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The two unifying expressions for the reduction are constructed by having equivalent expressions in the explanation structure occupy corresponding argument positions in the two constructed expressions. For example, following are the two expressions constructed for the explanation structure of the Cup example (Figure 2-4). x5}, which is the same as the global substitution EGGS constructed for this example (Table 2-1). xl}, which is again the same as the global substitution constructed by EGGS (Table 2-2).

In Sections 5 and 6, the correctness and computational complexity of the explanation generalization process is analyzed. Section 7 discusses the process of pruning explanations for operationality, and Section 8 presents some problems with integrating the generalization process with explanation construction. In Section 9, the process of explanation generalization is compared with chunking and composition methods used to learn productions in SOAR [18] and ACT* [19], respectively. Finally, in Sections 10 and 11, some examples are presented of learning macro-rules by generalizing Horn clause proofs and term rewritings.

Correctness of Explanation Generalizing Algorithms Intuitively, for an explanation generalizing algorithm to be "correct," its output should be logically entailed by the system's existing knowledge or domain theory, and it should be as general as possible given this constraint and the constraint that it retain the "structure" of the original explanation. One approach to proving correctness of explanation generalization, discussed by O'Rorke [7], involves demonstrating that a generalization algorithm maintains all of the equality or co-reference constraints in the explanation structure in the most general way possible.