## Reconstructing Proofs at the Assertion Level

- Most automated theorem provers suffer from the problem thatthey can produce proofs only in formalisms difficult to understand even forexperienced mathematicians. Effort has been made to reconstruct naturaldeduction (ND) proofs from such machine generated proofs. Although thesingle steps in ND proofs are easy to understand, the entire proof is usuallyat a low level of abstraction, containing too many tedious steps. To obtainproofs similar to those found in mathematical textbooks, we propose a newformalism, called ND style proofs at the assertion level , where derivationsare mostly justified by the application of a definition or a theorem. Aftercharacterizing the structure of compound ND proof segments allowing asser-tion level justification, we show that the same derivations can be achieved bydomain-specific inference rules as well. Furthermore, these rules can be rep-resented compactly in a tree structure. Finally, we describe a system calledPROVERB , which substantially shortens ND proofs by abstracting them tothe assertion level and then transforms them into natural language.

Author: | Xiaorong Huang |
---|---|

URN (permanent link): | urn:nbn:de:hbz:386-kluedo-2297 |

Document Type: | Article |

Language of publication: | English |

Year of Completion: | 1999 |

Year of Publication: | 1999 |

Publishing Institute: | Technische Universität Kaiserslautern |

Date of the Publication (Server): | 2000/04/03 |

Faculties / Organisational entities: | Fachbereich Informatik |

DDC-Cassification: | 0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik |

Licence (German): | Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011 |