Inquisitive Logic as an Epistemic Logic of Knowing How

TL;DR

This paper reinterprets propositional inquisitive logic as an epistemic logic of knowing how, using dynamic epistemic logic to capture the semantics and provide a complete axiomatization, offering an intuitive understanding of inquisitive reasoning.

Contribution

It introduces an epistemic interpretation of inquisitive logic as knowing how, with a complete axiomatization and expressivity results using dynamic epistemic logic.

Findings

Valid know-how formulas match inquisitive logic support

Both know-how and dynamic operators can be eliminated without loss of expressivity

The framework offers an intuitive interpretation of inquisitive concepts

Abstract

In this paper, we present an alternative interpretation of propositional inquisitive logic as an epistemic logic of knowing how. In our setting, an inquisitive logic formula $\alpha$ being supported by a state is formalized as "knowing how to resolve $\alpha$" (more colloquially, "knowing how $\alpha$ is true") holds on the S5 epistemic model corresponding to the state. Based on this epistemic interpretation, we use a dynamic epistemic logic with both know-how and know-that operators to capture the epistemic information behind the innocent-looking connectives in inquisitive logic. We show that the set of valid know-how formulas corresponds precisely to the inquisitive logic. The main result is a complete axiomatization with intuitive axioms using the full dynamic epistemic language. Moreover, we show that the know-how operator and the dynamic operator can both be eliminated without changing the expressivity over models, which is consistent with the modal translation of inquisitive logic existing in the literature. We hope our framework can give an intuitive alternative interpretation of various concepts and technical results in inquisitive logic, and also provide a powerful and flexible tool to do inquisitive reasoning in an epistemic context.