Granularity-Adaptive Proof Presentation (bibtex)

by Marvin Schiller, Christoph Benzmüller

Abstract:

When mathematicians present proofs they usually adapt their explanations to their didactic goals and to the (assumed) knowledge of their addressees. Modern automated theorem provers, in contrast, present proofs usually at a fixed level of detail (also called granularity). Often these presentations are neither intended nor suitable for human use. A challenge therefore is to develop user- and goal-adaptive proof presentation techniques that obey common mathematical practice. We present a flexible and adaptive approach to proof presentation that exploits machine learning techniques to extract a model of the specific granularity of proof examples and employs this model for the automated generation of further proofs at an adapted level of granularity.

Reference:

Granularity-Adaptive Proof Presentation (Marvin Schiller, Christoph Benzmüller), SEKI Publications (ISSN 1437-4447), SEKI Working-Paper SWP--2009--01, 2009. (arXiv:0903.0314)

Bibtex Entry:

@techreport{R44, Abstract = {When mathematicians present proofs they usually adapt their explanations to their didactic goals and to the (assumed) knowledge of their addressees. Modern automated theorem provers, in contrast, present proofs usually at a fixed level of detail (also called granularity). Often these presentations are neither intended nor suitable for human use. A challenge therefore is to develop user- and goal-adaptive proof presentation techniques that obey common mathematical practice. We present a flexible and adaptive approach to proof presentation that exploits machine learning techniques to extract a model of the specific granularity of proof examples and employs this model for the automated generation of further proofs at an adapted level of granularity.}, Institution = {Saarland University}, Address = {{DFKI Bremen GmbH, Safe and Secure Cognitive Systems, Cartesium, Enrique Schmidt Str.\,5, D--28359 Bremen, Germany}}, Author = {Schiller, Marvin and Benzm{\"u}ller, Christoph}, Keywords = {own, Proof Presentation, DIALOG, Natural Language Dialog, Proof Assistants, Machine Learning, Tutoring Systems}, Note = {arXiv:0903.0314}, Publisher = {{SEKI Publications (ISSN 1437-4447)}}, Series = {{SEKI Working-Paper SWP--2009--01}}, Title = {Granularity-Adaptive Proof Presentation}, Url = {http://arxiv.org/abs/0903.0314}, Year = 2009, }

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