Large state spaces pose a serious problem in many learning applications. This paper discusses a number of issues that arise when ranking functions are applied to such a domain. Since these functions, in their original introduction, need to store every possible world model, it seems obvious that they are applicable to small toy problems only. To disprove this we address a number of these issues and furthermore describe an application that indeed has a large state space. It is shown that an agent is enabled to learn in this environment by representing its belief state with a ranking function. This is achieved by introducing a new entailment operator that accounts for similarities in the state description.