RT Journal Article
SR 00
ID 10.3233/AIC-170723
A1 Herzig, Andreas
A1 Maffre, Faustine
T1 How to share knowledge by gossiping
JF AI Communications
YR 2017
FD 2017-03
VO vol. 30
IS n° 1
SP 1
OP 17
K1 Gossip protocol
K1 epistemic logic
K1 shared knowledge
K1 common knowledge
K1 theory of mind
K1 dynamic epistemic logic
K1 visibility
K1 observability
AB We provide a logical investigation of a simple case of communication in a network of agents called the gossip problem. Its classical version is: given n agents each of which has a secret - a fact not known to anybody else -, how many calls does it take to achieve shared knowledge of all secrets, i.e., to reach a state where every agent knows every secret? Several protocols achieving shared knowledge in 2(né2) calls exist and were proved to be optimal: no shorter sequence of calls exists. We generalize that problem and focus on higher-order shared knowledge: how many calls does it take to obtain that everybody knows that everybody knows all secrets? More generally, how many calls does it take to obtain shared knowledge of order k? This cannot be achieved simply by communicating facts: the agents also have to communicate higher-order knowledge of facts. We give an algorithm that works in (k+1)(né2) calls. We analyse its properties in a logic that we have investigated in previous work and that is based on the concept of observability of propositional variables by agents: Dynamic Epistemic Logic of Propositional Assignment and Observation DEL-PAO. This enables us in particular to give a formal proof of correctness of the algorithm.
PB IOS Press
SN 0921-7126
LK https://publications.ut-capitole.fr/id/eprint/27700/