Complex epistemic modalities in the situation calculus

We develop a formal account of complex group-level epis-temic modalities in the situation calculus, with a particular focus on reasoning about common knowledge. Expressions involving common knowledge cannot be handled by standard regression techniques and are thus difficult to reason about effectively. Taking our cue from recent promising work in dynamic epistemic logic, we overcome this limitation by in-creasing the expressive power of the epistemic language. The syntax of first-order dynamic logic is used to form complex epistemic modalities from the individual-level knowledge op-erators. Common knowledge is a special case of this syntax, using the unbounded iteration operator. We develop a regres-sion rule for these complex modalities and demonstrate its use to reason about common knowledge in an example domain. The result is a rich multi-agent theory of knowledge and ac-tion in which complex group-level epistemic modalities are amenable to effective automated reasoning