To support applications, such as efficient browsing in large knowledge bases and cooperative knowledge discovery in large databases, the concept of rule similarity is essential. In this paper we define such a measure, called distance, and then put in the service of various knowledge exploration processes. Rule distances allow us to place all the available knowledge on a “map”, in which proximity reflects similarity. Users can then browse in the knowledge, by iteratively visiting rules and examining their neighborhoods. In our cooperative knowledge discovery process, users suggest a hypothetical rule that has been observed. If the hypothesis is verified, the system may suggest other, even better, rules that hold; if refuted, the system attempts to focus the hypothesis until it holds; in either case, the system may offer other rules that hold and are close to the hypothesis. Our work is within the formal framework of logic databases, and we report on an experimental system that i...