Mixed Rational Assessments of Possibility and Probability Measures

In this paper we introduce the modal-fuzzy logic FPΠ(RŁΔ) for reasoning about probability and possibility at the same time. We will use such a logical formalism in order to treat mixed assessments of both those kinds of measures. The main result of this paper is a characterization of the coherence for rational mixed assessments by means of the logical consistency of a suitably defined FPΠ(RŁΔ)-theory. By means of this characterization, we will also prove that the problem of testing the coherence of a mixed assessment is NP-complete.