Motivation Architecture Services Conclusion

JOBAD – Interactive Mathematical DocumentsAI Mashup Challenge 2009

Michael Kohlhase, Jana Giceva, Christoph Lange, VyacheslavZholudev

Jacobs University, Bremen, Germany

KWARC – Knowledge Adaptation and Reasoning for Content

September 15, 2009

Kohlhase, Giceva, Lange, Zholudev (Jacobs University) JOBAD – Interactive Mathematical Documents September 15, 2009 1/8

Motivation Architecture Services Conclusion

Mathematics is Hard

Example (Math Jokes)“Let p be a point q, which we call r” –whatwas p again??The professor says A, writes B, means C, continues thecalculation using D, obtains E as a result, but F would have beenright.

concise and minimalistic style of writingabstract objectslayers of definitions and assertions, documents depend onothersoptimized for the initiated

However: Everyone will be a non-initiated, casual reader –eventually. Make documents comprehensible!

Kohlhase, Giceva, Lange, Zholudev (Jacobs University) JOBAD – Interactive Mathematical Documents September 15, 2009 2/8

Motivation Architecture Services Conclusion

Mathematical Web Services

Services for . . .flexibly adapting documents to varying audienceschecking users’ solutions to exercisesevaluating expressions, solving problems

. . . are available, but accessible from documents?

Yes, sometimes, but not really easy to integrate as mashups; most ofthe time only used in their native environment (e. g. the e-learningenvironment ActiveMath)

Kohlhase, Giceva, Lange, Zholudev (Jacobs University) JOBAD – Interactive Mathematical Documents September 15, 2009 3/8

Motivation Architecture Services Conclusion

Non-Interactive Mathematical Documents

People learn mathematics fromdocuments, also on the web.Our goal: make themmorecomprehensible by interactivity!

Kohlhase, Giceva, Lange, Zholudev (Jacobs University) JOBAD – Interactive Mathematical Documents September 15, 2009 4/8

Motivation Architecture Services Conclusion

JOBAD: An Architecture for InteractiveDocuments

JavaScript API for OMDoc-based Active Documents

integrated backend or independent web services

XHTML+MathML+OpenMath, JavaScript

GUI

menu

mouse

actionobjects Services

foldinglayers

keybddefinitionlookup

unitconversion

unitconverter

ontology/definitions

notationcollection

renderer

initially generates

Document

ClientModules

WebServices proxy

http://jomdoc.omdoc.org/wiki/AI-Mashup

Kohlhase, Giceva, Lange, Zholudev (Jacobs University) JOBAD – Interactive Mathematical Documents September 15, 2009 5/8

Motivation Architecture Services Conclusion

Definition Lookup

1 click on a symbol in a formula (e. g. in our lecture notes)2 URI of symbol is annotated in the document3 corresponding definition looked up in database (in semantic

markup)4 rendering service makes it readable, client displays a popup

http://jomdoc.omdoc.org/wiki/AI-Mashup→ relations,try ⊆

Kohlhase, Giceva, Lange, Zholudev (Jacobs University) JOBAD – Interactive Mathematical Documents September 15, 2009 6/8

Motivation Architecture Services Conclusion

Unit Conversion

Units in semantic markup: numbers multiplied with ‘‘unit symbols’’(or arithmetic compositions of unit symbols, optionally with prefix)<OMA><OMS cd="arith1" name="times"/>

<OMI>1</OMI><OMS cd="units_metric1" name="metre"/></OMA>

We integrated an existing unit conversion service (input: expression,target unit; output: converted expression) and render its output

http://jomdoc.omdoc.org/wiki/AI-Mashup→ unitconversion

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Motivation Architecture Services Conclusion

Conclusion and Futurehttp://jomdoc.omdoc.org/wiki/AI-Mashup

1 Architecture for interactive mathematical documents2 Reader can interactively adapt appearance3 Single document serves as interface to embedded and remote

services

Future plans:1 interactive adaptation of symbol notations, e. g. (nk) vs. Cnk2 guided tours (definition lookup ++)3 search formulæ on the web (→http://search.mathweb.org)

4 links to web resources (e. g. Wikipedia)5 save custom adaptations on a server

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