Current research in Explainable AI includes post-hoc explanation methods that focus on building transparent explaining agents able to emulate opaque ones. Such agents are naturally required to be accurate and trustworthy. However, what it means for an explaining agent to be accurate and trustworthy is far from being clear. We characterize accuracy and trustworthiness as measures of the distance between the formal properties of a given opaque system and those of its transparent explanantes. To this aim, we extend Probabilistic Computation Tree Logic with operators to specify degrees of accuracy and trustworthiness of explaining agents. We also provide a semantics for this logic, based on a multi-agent structure and relative model-checking algorithms. The paper concludes with a simple example of a possible application.
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