Distributed Optimization of Age of Incorrect Information with Dynamic Epistemic Logic

Distributed medium access schemes have a key advantage in anomaly tracking applications, as individual sensors know their own observations and can exploit them to reduce their Age of Incorrect Information (AoII). However, the risk of collisions has so far limited their performance. We present Dynamic Epistemic Logic for Tracking Anomalies (DELTA), a medium access protocol that limits collisions and minimizes AoII in anomaly reporting over dense networks. This is achieved by a process of inferring AoII from plain Age of Information (AoI). In a network scenario with randomly generated anomalies, the individual AoII for each sensor is known only to itself, but all nodes can infer its$A$oI by simply tracking the transmission process. Thus, we adopt an approach based on dynamic epistemic logic, which allows individual nodes to infer how their$A$oII values rank among the entire network by exploiting public information such as the$A$oI and the identity of transmitting nodes. We analyze the resulting DELTA protocol both from a theoretical standpoint and with Monte Carlo simulation, showing that our approach is significantly more efficient and robust than basic random access, while outperforming state-of-the-art scheduled schemes by at least 30%.