Exploiting the Addressee's Inferential Capabilities in Presenting Mathematical Proofs

Fehrer, Detlef; Horacek, Helmut

Exploiting the Addressee's Inferential Capabilities in Presenting Mathematical Proofs

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Proceedings of the Fifteenth International Joint Conference on Artificial Intelligence. Natural-language Processing and Graphical Presentation. Pages 959-963.

Abstract

Proof presentation systems and, in some more general context, many natural language generation systems suffer from a crucial problem: they present too much information explicitly which the intended audience could more naturally infer from a less detailed text. Moreover, proofs in mathematical textbooks make extensive use of building chains of inferences in specialized notations, which is not sufficiently taken into account by proof presentation systems. Encouraged by these observations, we present a model for presenting mathematical proofs that (1) features the implicit conveyance of information through concise texts, (2) organizes major lines in the proof presentation around focused chains of inferences in a specialized notation, (3) can adapt its output to some of the capabilities of its audience. The methods described in this paper allow us to present proofs of moderately complex size in a quality approaching that of proofs found in mathematical textbooks.

Detlef Fehrer, and Helmut Horacek. 1997. Exploiting the Addressee's Inferential Capabilities in Presenting Mathematical Proofs. In Proceedings of the Fifteenth International Joint Conference on Artificial Intelligence, IJCAI-97. IJCAI, 959–963. https://ijcai.org/proceedings/1997/138

@inproceedings{ijcai1997p138,
  title     = {Exploiting the Addressee's Inferential Capabilities in Presenting Mathematical Proofs},
  author    = {Fehrer, Detlef and Horacek, Helmut},
  booktitle = {Proceedings of the Fifteenth International Joint Conference on
               Artificial Intelligence, {IJCAI-97}},
  publisher = {International Joint Conferences on Artificial Intelligence},
  editor    = {Martha E. Pollack},
  pages     = {959--963},
  year      = {1997},
  note      = {Natural-language Processing and Graphical Presentation},
  url       = {https://ijcai.org/proceedings/1997/138},
}

TY  - CPAPER
TI  - Exploiting the Addressee's Inferential Capabilities in Presenting Mathematical Proofs
AU  - Fehrer, Detlef
AU  - Horacek, Helmut
T2  - Proceedings of the Fifteenth International Joint Conference on Artificial Intelligence, IJCAI-97
PB  - International Joint Conferences on Artificial Intelligence
PY  - 1997
SP  - 959
EP  - 963
UR  - https://ijcai.org/proceedings/1997/138
ER  -