In many automated methods for proving inductive theorems, finding a suitable generalization of a conjecture is a key for the success of proof attempts. On the other hand, an obtained generalized conjecture may not be a theorem, and in this case hopeless proof attempts for the incorrect conjecture are made, which is against the success and efficiency of theorem proving. Urso and Kounalis (2004) proposed a generalization method for proving inductive validity of equations, called sound generalization, that avoids such an over-generalization. Their method guarantees that if the original conjecture is an inductive theorem then so is the obtained generalization. In this paper, we revise and extend their method. We restore a condition on one of the characteristic argument positions imposed in their previous paper and show that otherwise there exists a counterexample to their main theorem. We also relax a condition imposed in their framework and add some flexibilities to some of other characteristic argument positions so as to enlarge the scope of the technique.
|ホスト出版物のタイトル||FSTTCS 2008 - IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science|
|出版ステータス||Published - 2008 12月 1|
|イベント||28th International Conference on the Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2008 - Bangalore, India|
継続期間: 2008 12月 9 → 2008 12月 11
|Other||28th International Conference on the Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2008|
|Period||08/12/9 → 08/12/11|
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