Comparing the Update Expressivity of Communication Patterns and Action Models

Abstract

Any kind of dynamics in dynamic epistemic logic can be represented as an action model. Right? Wrong! In this contribution we prove that the update expressivity of communication patterns is incomparable to that of action models. Action models, as update mechanisms, were proposed by Baltag, Moss, and Solecki in 1998 and have remained the nearly universally accepted update mechanism in dynamic epistemic logics since then. Alternatives, such as arrow updates that were proposed by Kooi and Renne in 2011, have update equivalent action models. More recently, the picture is shifting. Communication patterns are update mechanisms originally proposed in some form or other by Agotnes and Wang in 2017 (as resolving distributed knowledge), by Baltag and Smets in 2020 (as reading events), and by Velazquez, Castaneda, and Rosenblueth in 2021 (as communication patterns). All these logics have the same expressivity as the base logic of distributed knowledge. However, their update expressivity, the relation between pointed epistemic models induced by such an update, was conjectured to be different from that of action model logic. Indeed, we show that action model logic and communication pattern logic are incomparable in update expressivity. We also show that, given a history-based semantics and when restricted to (static) interpreted systems, action model logic is (strictly) more update expressive than communication pattern logic. Our results are relevant for distributed computing wherein oblivious models involve arbitrary iteration of communication patterns.