A capacity-based framework encompassing Belnap–Dunn logic for reasoning about multisource information

Belnap–Dunn four-valued logic is one of the best known logics for handling elementary information items coming from several sources. More recently, a conceptually simple framework, namely a two-tiered propositional logic augmented with classical modal axioms (here called BC logic), was suggested by the second author and colleagues, for the handling of multisource information. It is a fragment of the non-normal modal logic EMN, whose semantics is expressed in terms of two-valued monotonic set functions called Boolean capacities. We show BC logic is more expressive than Belnap–Dunn logic by proposing a consequence-preserving translation of Belnap–Dunn logic in this setting. As special cases, we can recover already studied translations of three-valued logics such as Kleene and Priest logics. Moreover, BC logic is compared with the source-processor logic of Avron, Ben Naim and Konikowska. Our translation bridges the gap between Belnap–Dunn logic, epistemic logic, and theories of uncertainty like possibility theory or belief functions, and paves the way to a unified approach to various methods for handling inconsistency due to several conflicting sources of information.