When Names Are Not Commonly Known: Epistemic Logic with Assignments

TL;DR

This paper introduces a new modal predicate logic that allows non-rigid agent names, enabling better modeling of knowledge distinctions, with a complete axiomatisation over S5 models.

Contribution

It presents a novel logic framework that relaxes the common knowledge assumption of agent names and provides a complete axiomatisation for it.

Findings

Logic handles de dicto and de re distinctions naturally

Provides a complete axiomatisation over S5 models

Enables modeling of non-common knowledge of agent names

Abstract

In standard epistemic logic, agent names are usually assumed to be common knowledge implicitly. This is unreasonable for various applications. Inspired by term modal logic and assignment operators in dynamic logic, we introduce a lightweight modal predicate logic where names can be non-rigid. The language can handle various de dicto and de re distinctions in a natural way. The main technical result is a complete axiomatisation of this logic over S5 models.