Belief-Desire-Intention (BDI) agents feature uncertain beliefs (e.g. sensor noise), probabilistic action outcomes (e.g. attempting and action and failing), and non-deterministic choices (e.g. what plan to execute next). To be safely applied in real-world scenarios we need reason about such agents, for example, we need probabilities of mission success and the strategies used to maximise this. Most agents do not currently consider uncertain beliefs, instead a belief either holds or does not. We show how to use epistemic states to model uncertain beliefs, and define a Markov Decision Process for the semantics of the Conceptual Agent Notation (Can) agent language allowing support for uncertain beliefs, non-deterministic event, plan, and intention selection, and probabilistic action outcomes. The model is executable using an automated tool—CAN-verify—that supports error checking, agent simulation, and exhaustive exploration via an encoding to Bigraphs that produces transition systems for probabilistic model checkers such as PRISM. These model checkers allow reasoning over quantitative properties and strategy synthesis. Using the example of an autonomous submarine and drone surveillance together with scalability experiments, we demonstrate our approach supports uncertain belief modelling, quantitative model checking, and strategy synthesis in practice.
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