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An XML-Format for Conjectures in Geometry (Work-in-Progress) Pedro - - PowerPoint PPT Presentation

Jan 03, 2024 259 likes •472 views

Introduction i2gatp XML-Format Conclusions and Further Work An XML-Format for Conjectures in Geometry (Work-in-Progress) Pedro Quaresma CISUC, Mathematics Department University of Coimbra CICM 2012, 8-13 July 2012, Jacobs University, Bremen,

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Introduction i2gatp XML-Format Conclusions and Further Work

An XML-Format for Conjectures in Geometry

(Work-in-Progress) Pedro Quaresma

CISUC, Mathematics Department University of Coimbra

CICM 2012, 8-13 July 2012, Jacobs University, Bremen, Germany

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Introduction i2gatp XML-Format Conclusions and Further Work

An XML-Format for Conjectures in Geometry

DGSs & GATPs & Repositories of geometric constructions.

◮ loose coupling of tools; ◮ wide availability of their corpora; ◮ (+) describe constructions created with a DGS, allows sharing

interactive geometry constructions across boundaries.

◮ (-) does not provide support for the conjectures.

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Introduction i2gatp XML-Format Conclusions and Further Work

An XML-Format for Conjectures in Geometry

DGSs & GATPs & Repositories of geometric constructions.

◮ loose coupling of tools; ◮ wide availability of their corpora; ◮ (+) describe constructions created with a DGS, allows sharing

interactive geometry constructions across boundaries.

◮ (-) does not provide support for the conjectures.

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Introduction i2gatp XML-Format Conclusions and Further Work

An XML-Format for Conjectures in Geometry

DGSs & GATPs & Repositories of geometric constructions.

◮ loose coupling of tools; ◮ wide availability of their corpora;

The Intergeo (i2g) file format.

◮ (+) describe constructions created with a DGS, allows sharing

interactive geometry constructions across boundaries.

◮ (-) does not provide support for the conjectures.

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Introduction i2gatp XML-Format Conclusions and Further Work

An XML-Format for Conjectures in Geometry

DGSs & GATPs & Repositories of geometric constructions.

◮ loose coupling of tools; ◮ wide availability of their corpora;

The Intergeo (i2g) file format.

◮ (+) describe constructions created with a DGS, allows sharing

interactive geometry constructions across boundaries.

◮ (-) does not provide support for the conjectures.

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Introduction i2gatp XML-Format Conclusions and Further Work

An XML-Format for Conjectures in Geometry

The i2gatp format.

◮ An extension of the i2g format. ◮ support for geometric conjectures and proofs. ◮ Converters from/to the format. ◮ Integration with GeoThms & TGTP & Web Geometry

Laboratory

◮ Supported by other tools DGSs, GATPs, . . . .

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Introduction i2gatp XML-Format Conclusions and Further Work

An XML-Format for Conjectures in Geometry

The i2gatp format.

◮ An extension of the i2g format. ◮ support for geometric conjectures and proofs. ◮ Converters from/to the format. ◮ Integration with GeoThms & TGTP & Web Geometry

Laboratory

◮ Supported by other tools DGSs, GATPs, . . . .

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Introduction i2gatp XML-Format Conclusions and Further Work

An XML-Format for Conjectures in Geometry

The i2gatp format.

◮ An extension of the i2g format. ◮ support for geometric conjectures and proofs. ◮ Converters from/to the format. ◮ Integration with GeoThms & TGTP & Web Geometry

Laboratory

◮ Supported by other tools DGSs, GATPs, . . . .

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Introduction i2gatp XML-Format Conclusions and Further Work

An XML-Format for Conjectures in Geometry

The i2gatp format.

◮ An extension of the i2g format. ◮ support for geometric conjectures and proofs. ◮ Converters from/to the format. ◮ Integration with GeoThms & TGTP & Web Geometry

Laboratory

◮ Supported by other tools DGSs, GATPs, . . . .

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Introduction i2gatp XML-Format Conclusions and Further Work

An XML-Format for Conjectures in Geometry

The i2gatp format.

◮ An extension of the i2g format. ◮ support for geometric conjectures and proofs. ◮ Converters from/to the format. ◮ Integration with GeoThms & TGTP & Web Geometry

Laboratory

◮ Supported by other tools DGSs, GATPs, . . . .

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Introduction i2gatp XML-Format Conclusions and Further Work

An XML-Format for Conjectures in Geometry

The i2gatp format.

◮ An extension of the i2g format. ◮ support for geometric conjectures and proofs. ◮ Converters from/to the format. ◮ Integration with GeoThms & TGTP & Web Geometry

Laboratory

◮ Supported by other tools DGSs, GATPs, . . . .

