A Logic of Expertise

TL;DR

This paper introduces a modal logic framework to model and reason about the expertise of information sources, including cases where sources make claims beyond their expertise, with a formal semantics linked to S5 epistemic logic.

Contribution

It presents a novel modal logic for expertise with non-standard semantics and establishes a connection to S5 epistemic logic, providing a sound and complete axiomatisation.

Findings

Established a formal semantics for expertise based on expertise sets.

Connected expertise logic to S5 epistemic logic.

Provided a sound and complete axiomatisation for the logic.

Abstract

In this paper we introduce a simple modal logic framework to reason about the expertise of an information source. In the framework, a source is an expert on a proposition $p$ if they are able to correctly determine the truth value of $p$ in any possible world. We also consider how information may be false, but true after accounting for the lack of expertise of the source. This is relevant for modelling situations in which information sources make claims beyond their domain of expertise. We use non-standard semantics for the language based on an expertise set with certain closure properties. It turns out there is a close connection between our semantics and S5 epistemic logic, so that expertise can be expressed in terms of knowledge at all possible states. We use this connection to obtain a sound and complete axiomatisation.