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In this paper we describe AGATHA, a program designed to automate the process of theory construction in case based domains. Given a seed case and a number of precedent cases, the program uses a set of argument moves to generate a search space for a dialogue between the parties to the dispute. Each move is associated with a set of theory constructors, and thus each point in the space can be associated with a theory intended to explain the seed case and the other cases in the domain. The space is large, and so a heuristic search method based on A* is used to guide the selection of moves and precedent cases. The paper describes a series of experiments designed to explore the appropriateness of different evaluation functions, the most useful precedents and the quality of the resulting theories.