Belief Based on Inconsistent Information

A recent line of research has developed around logics of belief based on evidence. The approach of Bilkova 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 Łukasiewicz logic, or a bilattice logic, within a two-layer modal logical framework to account for belief.