Speaker: Hans van Ditmarsch (University of Toulouse, CNRS, IRIT)
Date and Time: Thursday, April 18th 2024, 16:30-18:00
Venue: room L3.33 in Lab 42 and online.
Title: Distributed Knowledge Revisited.
Abstract. We review the history and some recent work on what is known since the 1990s as distributed knowledge. Such epistemic group notions are currently getting more and more attention both from the modal logical community and from distributed computing, in various settings with communicating processes or agents. The typical intuition is that if a knows p, and b knows that p implies q, then together they know that q: they have distributed knowledge of q. In order to get to know q they need to share their knowledge. We will discuss:
(i) the complete axiomatization, (ii) why not everything that is distributed knowledge can become common knowledge, (iii) the notion of collective bisimulation, (iv) distributed knowledge for infinitely many agents, (v) the novel update called resolving distributed knowledge and some variations (and its incomparable update expressivity to action models), (vi) distributed knowledge that is stronger than the sum of individual knowledge (where the relation for the group of agents is strictly contained in their intersection), (vii) common distributed knowledge and its topological interpretations, (viii) dynamic distributed knowledge, a version of the semantics ensuring that what is distributed knowledge becomes common knowledge, and the axiomatization, expressivity and bisimulation characterization of this logic.