## Assertion-level proof representation with under-specification (2003)

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Citations: | 15 - 7 self |

### BibTeX

@INPROCEEDINGS{Autexier03assertion-levelproof,

author = {Serge Autexier and Christoph Benzmüller and Armin Fiedler and Helmut Horacek and Bao Quoc Vo},

title = {Assertion-level proof representation with under-specification},

booktitle = {},

year = {2003},

pages = {5--23}

}

### Years of Citing Articles

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### Abstract

We propose a proof representation format for human-oriented proofs at the assertion level with underspecification. This work aims at providing a possible solution to challenging phenomena worked out in empirical studies in the DIALOG project at Saarland University. A particular challenge in this project is to bridge the gap between the human-oriented proof representation format with under-specification used in the proof manager of the tutorial dialogue system and the calculus- and machine-oriented representation format of the domain reasoner.

### Citations

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Citation Context ...haviour. Note that it is important that the subjects think that they interact with a computer system, since it has been observed that humans interact differently with computers than with other humans =-=[10,6]-=-. In our project, we plan for a series of experiments where the wizard will be first increasingly restricted in his possibilities to comply with the specific algorithms of the envisioned system and th... |

97 |
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Citation Context ...ystem, we started with empirical investigations to pinpoint linguistic phenomena and relevant aspects of the domain that need to be addressed. To this end, we followed the Wizard-of-Oz (WOz) approach =-=[5]-=-, where the subjects in an experiment are told that they interact with a computer system, but where the computer system is, either as a whole or in part, simulated by a human expert, called the wizard... |

63 | Reconstructing proofs at the assertion level
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Citation Context ...r [12]. Therefore, it is required to present logically redundant information for more complex reasoning tasks in conversation with humans [22]. By and large, these insights favour the assertion level =-=[11]-=- as the most appropriate level of granularity, unless complex reasoning patterns are to be described. Moreover, humans typically exploit contextual expectations, so that several details can be left im... |

56 |
The Mathematical Vernacular, a language for mathematics with typed sets
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- 1987
(Show Context)
Citation Context ...al goals is crucial. As further related work, Weak Type Theory as employed in the MathLang project [14] is to be mentioned. The MathLang framework is based on de Bruijn’s Mathematical Vernacular (MV) =-=[7]-=- but imposes fewer logical constraints. Several other proof languages aiming for better human-oriented support in interactive proof construction have been developed and we mention some of them: the de... |

51 | The E ect of Resource Limits and Task Complexity on Collaborative Planning in Dialogue
- Walker
- 1996
(Show Context)
Citation Context ...derstanding the most frequent one, modus ponens, is much easier [12]. Therefore, it is required to present logically redundant information for more complex reasoning tasks in conversation with humans =-=[22]-=-. By and large, these insights favour the assertion level [11] as the most appropriate level of granularity, unless complex reasoning patterns are to be described. Moreover, humans typically exploit c... |

38 | Structured Proofs in Isar/HOL
- Nipkow
(Show Context)
Citation Context ...hes in OMEGA [18], the Math4 www.mizar.org S. Autexier et al. / Electronic Notes in Theoretical Computer Science 93 (2004) 5–23sematical Proof Language of Barendregt [3], and Isabelle’s ISAR language =-=[16]-=-. However, so far none of these approaches explicitly addresses the phenomena of under-specification and user adaptation as discussed above. 7 Conclusion In the DIALOG project we investigate tutorial ... |

30 | Human-readable machine-verifiable proofs for teaching constructive logic
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- 2001
(Show Context)
Citation Context ...trategy that only checks whether some of the goal formulae in ∆ occurs in Γ. If the student is stronger, then it may use a slightly stronger strategy, such as for instance the finishing strategy from =-=[1]-=-. From Proof Manager to Dialogue Manager The proof manager works on an actual, possibly partial proof and is configured with a set of strategies to use for the individual arising lemmata. The attempts... |

