We address an open problem in the philosophy of artificial intelligence (AI): how to justify the epistemic attitudes we have towards the trustworthiness of AI systems. The problem is important, as providing reasons to believe that AI systems are worthy of trust is key to appropriately rely on these systems in human-AI interactions. In our approach, we consider the trustworthiness of an AI as a time-relative, composite property of the system with two distinct facets. One is the actual trustworthiness of (...) the AI and the other is the perceived trustworthiness of the system as assessed by its users while interacting with it. We show that credences, namely, beliefs we hold with a degree of confidence, are the appropriate attitude for capturing the facets of the trustworthiness of an AI over time. Then, we introduce a reliabilistic account providing justification to the credences in the trustworthiness of AI, which we derive from Tang’s probabilistic theory of justified credence. Our account stipulates that a credence in the trustworthiness of an AI system is justified if and only if it is caused by an assessment process that tends to result in a high proportion of credences for which the actual and perceived trustworthiness of the AI are calibrated. This approach informs research on the ethics of AI and human-AI interactions by providing actionable recommendations on how to measure the reliability of the process through which users perceive the trustworthiness of the system, investigating its calibration to the actual levels of trustworthiness of the AI as well as users’ appropriate reliance on the system. (shrink)