Maximizing theory accuracy through selective reinterpretation

Existing methods for exploiting flawed domain theories depend on the use of a sufficiently large set of training examples for diagnosing and repairing flaws in the theory. In this paper, we offer a method of theory reinterpretation that makes only marginal use of training examples. The idea is as follows: Often a small number of flaws in a theory can completely destroy the theory's classification accuracy. Yet it is clear that valuable information is available even from such flawed theories. For example, an instance with several independent proofs in a slightly flawed theory is certainly more likely to be correctly classified as positive than an instance with only a single proof. This idea can be generalized to a numerical notion of `degree of provedness' which measures the robustness of proofs or refutations for a given instance. This `degree of provedness' can be easily computed using a `soft' interpretation of the theory. Given a ranking of instances based on the values so obtained, all that is required to classify instances is to determine some cutoff threshold above which instances are classified as positive. Such a threshold can be determined on the basis of a small set of training examples. For theories with a few localized flaws, we improve the method by `rehardening': interpreting only parts of the theory softly, while interpreting the rest of the theory in the usual manner. Isolating those parts of the theory that should be interpreted softly can be done on the basis of a small number of training examples. Softening, with or without rehardening, can be used by itself as a quick way of handling theories with suspected flaws where few training examples are available. Additionally softening and rehardening can be used in conjunction with other methods as a meta-algorithm for determining which theory revision methods are appropriate for a given theory.