Towards a logical belief function theory

This paper presents a version of belief function theory in which masses are assigned to propositional formulas and which allows the modeler to consider integrity constraints. It also provides three combination rules which apply within this framework. It proves that the initial version of belief function theory and its extension to non-exclusive hypotheses are two particular cases of this proposal. It finally shows that, even if this framework is not more expressive than the belief function theory as defined by Dempster and Shafer, its interest resides in the fact that it offers the modeler a rich language to express its beliefs, i.e., the propositional language.