Action Language mA* with Higher-Order Action Observability

This paper presents a novel semantics for the mA* epistemic action language that takes into consideration dynamic per-agent observability of events. Different from the original mA* semantics, the observability of events is defined locally at the level of possible worlds, giving a new method for compiling event models. Locally defined observability represents agents' uncertainty and false-beliefs about each others' ability to observe events. This allows for modeling second-order false-belief tasks where one agent does not know the truth about another agent's observations and resultant beliefs. The paper presents detailed constructions of event models for ontic, sensing, and truthful announcement action occurrences and proves various properties relating to agents' beliefs after the execution of an action. It also shows that the proposed approach can model second order false-belief tasks and satisfies the robustness and faithfulness criteria discussed by Bolander (2018, https://doi.org/10. 1007/978-3-319-62864-6_8).