AI Mashup Challenge at KI 20

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