29 | 2004, A refinement of de Bruijn’s formal language of mathematics. Journal of Logic, Language and Information
- Kamareddine, Nederpelt
(Show Context)
Citation Context ...like ours, however, the ability of a framework to adapt to the student’s skills and the chosen tutorial goals is crucial. As further related work, Weak Type Theory as employed in the MathLang project =-=[14]-=- is to be mentioned. The MathLang framework is based on de Bruijn’s Mathematical Vernacular (MV) [7] but imposes fewer logical constraints. Several other proof languages aiming for better human-orient... |

14 |
Malte Gabsdil, Helmut Horacek, Ivana Kruijff-Korbayová, Manfred Pinkal, Jörg Siekmann, Dimitra Tsovaltzi, Bao Quoc Vo, and Magdalena Wolska. 2003. A Wizard-ofOz experiment for tutorial dialogues in mathematics
- Benzmüller, Fiedler
(Show Context)
Citation Context ...otherwise a hinting algorithm was invoked that decided what kind of hint should be produced by the system and the wizard had to verbalise the hint. The experiment setup is presented in more detail in =-=[4]-=-. The details of the hinting algorithm can be found in [9]. In the next section, we shall show some example dialogues recorded during the first experiment. 3 An Example Dialogue In the example session... |

11 | A.: An Approach to Facilitating Reflection in a Mathematics Tutoring System
- Tsovaltzi, Fiedler
- 2003
(Show Context)
Citation Context ...ecified and further information as already discusses above (position, intantiations, etc.) may be taken into account. We call a proof step correct if it is both accurate and information complete (cf. =-=[21]-=- for details of a student answer categorisation). Granularity: The level of granularity reflects the number of inference steps required to establish the asserted proof step. The assessment whether the... |

8 |
Teilprojekt MI 3: DIALOG: Tutorieller Dialog mit einem Mathematik-Assistenten. 2001
- Pinkal, Siekmann, et al.
(Show Context)
Citation Context ...all discuss related work and conclude the paper.s8 S. Autexier et al. / Electronic Notes in Theoretical Computer Science 93 (2004) 5–23 2 Empirical Studies in the DIALOG Project In the DIALOG project =-=[17]-=-, we aim at a mathematical tutoring system that employs an elaborate natural language dialogue component. To tutor mathematics, we need a formally encoded mathematical theory including definitions and... |

6 |
Towards an Interactive Mathematical Proof Mode
- Barendregt
- 2003
(Show Context)
Citation Context ...f MIZAR 4 , the island proof sketches in OMEGA [18], the Math4 www.mizar.org S. Autexier et al. / Electronic Notes in Theoretical Computer Science 93 (2004) 5–23sematical Proof Language of Barendregt =-=[3]-=-, and Isabelle’s ISAR language [16]. However, so far none of these approaches explicitly addresses the phenomena of under-specification and user adaptation as discussed above. 7 Conclusion In the DIAL... |

5 |
Formal proof authoring: An experiment
- Théry
- 2003
(Show Context)
Citation Context ...at. • User-Interfaces for Theorem Provers: The clarification of the notion of humanoriented proofs is very relevant for the design of user-interfaces for theorem provers. Our viewpoint coincides with =-=[19]-=-, which investigates paper proofs instead of interactively constructed proofs with under-specification, in the sense that a clear separation between the optimally user-oriented proof representation in... |

3 |
Dimitra Tsovaltzi. An approach to automating hinting in an intelligent tutorial system
- Fiedler
- 2003
(Show Context)
Citation Context ...t kind of hint should be produced by the system and the wizard had to verbalise the hint. The experiment setup is presented in more detail in [4]. The details of the hinting algorithm can be found in =-=[9]-=-. In the next section, we shall show some example dialogues recorded during the first experiment. 3 An Example Dialogue In the example sessions presented below the utterances of tutor (wizard) and sub... |

3 |
Über kausale Inferenzen beim Lesen. Sprache und Kognition
- Thüring, Wender
- 1985
(Show Context)
Citation Context ...e level of granularity, unless complex reasoning patterns are to be described. Moreover, humans typically exploit contextual expectations, so that several details can be left implicit in descriptions =-=[20]-=-. From the perS. Autexier et al. / Electronic Notes in Theoretical Computer Science 93 (2004) 5–23 7 spective of referring to proof fragments, this corresponds to under-specification. However, rather... |

2 | Disproving false conjectures - Autexier, Schürmann - 2003 |