We have developed a syntactic approach to representing knowledge within the situation calculus using interval arithmetic. Knowledge was first incorporated into the situation calculus using a possible-worlds approach. Unfortunately, this previous approach is not amenable to easy implementation. This is because it is not clear how to specify the initial situation as the number of possible worlds is potentially uncountable. We solve this problem by using interval-valued epistemic (IVE) fluents to represent the agent’s knowledge of its world. With respect to the previous possible worlds approach, our approach is provably sound and (sometimes) complete.