Positive and Negative Explanations of Uncertain Reasoning in the Framework of Possibility Theory

This paper presents an approach for developing the explanation capabilities of rule-based expert systems managing imprecise and uncertain knowledge. The treatment of uncertainty takes place in the framework of possibility theory where the available information concerning the value of a logical or numerical variable is represented by a possibility distribution which restricts its more or less possible values. We first discuss different kinds of queries asking for explanations before focusing on the two following types : i) how, a particular possibility distribution is obtained (emphasizing the main reasons only) ; ii) why in a computed possibility distribution, a particular value has received a possibility degree which is so high, so low or so contrary to the expectation. The approach is based on the exploitation of equations in max-min algebra. This formalism includes the limit case of certain and precise information.