A Logic for Reasoning about Evidence

TL;DR

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

Contribution

It introduces a novel logic for evidence reasoning that includes quantification over numerical variables, providing soundness, completeness, and complexity insights.

Findings

Logic effectively models evidence as belief updates

Complete axiomatization established for the logic

Complexity analysis of decision procedures

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.