### Abstract

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.

Original language | English |
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Title of host publication | FSTTCS 2008 - IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science |

Pages | 13-24 |

Number of pages | 12 |

Volume | 2 |

Publication status | Published - 2008 Dec 1 |

Event | 28th International Conference on the Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2008 - Bangalore, India Duration: 2008 Dec 9 → 2008 Dec 11 |

### Other

Other | 28th International Conference on the Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2008 |
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Country | India |

City | Bangalore |

Period | 08/12/9 → 08/12/11 |

### Keywords

- Automated theorem proving
- Inductive theorem
- Sound generalization
- Term rewriting

### ASJC Scopus subject areas

- Software

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## Cite this

*FSTTCS 2008 - IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science*(Vol. 2, pp. 13-24)