Reasoning with belief functions over Belnap–Dunn logic

We design an expansion of Belnap–Dunn logic with belief and plausibility functions that allows non-trivial reasoning contradictory incomplete probabilistic information. also formalise non-standard probabilities in two ways. First, using a calculus linear inequalities, akin to the one presented [23]. Second, as two-layered modal wherein evidence (the outer layer) utilises paraconsistent expansions Łukasiewicz logic. The second approach is inspired by [3]. prove completeness for both kinds calculi show their equivalence establishing faithful translations directions.