  Belief and plausibility are weaker measures of uncertainty than that of
probability. They are motivated by the situations when full probabilistic
information is not available. However, information can also be contradictory.
Therefore, the framework of classical logic is not necessarily the most
adequate. Belnap-Dunn logic was introduced to reason about incomplete and
contradictory information. Klein et al and Bilkova et al generalize the notion
of probability measures and belief functions to Belnap-Dunn logic,
respectively. In this article, we study how to update belief functions with new
pieces of information. We present a first approach via a frame semantics of
Belnap-Dunn logic.
