A THEORETICAL INVESTIGATION INTO QUANTITATIVE MODAL LOGIC

Quantitative modal logic (QML) is a multi-modal formulation of possibilistic reasoning with the capacity of representing and reasoning about higher order uncertainty. In this paper, some results about QML and possibility theory are investigated. First, the concept of filtration in classical modal logic is introduced into QML and the fundamental filtration theorem is proved. Second, as a corollary, the finite model property of QML is provided. Finally, the theoretical and practical implications of finite model property are discussed.