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