Viewing hypothesis theories as constrained graded theories

Abstract

Modeling expert tasks often leads to consider uncertain and/or incomplete knowledge. This generally requires reasoning about uncertain beliefs and sometimes making additional hypotheses. While numerical models are often used to model uncertainty, the estimation of precise and meaningful values for certainty degrees is sometimes problematic. Moreover, the use of a numerical scale implies that any two certainty degrees are comparable. This paper presents a qualitative approach, where uncertainty is represented by means of partially ordered symbolic grades. The framework is a multimodal logic in which each grade is expressed as a modal operator. An extension of this framework is proposed which makes it possible to state additional hypotheses in the spirit of Siegel and Schwind's hypothesis theory. We show that such hypotheses may be interpreted as constraints on the set of possible beliefs. We thus obtain a very natural integration of multimodal graded logic and hypothesis theory. The resulting framework allows for the simultaneous representation of uncertain and/or incomplete information. Some correspondence results between extensions of graded default logic and those of such new graded hypothesis theories are established.