## Discoveries and Experiments in the Automation of Mathematical Reasoning (2002)

Citations: | 1 - 0 self |

### BibTeX

@MISC{Shults02discoveriesand,

author = {Benjamin Price Shults},

title = {Discoveries and Experiments in the Automation of Mathematical Reasoning},

year = {2002}

}

### OpenURL

### Abstract

### Citations

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Citation Context ...s extended in this way, reasoning typically becomes much more complex. Several methods have been developed for handling higher-order reasoning. Some have developed provers for full higher-order logic =-=[2, 4]-=-. Others have implemented Godel's axioms in order to keep set theory completely within first-order logic [102]. Others have despaired of handling the problem automatically and resorted to proof checke... |

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Citation Context ...lays them. If the user asks IPR to stop and display after each step taken in the proof, the following sequents will be displayed in sequence each time the user strikes the space key. If IPR is in 122 =-=[1]-=- Show that if the product of (X) over the index set (A) is locally compact then for every B the Bth coordinate space is locally compact [2] PROMOTE Suppose that the product of (X) over the index set (... |

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Citation Context ...the Bth coordinate space is locally compact [2] PROMOTE Suppose that the product of (X) over the index set (A) is locally compact and show that for every B the Bth coordinate space is locally compact =-=[3]-=- CONSIDER Suppose that the product of (X) over the index set (A) is locally compact and show that the (B)th coordinate space is locally compact [4] (1) APPLY-THEOREM-SPLIT Suppose that the product of ... |

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Citation Context ...he unifier. It was at that time that the more complex equality problems were solved by the prover. At the same time, I experimented with the sequent calculus and its variations including "lemmaiz=-=ing" [5]-=-, mixed universal and rigid variables [18], various ffi -rules [8], equality methods [18, 85] and unification strategies. In those early days, the prover was tested on Pelletier's problems [97] and wa... |

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Citation Context ...terms are equal, those equalities are automatically used to decide whether some new pair of terms are equal. This technique has been expanded, specialized and generalized by Kapur [76, 124], Bachmair =-=[9]-=- and Dershowitz [51]. Larry Wos and his group incorporated their own rewriting techniques into their resolution provers [122]. These methods are called demodulation and paramodulation. Another method ... |

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Citation Context ...s completes the description of the analytic tableau method. The method is complete, i.e., any true sentence can be proved by the method [54], and there are various methods of making it more efficient =-=[8, 20, 82, 94]-=-. We emphasize how easy it is to translate proofs in this system into natural, readable proofs. Section 5.2 gives some examples of proofs translated automatically into English by the IPR program. Now ... |

18 | A man-machine theorem-proving system - Bledsoe, Bruell - 1974 |

17 | A model elimination calculus with built-in theories
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(Show Context)
Citation Context ...ledge from a large knowledge base. But let us not give up before we begin. Indeed, computer systems have already been developed that use rather large knowledge bases and make selections automatically =-=[11, 13, 62, 84, 123]-=-. These systems show their strength in and, to a large extent, are limited to Horn theories and theories that have the nature of rewrite rules. Other systems exist that apply knowledge based on hints ... |

17 | A-Ordered Tableaux - Hahnle, Klingenbeck - 1996 |

14 | IMPS: System description - Farmer, Guttman - 1992 |

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Citation Context ...order languages is much less tractable. Many theorem proving programs use tableaux and related methods. PROTEIN [14], 3 T A P [19], lean-T A P [16], SETHEO [82], MGTP and it variants [66, 65], METEOR =-=[6]-=-, Parthenon [35] and PTTP [115] are some of the better known systems. Most existing systems and calculi use clausal form for storing the theory. Some save some space by breaking a formula only to nega... |

11 |
Gazing: an Approach to the Problem of Definition and Lemma Use
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(Show Context)
Citation Context ...ledge from a large knowledge base. But let us not give up before we begin. Indeed, computer systems have already been developed that use rather large knowledge bases and make selections automatically =-=[11, 13, 62, 84, 123]-=-. These systems show their strength in and, to a large extent, are limited to Horn theories and theories that have the nature of rewrite rules. Other systems exist that apply knowledge based on hints ... |

11 | Towards the Automation of Set Theory and its Logic - Brown - 1978 |

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9 |
PROTEIN: A PROver with a Theory Extension I nterface
- Baumgartner, Furbach
(Show Context)
Citation Context ...anguages are more convenient for expressing mathematical facts, the reasoning in higher-order languages is much less tractable. Many theorem proving programs use tableaux and related methods. PROTEIN =-=[14]-=-, 3 T A P [19], lean-T A P [16], SETHEO [82], MGTP and it variants [66, 65], METEOR [6], Parthenon [35] and PTTP [115] are some of the better known systems. Most existing systems and calculi use claus... |

8 | The even more liberalized δ-rule in free variable semantic tableaux - Beckert, Hähnle, et al. - 1993 |

8 | Completeness for linear regular negation normal form inference systems - Hähnle, Murray, et al. - 1997 |

7 | Adding equality to semantic tableaux - Beckert - 1994 |

6 | What is automated theorem proving - Bledsoe, Loveland - 1985 |

6 | Ordered tableaux: Extensions and applications - Hahnle, Pape - 1997 |

5 | Axiomatic Set Theory: with a Historical Introduction by Abraham A. Fraenkel - Bernays - 1958 |