Approximation in Mathematical Domains
Explanation-based learning is accomplished through the generalization of an explanation produced by analysis of a single example. A theory of the domain is utilized in generating the explanation. However, problems arise when the domain theory is intractable. Simplifications must be made in order to make the problem tractable. Well-founded simplifications based on our real world knowledge are termed approximations. This paper discusses how approximations can be used to deal with the intractable domain problem in mathematical domains. The approximation method strongly supports the use of a mix of quantitative and qualitative reasoning over either a purely quantitative or qualitative approach. The approximation technique is demonstrated on one of the examples which has been implemented in the chemistry domain.