Reasoning About Justified Belief Based on the Fusion of Evidence

In this paper, we propose logics for reasoning about belief and evidence. Starting from justification logic (JL) in which the reasons why a fact is believed are explicitly represented as justification terms, we explore the relationship between justified belief and fused information from different evidential sources. We argue that the expressive power of JL is inadequate for our purpose, because, while a justification formula can represent that a piece of evidence is admissible for the belief, it cannot express whether the evidence has been actually observed. Therefore, to address the issue, we propose more fine-grained JL's that can express the informational content of evidence, and the actual observation of evidence is definable in such logics. As a byproduct, we also show that the proposed logics are easily extended to accommodate dynamic evidential reasoning. Consequently, we can integrate JL and dynamic epistemic logic (DEL) paradigms in a natural way.