The computability power of a distributed computing model is determined by the communication media available to the processes, the timing assumptions about processes and communication, and the nature of failures that processes can suffer. In a companion paper we showed how dynamic epistemic logic can be used to give a formal semantics to a given distributed computing model, to capture precisely the knowledge needed to solve a distributed task, such as consensus. Furthermore, by moving to a dual model of epistemic logic defined by simplicial complexes, topological invariants are exposed, which determine task solvability. In this paper we show how to extend the setting above to include in the knowledge of the processes, knowledge about the model of computation itself. The extension describes the knowledge processes gain about the current execution, in problems where processes have no input values at all.