  A recent line of research has developed around logics of belief based on
evidence. The approach of B\'ilkov\'a et al understands belief as based on
information confirmed by a reliable source. We propose a finer analysis of how
belief can be based on information, where the confirmation comes from multiple
possibly conflicting sources and is of a probabilistic nature. We use
Belnap-Dunn logic and its probabilistic extensions to account for potentially
contradictory information on which belief is grounded. We combine it with an
extension of Lukasiewicz logic, or a bilattice logic, within a two-layer modal
logical framework to account for belief.
