Revisiting Epistemic Logic with Names

TL;DR

This paper reexamines a multi-agent epistemic logic using abstract names, exploring its model theory, semantics, and extensions with knowledge operators, thereby modernizing the framework and enabling analysis of uncertain group membership.

Contribution

It provides a detailed model-theoretic analysis, introduces neighborhood semantics, and extends the logic with common and distributed knowledge, including axiomatizations.

Findings

Established bisimulation and frame morphisms for the logic.

Showed the logic's neighborhood semantics and independence from introspective assumptions.

Provided sound and complete axiomatizations for extended logics.

Abstract

This paper revisits the multi-agent epistemic logic presented in [10], where agents and sets of agents are replaced by abstract, intensional "names". We make three contributions. First, we study its model theory, providing adequate notions of bisimulation and frame morphisms, and use them to study the logic's expressive power and definability. Second, we show that the logic has a natural neighborhood semantics, which in turn allows to show that the axiomatization in [10] does not rely on possibly controversial introspective properties of knowledge. Finally, we extend the logic with common and distributed knowledge operators, and provide a sound and complete axiomatization for each of these extensions. These results together put the original epistemic logic with names in a more modern context and opens the door for a logical analysis of epistemic phenomena where group membership is uncertain or variable.