4 research outputs found
Comparing the Update Expressivity of Communication Patterns and Action Models
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.Comment: In Proceedings TARK 2023, arXiv:2307.0400
Logics with Group Announcements and Distributed Knowledge: Completeness and Expressive Power
Public announcement logic (PAL) is an extension of epistemic logic with dynamic operators that model the effects of all agents simultaneously and publicly acquiring the same piece of information. One of the extensions of PAL, group announcement logic (GAL), allows quantification over (possibly joint) announcements made by agents. In GAL, it is possible to reason about what groups can achieve by making such announcements. It seems intuitive that this notion of coalitional ability should be closely related to the notion of distributed knowledge, the implicit knowledge of a group. Thus, we study the extension of GAL with distributed knowledge, and in particular possible interaction properties between GAL operators and distributed knowledge. The perhaps surprising result is that, in fact, there are no interaction properties, contrary to intuition. We make this claim precise by providing a sound and complete axiomatisation of GAL with distributed knowledge. We also consider several natural variants of GAL with distributed knowledge, as well as some other related logic, and compare their expressive power.publishedVersio
Logics with Group Announcements and Distributed Knowledge: Completeness and Expressive Power.
Public announcement logic (PAL) is an extension of epistemic logic with dynamic operators that model the effects of all agents simultaneously and publicly acquiring the same piece of information. One of the extensions of PAL, group announcement logic (GAL), allows quantification over (possibly joint) announcements made by agents. In GAL, it is possible to reason about what groups can achieve by making such announcements. It seems intuitive that this notion of coalitional ability should be closely related to the notion of distributed knowledge, the implicit knowledge of a group. Thus, we study the extension of GAL with distributed knowledge, and in particular possible interaction properties between GAL operators and distributed knowledge. The perhaps surprising result is that, in fact, there are no interaction properties, contrary to intuition. We make this claim precise by providing a sound and complete axiomatisation of GAL with distributed knowledge. We also consider several natural variants of GAL with distributed knowledge, as well as some other related logic, and compare their expressive power