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for conformable matrices A and B and a matrix norm k kM . This is a good property to have for some applications. One might also insist on a similar property with respect to multiplication by vector x, for which a norm k kV1 may already be de ned: kAxkV2 kAkM kxkV1 :

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The rst step in solving a new problem using a CBR system, as described in 3, is retrieving the most similar case(s) from the case base. Assuming that similar problems have similar solutions, the case(s) retrieved are used to derive the solution for the new problem. Usually, the past solution needs adjustment to t the new situation. The process of xing (i.e., adapting) the old solution is called case adaptation. The knowledge repaired to carry out the adaptation is referred to as adaptation knowledge. There are two ways to acquire adaptation knowledge. The traditional approach is by interviewing domain experts and coding the task-speci c adaptation knowledge manually into the CBR system. This knowledge may be represented as a decision table, semantic tree, or IF THEN rules. Alternatively, the adaptation knowledge can be learned from the cases using machine-learning techniques. Through learning we generate specialized heuristics that relate the differences in the input speci cations (i.e., problem attributes) to the differences in the output speci cations (i.e., solution attributes). These heuristics can be used to determine the amount of adaptation that is suitable. Acquiring adaptation knowledge through interviews with domain experts is both labor intensive and time consuming. It is also dif cult to maintain the adaptation knowledge that has been acquired. Many application systems developed in the past, such as Chef, Judge, Clavier, and Juliana [1], employed this approach.

metaphors, as long as you re aware you re using it, and you choose a different metaphor at times and situations when the organic approach doesn t serve you.