The machine-learning technique of decision graphs, a generalization of decision trees, is applied to the prediction of protein secondary structure to infer a theory for this problem. The resulting decision graph provides both a prediction method and an explanation for the problem. Many decision graphs are possible for the problem. A particular graph is just one theory or hypothesis of secondary structure formation. Minimum message length encoding is used to judge the quality of different theories. It is a general technique of inductive inference and is resistant to learning the noise in the training data. The method was applied to 75 sequences from nonhomologous proteins comprising 13 K amino acids. The predictive accuracy for three states (extended, helix, other) was in the range achieved by current methods.