Common knowledge in interaction structures

Abstract

We consider two simple variants of a framework for reasoning about knowledge amongst communicating groups of players. Our goal is to clarify the resulting epistemic issues. In particular, we investigate what is the impact of common knowledge of the underlying hypergraph connecting the players, and under what conditions common knowledge distributes over disjunction. We also obtain two versions of the classic result that common knowledge cannot be achieved in the absence of a simultaneous event (here a message sent to the whole group).

A Logic for Knowledge Flow in Social Networks

“…They use a history-based semantics rather than dynamic epistemic semantics of [3,4]. Apt et al [2] and Wang et al [15] also use a history-based semantics, but the communication structure (named hypergraph) is formed on groups: A message from an agent is received by all members of the same group. Both [10] and [2] limit the message contents to atomic propositions, and message actions are specified only in the history model, while [15] has a richer language to represent both message contents and actions.…”

“…Apt et al [2] and Wang et al [15] also use a history-based semantics, but the communication structure (named hypergraph) is formed on groups: A message from an agent is received by all members of the same group. Both [10] and [2] limit the message contents to atomic propositions, and message actions are specified only in the history model, while [15] has a richer language to represent both message contents and actions. Sietsma and van Eijck in their recent paper [14] propose a framework for message passing that combines the dynamic epistemic semantics and history-based approaches.…”

Logic of Information Flow on Communication Channels

“…Communication channels in an IS framework made their appearance in Parikh and Ramanujam (2003). Recent work Pacuit and Parikh (2007), Apt et al (2009) addresses the information passing on so-called communication graphs or interaction structures, where "messages" are either atomic propositions or Boolean combinations of atomic propositions. In Wang et al (2009) a PDL-style DEL language is developed that allows explicit specification of protocols.…”

“…Unlike in previous work Pacuit and Parikh (2007), Apt et al (2009), Roelofsen (2005, we can specify the communication protocols in our language and deal with information flow in terms of both the messages and propositions.…”

Message passing in a dynamic epistemic logic setting

“…History-based message semantics was defined by Parikh and Ramanujam [10] in terms of states consisting of message sequences (see also [1]). Another approach to message passing is via the update construction in ACM COPYRIGHT NOTICE.…”