Distributed Knowledge Revisited

Hans van Ditmarsch will be our guest on Wednesday, October 18, 2023. He has previously held talks hosted by the VCLA [One Hundred Prisoners and a Light Bulb (2021), Reasoning about Gossip (2022)]; this time, he will be talking about the concept of distributed knowledge.

Hans van Ditmarsch (source: researcher’s website)

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.

Biography

Hans van Ditmarsch is senior researcher at CNRS, France. He has previously been based at the Open University of the Netherlands, the University of Groningen, the University of Otago, the University of Aberdeen, the University of Sevilla, and CNRS (the University of Lorraine / LORIA). He has also been associated researcher at Institute of Mathematical Sciences, Chennai, India, for many years. His PhD is from the University of Groningen. His research is on the dynamics of knowledge and belief, information-based security protocols, modal logics, and combinatorics. He has frequently taught at ESSLLI summer schools, and he was an organizer or chair of events such as LOFT, M4M, ESSLLI, Tools for Teaching Logic, and LORI. He has been an editor of the Journal of Philosophical Logic. He is an author of the textbook and monograph Dynamic Epistemic Logic, an editor of the Handbook of Epistemic Logic, and an author of the logic puzzles book One Hundred Prisoners and a Light Bulb. He has been the recipient of an ERC (European Research Council) starting grant Epistemic Protocol Synthesis.