Logics for strict coherence and carnap-regular probability functions

Abstract

In this paper we provide a characterization of strict coherence in terms of the logical consistency of suitably defined formulas in fuzzy-modal logics for probabilistic reasoning. As a direct consequence of our characterization, we also show the decidability for the problem of checking the strict coherence of rational-valued books on classical events. Further, we introduce a fuzzy modal logic that captures Carnap-regular probability functions, that is normalized and finitely additive measures which maps to 0 only the impossible event.