A Logic for Reasoning about Evidence

TL;DR

This paper presents a formal logic framework for reasoning about evidence, modeling how evidence updates beliefs, with a sound and complete axiomatization and analysis of decision complexity, incorporating propositional and numerical variables.

Contribution

It introduces a novel logic for evidence reasoning that captures belief updates and provides a complete axiomatization with complexity analysis.

Findings

Logic is sound and complete

Decision problem complexity analyzed

Incorporates propositional and numerical variables

Abstract

We introduce a logic for reasoning about evidence, that essentially views evidence as a function from prior beliefs (before making an observation) to posterior beliefs (after making the observation). We provide a sound and complete axiomatization for the logic, and consider the complexity of the decision problem. Although the reasoning in the logic is mainly propositional, we allow variables representing numbers and quantification over them. This expressive power seems necessary to capture important properties of evidence