Updating belief functions over Belnap--Dunn logic

TL;DR

This paper explores how to update belief functions within Belnap-Dunn logic, a framework suited for reasoning with incomplete and contradictory information, using a novel frame semantics approach.

Contribution

It introduces a new method for updating belief functions in Belnap-Dunn logic based on a frame semantics framework, addressing contradictions and incompleteness.

Findings

Proposes a novel update method for belief functions in Belnap-Dunn logic

Utilizes frame semantics to handle contradictory information effectively

Extends belief function theory to non-classical logic setting

Abstract

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.