The integration of symbolic knowledge with artificial neural networks is becoming an increasingly popular paradigm for solving real-world applications. The paradigm provides means for using prior knowledge to determine the network architecture, to program a subset of weights to induce a learning bias which guide network training, and to extract knowledge from trained networks. The role of neural networks then becomes that of knowledge refinement. It thus provides a methodology for dealing with uncertainty in the prior knowledge. We address the open question of how to determine the strength of the inductive bias of programmed weights; we present a quantitative solution which takes the network architecture, the prior knowledge, and the training data into consideration. We apply our solution to the difficult problem of analyzing breast tissue from magnetic resonance spectroscopy (MRS); the available database is extremely limited and cannot be adequately explained by expert knowledge alone.