Dynamic Logics of Evidence-Based Belief

It is generally accepted that a rational belief must be grounded in the evidence available to an agent. However, there is much less agreement about the precise relationship between an agent’s beliefs and her evidence. Understanding this complex mechanism raises many interesting philosophical and technical issues. Modeling evidence requires richer structures than found in standard epistemic semantics where the accessible worlds aggregate all reliable evidence gathered so far. Even recent more finely-grained plausibility models ordering the epistemic ranges identify too much: belief is indistinguishable from aggregated best evidence. At the opposite extreme, one might model evidence syntactically as “formulas received”, but this seems overly detailed, and we we lose the intuition that evidence can be semantic in nature, zooming in on some actual world. Our proposal in this paper is to explore an intermediate semantic level, viz. that of neighborhood semantics, where evidence is recorded as a family of sets of worlds. Neighborhood models have been proposed as a technical tool for studying weak modal logics in the past. But here, we show how they support a notion of evidence with matching languages for attitudes based on it, as well as an array of natural actions that transform evidence.1 Our paper is mainly a pilot study. We develop the basics of neighborhood models for evidence and belief, and the logics that they support. Then we move to the main theme of the paper, showing how these models support natural actions of “evidence management”, ranging from external new information to internal rearrangement. Our main results are relative completeness theorems for these actions over the static base logic of evidence and belief, identifying the major ‘dynamic equations’ that govern the flow of information. Finally, we show via some representation theorems how the neighborhood framework extends the currently popular approach to dynamic logics of belief revision via plausibility pre-orders. All this is just the start of a much larger research project, and we indicate some further directions at the end.