Abstract
[3] and [7] generalize the notion of probability measures and belief functions to Belnap-Dunn (\(\textsf{BD}\)) logic, respectively. This work aims at providing an alternative way to treat contradictory information by relying on a logic that was introduced to reason about incomplete and contradictory information rather than on classical logic. In this article, we study how to update belief functions over \(\textsf{BD}\) logic with new pieces of information. We present a first approach via a frame semantics of \(\textsf{BD}\) logic. This frame semantics relying on sets, we can use Bayesian update and Dempster-Shafer combination rule over powerset algebras to define their corresponding updates within the framework of \(\textsf{BD}\) logic.
The research of Sabine Frittella and Sajad Nazari was funded by the grant ANR JCJC 2019, project PRELAP (ANR-19-CE48-0006).
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Frittella, S., Majer, O., Nazari, S. (2022). Toward Updating Belief Functions over Belnap-Dunn Logic. In: Le Hégarat-Mascle, S., Bloch, I., Aldea, E. (eds) Belief Functions: Theory and Applications. BELIEF 2022. Lecture Notes in Computer Science(), vol 13506. Springer, Cham. https://doi.org/10.1007/978-3-031-17801-6_25
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