A Logic of Expertise
This work addresses the issue of modeling when information sources make claims beyond their expertise, which is relevant for domains like AI and knowledge representation, but it is incremental as it builds on existing epistemic logic frameworks.
The paper tackles the problem of formally reasoning about the expertise of information sources by introducing a modal logic framework where a source is an expert on a proposition if they can determine its truth in all possible worlds, and it provides a sound and complete axiomatization by connecting to S5 epistemic logic.
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.