JOBAD – Interactive Mathematical Documents

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The document proposes an architecture called JOBAD that allows mathematical documents to interactively access web services. JOBAD uses JavaScript to integrate definition lookup, unit conversion, and other services directly into OMDoc-based documents. This allows readers to interactively adapt document appearance and access remote explanations and computations without leaving the document interface. Future plans include more interactive customization and linking documents to external search and information resources.

Technology Education

Motivation Architecture Services Conclusion

JOBAD – Interactive Mathematical Documents
AI Mashup Challenge 2009

Michael Kohlhase, Jana Giceva, Christoph Lange, Vyacheslav
Zholudev
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” – what was p again??
The professor says A, writes B, means C, continues the
calculation using D, obtains E as a result, but F would have been
right.

concise and minimalistic style of writing
abstract objects
layers of definitions and assertions, documents depend on
others
optimized 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 audiences
checking users’ solutions to exercises
evaluating expressions, solving problems
. . . are available, but accessible from documents?

Yes, sometimes, but not really easy to integrate as mashups; most of
the time only used in their native environment (e. g. the e-learning
environment 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 from
documents, also on the web.
Our goal: make them more
comprehensible 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 Interactive
Documents

JavaScript API for OMDoc-based Active Documents
integrated backend or
independent web services ontology/ notation
definitions collection
initially
Web unit generates
Services converter proxy renderer

menu layers folding unit definition
mouse keybd conversion lookup
Client
Modules action
GUI objects Services
Document XHTML+MathML+OpenMath, JavaScript

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 document
3 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 → unit
conversion
Kohlhase, Giceva, Lange, Zholudev (Jacobs University) JOBAD – Interactive Mathematical Documents September 15, 2009 7/8

Motivation Architecture Services Conclusion

Conclusion and Future
http://jomdoc.omdoc.org/wiki/AI-Mashup
1 Architecture for interactive mathematical documents
2 Reader can interactively adapt appearance
3 Single document serves as interface to embedded and remote
services
Future plans:
1 interactive adaptation of symbol notations, e. g. n
k vs. Ck
n

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

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1. Motivation Architecture Services Conclusion JOBAD – Interactive Mathematical Documents AI Mashup Challenge 2009 Michael Kohlhase, Jana Giceva, Christoph Lange, Vyacheslav Zholudev 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

2. Motivation Architecture Services Conclusion Mathematics is Hard Example (Math Jokes) “Let p be a point q, which we call r” – what was p again?? The professor says A, writes B, means C, continues the calculation using D, obtains E as a result, but F would have been right. concise and minimalistic style of writing abstract objects layers of definitions and assertions, documents depend on others optimized 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

3. Motivation Architecture Services Conclusion Mathematical Web Services Services for . . . flexibly adapting documents to varying audiences checking users’ solutions to exercises evaluating expressions, solving problems . . . are available, but accessible from documents? Yes, sometimes, but not really easy to integrate as mashups; most of the time only used in their native environment (e. g. the e-learning environment ActiveMath) Kohlhase, Giceva, Lange, Zholudev (Jacobs University) JOBAD – Interactive Mathematical Documents September 15, 2009 3/8

4. Motivation Architecture Services Conclusion Non-Interactive Mathematical Documents People learn mathematics from documents, also on the web. Our goal: make them more comprehensible by interactivity! Kohlhase, Giceva, Lange, Zholudev (Jacobs University) JOBAD – Interactive Mathematical Documents September 15, 2009 4/8

5. Motivation Architecture Services Conclusion JOBAD: An Architecture for Interactive Documents JavaScript API for OMDoc-based Active Documents integrated backend or independent web services ontology/ notation definitions collection initially Web unit generates Services converter proxy renderer menu layers folding unit definition mouse keybd conversion lookup Client Modules action GUI objects Services Document XHTML+MathML+OpenMath, JavaScript http://jomdoc.omdoc.org/wiki/AI-Mashup Kohlhase, Giceva, Lange, Zholudev (Jacobs University) JOBAD – Interactive Mathematical Documents September 15, 2009 5/8

6. 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 document 3 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

7. 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 → unit conversion Kohlhase, Giceva, Lange, Zholudev (Jacobs University) JOBAD – Interactive Mathematical Documents September 15, 2009 7/8

8. Motivation Architecture Services Conclusion Conclusion and Future http://jomdoc.omdoc.org/wiki/AI-Mashup 1 Architecture for interactive mathematical documents 2 Reader can interactively adapt appearance 3 Single document serves as interface to embedded and remote services Future plans: 1 interactive adaptation of symbol notations, e. g. n k vs. Ck n 2 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 Kohlhase, Giceva, Lange, Zholudev (Jacobs University) JOBAD – Interactive Mathematical Documents September 15, 2009 8/8

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