ANALYZING VARIABLE CANCELLATIONS TO GENERALIZE SYMBOLIC MATHEMATICAL CALCULATIONS.

Mathematical reasoning provides the basis for problem-solving and learning in many complex domains. A model for mathematical reasoning in support of explanation-based learning is presented, and an implemented learning system in the domain of classifical physics is described. The system's mathematical reasoning processes are guided by the manner in which variables are canceled in specific problem solutions. Attention focusses on how obstacles are eliminated from calculations. Obstacles are variables that preclude the direct evaluation of the problem's unknown. Analyzing the cancellation of obstacles leads to the generalization of the specific solution. An illustrative example highlights an important issue in explanation-based learning, namely generalizing number. It is argued that such generalization requires extension of the sample solution's explanation. This type of generalization cannot be performed by the standard explanation-based approach of propagating constraints. An approach that overcomes this shortcoming is presented.