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Introduction i2gatp XML-Format Conclusions and Further Work Overall Architecture

Overall Architecture

I2GATP Format proofInfo method status limits measures conjecture platform conclusion hypothesis bibentry keyword information [keywords] [bibrefs] statement description name construction (I2G) elements constraints display ndg

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Introduction i2gatp XML-Format Conclusions and Further Work Overall Architecture

Overall Architecture

I2GATP Format proofInfo method status limits measures construction (I2G) elements constraints display conjecture platform conclusion hypothesis bibentry keyword information [keywords] [bibrefs] statement description name ndg

intergeo.xsd;

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Introduction i2gatp XML-Format Conclusions and Further Work Overall Architecture

Overall Architecture

I2GATP Format proofInfo method status limits measures construction (I2G) elements constraints display conjecture platform conclusion hypothesis bibentry keyword information [keywords] [bibrefs] statement description name ndg

intergeo.xsd; proofInfo.xsd;

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Introduction i2gatp XML-Format Conclusions and Further Work Overall Architecture

Overall Architecture

I2GATP Format proofInfo method status limits measures construction (I2G) elements constraints display conjecture platform conclusion hypothesis bibentry keyword information [keywords] [bibrefs] statement description name ndg

intergeo.xsd; proofInfo.xsd; information.xsd; conjecture.xsd.

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Introduction i2gatp XML-Format Conclusions and Further Work The Container

The Container

A zip file, superset of the i2g container.

information/ mandatory information/information.xml

  • ptional

construction/ mandatory construction/intergeo.xml mandatory construction/preview.pdf

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construction/preview.svg

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construction/(. . . ) conjecture/ mandatory conjecture/conjecture.xml

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proofs/ mandatory proofs/proof<GATP><Version><Method>/

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proofs/proof<GATP><Version><Method>/proofInfo.xml

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proofs/proof<GATP><Version><Method>/proofOutput.pdf

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proofs/proof<GATP><Version><Method>/(. . . ) metadata/

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metadata/i2g-lom.xml

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resources/

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resources/<image files>

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resources/(. . . ) private/

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private/<domain-name>

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private/<domain-name>/<files>

  • ptional

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Introduction i2gatp XML-Format Conclusions and Further Work Implementation

Implementation

Human−Language Rendering (HTML) DGS code (GCLC) DGS code (GeoGebra) GATP code (GCLC AM) GATP code (Coq AM) 2 − From/to GeoGebra to/from I2G(ATP) 1 − From/to GCLC to/from I2G(ATP) 4 − SVG rendering 5 − HTML rendering 6 − other: proofs; bibrefs., etc. 8 − From/to I2GATP to/from Coq AM 7 − From/to I2GATP to/from GCLC AM 9 − From/to I2GATP to/from GATP

  • thers
  • thers

Graphical Rendering (SVG)

  • thers

1 2 3 4 5 7 8 9 3 − From/to DGS to/from I2G(ATP) I2GATP

Container XML files

6 TGTP GeoThms WGL 17 / 20

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Introduction i2gatp XML-Format Conclusions and Further Work Implementation

Implementation

Human−Language Rendering (HTML) DGS code (GCLC) DGS code (GeoGebra) GATP code (GCLC AM) GATP code (Coq AM) 2 − From/to GeoGebra to/from I2G(ATP) 1 − From/to GCLC to/from I2G(ATP) 4 − SVG rendering 5 − HTML rendering 6 − other: proofs; bibrefs., etc. 8 − From/to I2GATP to/from Coq AM 7 − From/to I2GATP to/from GCLC AM 9 − From/to I2GATP to/from GATP

  • thers
  • thers

Graphical Rendering (SVG)

  • thers

1 2 3 4 5 7 8 9 3 − From/to DGS to/from I2G(ATP) I2GATP

Container XML files

6 TGTP GeoThms WGL 18 / 20

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Introduction i2gatp XML-Format Conclusions and Further Work

Conclusions and Further Work

This is a work-in-progress. Questions and future work to be addressed:

◮ The xml/xsd format must be complemented with an

extensive set of converters allowing the exchange of information between as many geometric tools as possible.

◮ The databases queries, as in TGTP, raise the question of

selecting appropriate keywords. A fine grain index and/or an appropriate geometry ontology should be addressed.

◮ The i2gatp format does not address proofs. Should we try to

create such a format? The GATPs produce proofs in quite different formats, maybe the construction of such unifying format it is not possible and/or desirable in this area.

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Introduction i2gatp XML-Format Conclusions and Further Work

Thank You

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