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The rise of AI in human contexts places new demands on automated systems tobe transparent and explainable. We examine some anthropomorphic ideas andprinciples relevant to such accountablity in order to develop a theoreticalframework for thinking about digital systems in complex human contexts and theproblem of explaining their behaviour. Structurally, systems are made ofmodular and hierachical components, which we abstract in a new system modelusing notions of modes and mode transitions. A mode is an independent componentof the system with its own objectives, monitoring data, and algorithms. Thebehaviour of a mode, including its transitions to other modes, is determined byfunctions that interpret each mode's monitoring data in the light of itsobjectives and algorithms. We show how these belief functions can help explainsystem behaviour by visualising their evaluation as trajectories inhigher-dimensional geometric spaces. These ideas are formalised mathematicallyby abstract and concrete simplicial complexes. We offer three techniques: aframework for design heuristics, a general system theory based on modes, and ageometric visualisation, and apply them in three types of human-centredsystems.

The dynamics of belief: continuously monitoring and visualising complex systems