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

In a recent paper, we presented a Situation Calculus-based framework for modelling an agent that has incomplete or inaccurate knowledge about its environments, whose actions are non-deterministic, and whose sensor might give incorrect results. Generalizing earlier proposals, the presented approach represented the agent's epistemic state by a set of situations ranked by their respective plausibility, which would then be updated by modifying the plausibility ranks accordingly. In this short paper, we extend our earlier work by considering the problem of 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.