describe a new approach to modeling defeasible reasoning, based on the concept of Auncertainty [2]. We discuss the conceptual advantages of this approach and we show that it can be properly used to deal with the "ill secretary" example and with similar kinds of defeasible reasoning activity.