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An intelligent system must routinely deal with massive information processing complexity. The research discussed in this document is concerned with finding representations and processes to deal with a part of this complexity. At a high level, the proposed idea is that a synthesis between the symbolic reasoning of classic artificial intelligence research and the statistical inference mechanisms of machine learning provides answers to some of these issues of complexity. This research is specifically concerned with a subset of classification problems that we call ”compositional classification”, where both the class label and values produced at internal nodes in the classification structure entail verifiable predictions. This research specifies and evaluates a technique for compositional classification. This investigation will consist of (i) implementing a framework for the construction of supervised classification learning systems that codifies the technique, (ii) instantiating a number of learning systems for various specific classification problems using the framework, (iii) using a synthetic problem setting to systematically vary the problem characteristics and system parameters and assess the impact on performance, and (iv) formally analyzing the properties of the technique. A central problem addressed by this technique is how diverse techniques for representation, reasoning and learning that arise from differing viewpoints on intelligence can be reconciled to form a consistent and effective whole. For example, how can neural network backpropagation and knowledge-based diagnosis be combined to achieve an effective structural credit assignment technique for a hybrid knowledge representation?