Projection of Belief in the Presence of Nondeterministic Actions and Fallible Sensing

We recently presented a Situation Calculus-based framework for modelling an agent who has incomplete or inaccurate knowledge about its environments, whose actions are nondeterministic, and whose sensors might give incorrect results. Generalizing earlier proposals, the approach represented the agent's epistemic state by a set of situations ranked by their respective plausibility, and which would then be updated by modifying the plausibility ranks accordingly. Here we extend our earlier work by considering projection in this framework, i.e. the question whether a certain (epistemic) formula will hold after a given sequence of actions. We present results on both regression, where the query is transformed into an equivalent one about the initial situation, as well as progression, where the knowledge base is updated to reflect the situation after executing the action sequence in question.