Graded hypothesis theories

AbstractReasoning about expert domains often involves imperfect knowledge. In such cases any piece of information may prove to be useful. This requires considering uncertain beliefs and sometimes, when the expected information is missing, making additional assumptions. This paper presents a qualitative approach, which allows for the simultaneous representation of uncertain and/or incomplete information. A running example illustrates the need for such a representation. The proposed framework is a multimodal logic in which uncertainty is represented by means of a set of partially ordered symbolic grades, expressed as modal operators. Assumptions are formulated as hypotheses in 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. We also study various properties of this formalism in presence of partial inconsistency