Arrow Update Logic

Abstract

We present Arrow Update Logic, a theory of epistemic access elimination that can be used to reason about multi-agent belief change. While the belief-changing "arrow updates" of Arrow Update Logic can be transformed into equivalent belief-changing "action models" from the popular Dynamic Epistemic Logic approach, we prove that arrow updates are sometimes exponentially more succinct than action models. Further, since many examples of belief change are naturally thought of from Arrow Update Logic's perspective of eliminating access to epistemic possibilities, Arrow Update Logic is a valuable addition to the repertoire of logics of information change. In addition to proving basic results about Arrow Update Logic, we introduce a new notion of common knowledge that generalizes both ordinary common knowledge and the "relativized" common knowledge familiar from the Dynamic Epistemic Logic literature.

Reflecting on Social Influence in Networks

“…To this logic, we will then add the modality for social influence from (Christoff and Hansen 2013) -also mentioned in Section 1. Finally, we will add learning modalities inspired by the graph modifiers of (Aucher et al 2009) and the Arrow Update Logic of (Kooi and Renne 2011). First, we fix a countable set of nominals NOM, which will be used to name agents in the social networks.…”

Relativized common knowledge for dynamic epistemic logic

“…We also studied expressive power, and filled some gaps in expressivity results for standard relativized common knowledge as well. Transforming a dynamic model transformation operator to a special common knowledge operator is not a new idea; it was also exploited in [9] for arrow update logic. This technique thus works for public announcements, action models and arrow updates.…”

Epistemic Resistance Moves

“…The discourse updates in this paper will all leave W intact and alter only structures defined over this space (more closely resembling the dynamic systems in Gerbrandy & Groeneveld 1997;van Benthem & Liu 2007;Kooi & Renne 2011;van Benthem & Minicȃ 2012;etc. ).…”