Model Checking Degrees of Belief in a System of Agents

In this paper we present a unified framework to model and verify degrees of belief in a system of agents. In particular, we describe an extension of the temporal-epistemic logic CTLK and we introduce a semantics based on interpreted systems for this extension. In this way, degrees of beliefs do not need to be provided externally, but can be derived automatically from the possible executions of the system, thereby providing a computationally grounded formalism. We leverage the semantics to (a) construct a model checking algorithm, (b) investigate its complexity, (c) provide a Java implementation of the model checking algorithm, and (d) evaluate our approach using the standard benchmark of the dining cryptographers. Finally, we provide a detailed case study: using our framework and our implementation, we assess and verify the situational awareness of the pilot of Air France 447 flying in off-nominal conditions.