Changing agents and ascribing beliefs in dynamic epistemic logic

TL;DR

This paper extends dynamic epistemic logic to include agent updates, allowing for selective information sharing and modeling complex scenarios like private updates and deception, while maintaining soundness, completeness, and feasible decision procedures.

Contribution

It introduces agent-update frames for dynamic epistemic logic, enabling the addition or removal of agents and selective information updates, with formal semantics and proof systems.

Findings

Extended action frames to include agent updates

Maintained soundness and completeness of proof systems

Developed decision procedures with expected complexity

Abstract

In dynamic epistemic logic (Van Ditmarsch, Van Der Hoek, & Kooi, 2008) it is customary to use an action frame (Baltag & Moss, 2004; Baltag, Moss, & Solecki, 1998) to describe different views of a single action. In this article, action frames are extended to add or remove agents, we call these agent-update frames. This can be done selectively so that only some specified agents get information of the update, which can be used to model several interesting examples such as private update and deception, studied earlier by Baltag and Moss (2004); Sakama (2015); Van Ditmarsch, Van Eijck, Sietsma, and Wang (2012). The product update of a Kripke model by an action frame is an abbreviated way of describing the transformed Kripke model which is the result of performing the action. This is substantially extended to a sum-product update of a Kripke model by an agent-update frame in the new setting. These ideas are applied to an AI problem of modelling a story. We show that dynamic epistemic logics, with update modalities now based on agent-update frames, continue to have sound and complete proof systems. Decision procedures for model checking and satisfiability have expected complexity. For a sublanguage, there are polynomial space algorithms.