Evidence Logic: A New Look at Neighborhood Structures

Two of the authors (van Benthem and Pacuit) recently introduced evidence logic as a way to model epistemic agents faced with possibly contradictory evidence from different sources. For this the authors used neighborhood semantics, where a neighborhood N indicates that the agent has reason to believe that the true state of the world lies in N. A normal belief modality is defined in terms of the neighborhood structure. In this paper we consider four variants of evidence logic which hold for different classes of evidence models. For each of these logics we give a representation theorem using extended evidence models, where the belief operator is replaced by a standard relational modality. With this, we axiomatize all four logics, and determine whether each has the finite model property.