LWA 2008, Workshop Knowledge Management (FGWM)

1. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Arguing on Issues with Mathematical Knowledge Items
in a Semantic Wiki
LWA/FGWM 2008
Christoph Lange, Tuukka Hastrup, Stéphane Corlosquet
Jacobs University, Bremen, Germany
KWARC – Knowledge Adaptation and Reasoning for Content
Digital Enterprise Research Institute, National University of Ireland, Galway
This work was supported by JEM-Thematic-Network ECP-038208.
October 7, 2008
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 1

2. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Resource Edit Discussion History
Issue Anna 2008–05–30 [Idea][Argument][Agree][Disagree][Decision]
It’s hard to find out how to improve content (= resources) in wikis
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 2

3. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Resource Edit Discussion History
Issue Anna 2008–05–30 [Idea][Argument][Agree][Disagree][Decision]
It’s hard to find out how to improve content (= resources) in wikis
Agree Bert 2008–05–31
Indeed, besides automated approaches it’s hard to get focused feedback from users.
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 2

4. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Resource Edit Discussion History
Issue Anna 2008–05–30 [Idea][Argument][Agree][Disagree][Decision]
It’s hard to find out how to improve content (= resources) in wikis
Agree Bert 2008–05–31
Indeed, besides automated approaches it’s hard to get focused feedback from users.
Idea Carl 2008–06–01 [Argument][Agree][Disagree][Decision]
So let’s make wiki discussions semantic!
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 2

5. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Resource Edit Discussion History
Issue Anna 2008–05–30 [Idea][Argument][Agree][Disagree][Decision]
It’s hard to find out how to improve content (= resources) in wikis
Agree Bert 2008–05–31
Indeed, besides automated approaches it’s hard to get focused feedback from users.
Idea Carl 2008–06–01 [Argument][Agree][Disagree][Decision]
So let’s make wiki discussions semantic!
Argument Doro 2008–06–02 [Agree][Disagree]
We could take types from an argumentation ontology for the posts.
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 2

6. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Resource Edit Discussion History
Issue Anna 2008–05–30 [Idea][Argument][Agree][Disagree][Decision]
It’s hard to find out how to improve content (= resources) in wikis
Agree Bert 2008–05–31
Indeed, besides automated approaches it’s hard to get focused feedback from users.
Idea Carl 2008–06–01 [Argument][Agree][Disagree][Decision]
So let’s make wiki discussions semantic!
Argument Doro 2008–06–02 [Agree][Disagree]
We could take types from an argumentation ontology for the posts.
Argument Erwin 2008–06–03 [Agree][Disagree]
And every discourse should be connected to resources corresponding to the wiki
page, and there should be domain-specific Idea and Issue subclasses.
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 2

7. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Resource Edit Discussion History
Issue Anna 2008–05–30 [Idea][Argument][Agree][Disagree][Decision]
It’s hard to find out how to improve content (= resources) in wikis
Agree Bert 2008–05–31
Indeed, besides automated approaches it’s hard to get focused feedback from users.
Idea Carl 2008–06–01 [Argument][Agree][Disagree][Decision]
So let’s make wiki discussions semantic!
Argument Doro 2008–06–02 [Agree][Disagree]
We could take types from an argumentation ontology for the posts.
Argument Erwin 2008–06–03 [Agree][Disagree]
And every discourse should be connected to resources corresponding to the wiki
page, and there should be domain-specific Idea and Issue subclasses.
Agree Anonymous 2008–06–04
That’s great, then the wiki could assist with the realisation of an approved idea.
And old decisions would be documented.
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 2

8. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Resource Edit Discussion History
Issue Anna 2008–05–30 [Idea][Argument][Agree][Disagree][Decision]
It’s hard to find out how to improve content (= resources) in wikis
Agree Bert 2008–05–31
Indeed, besides automated approaches it’s hard to get focused feedback from users.
Idea Carl 2008–06–01 [Argument][Agree][Disagree][Decision]
So let’s make wiki discussions semantic!
Argument Doro 2008–06–02 [Agree][Disagree]
We could take types from an argumentation ontology for the posts.
Argument Erwin 2008–06–03 [Agree][Disagree]
And every discourse should be connected to resources corresponding to the wiki
page, and there should be domain-specific Idea and Issue subclasses.
Agree Anonymous 2008–06–04
That’s great, then the wiki could assist with the realisation of an approved idea.
And old decisions would be documented.
Decision Christoph 2008–06–05
So let’s do it! (Available in the semantic wiki IkeWiki, domain-specific extension
for mathematics in SWiM presented here)
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 2

9. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Resource Edit Discussion History
Issue Anna 2008–05–30 [Idea][Argument][Agree][Disagree][Decision]
It’s hard to find out how to improve content (= resources) in wikis
Agree Bert 2008–05–31
Indeed, besides automated approaches it’s hard to get focused feedback from users.
Idea Carl 2008–06–01 [Argument][Agree][Disagree][Decision]
So let’s make wiki discussions semantic!
Argument Doro 2008–06–02 [Agree][Disagree]
We could take types from an argumentation ontology for the posts.
Argument Erwin 2008–06–03 [Agree][Disagree]
And every discourse should be connected to resources corresponding to the wiki
page, and there should be domain-specific Idea and Issue subclasses.
Agree Anonymous 2008–06–04
That’s great, then the wiki could assist with the realisation of an approved idea.
And old decisions would be documented.
Decision Christoph 2008–06–05
So let’s do it! (Available in the semantic wiki IkeWiki, domain-specific extension
for mathematics in SWiM presented here)
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 2

10. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Issues with Knowledge Items
Terms used in this talk:
Knowledge Item: A piece of knowledge about a distinct subject of interest
Issue: Any problem by which a knowledge item could be affected
Example
A Wikipedia article is not written from a neutral point of view
A mathematical theorem is hard to understand or wrong
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 3

11. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Resolving Issues
1 Report: What is affected by what issue
2 Propose a solution
3 Argue about the solution
4 Vote on the solution or on the arguments
5 Take a decision
6 Implement the decision
Benefit
Afterwards, anybody can retrace these steps. Argumentations are part
of the collective experience of the community.
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 4

12. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Solving Issues in Wikipedia (1)
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 5

13. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Solving Issues in Wikipedia (1)
{{Neutralität}}
’’’Würzburg’’’ ist ein trostloses Nest in [[Unterfranken]],
wo weder das Bier noch der Wein schmeckt.
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 5

14. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Solving Issues in Wikipedia (2)
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 6

15. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Solving Issues in Wikipedia (2)
Das ist ja wohl eine sehr verkürzte Betrachtung.
--[[Benutzer:Alfred|Alfred]] 13:41, 27. Aug. 2008 (CEST)
:Stimmt. Sollte man nicht noch was zum Weltkulturerbe
schreiben? --[[Benutzer:Bernd|Bernd]] 13:47, 27. Aug.
2008 (CEST)
::Bin ich sehr dafür. --~~~~
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 6

16. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Solving Issues in Wikipedia (3)
Does that work? – Sufficiently, because:
Quote [Brändle]
Zu wenige Köche verderben den Brei
Wikipedia has a large user base
. . . and deals with topics of general interest
Our system does neither!
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 7

17. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Semantic Wikis
Generally: wikis that employ semantic web technologies like RDF or
ontologies
Most commonly: 1 article = 1 knowledge item
Articles and links have types (taken from ontologies)
Applications
In Würzburg: Problem solving using expert knowledge (KnowWE)
In Karlsruhe: Semantic MediaWiki Semantic Wikipedia
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 8

18. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Semantic Discussions
SIOC (Semantically Interlinked Online Communities)
ontology for user-generated content, particularly online discussions
applied in forums, blogs, content management systems, . . .
. . . and in one (!) semantic wiki – which ours is based on
Did you know?
Discussions in semantic wikis are rarely semantic
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 9

19. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Wicked Problems
Warning
Issues can be wicked problems
A wicked problem
does not allow for a definitive formulation
has solutions that are not true-or-false but good-or-bad
There is no immediate and ultimate test of a solution
IBIS: model for structured argumentation about wicked problems
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 10

20. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Argumentation Ontologies
DILIGENT: IBIS applied to ontology engineering
DILIGENT workflow
1 Issue (“some concept is not covered by our ontology”, “some
requirement is not satisfied”)
2 Idea (how to conceptualise/formalise it)
3 Arguments challenge or justify ideas
4 Positions: opinions/votes on ideas
5 Decision: points to Issue, Idea, and supporting votes
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 11

21. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Domain-Specific Argumentation Ontology
Agree Disagree
DILIGENT
argumentation ……
ontology subClassOf Theorem Example
Position subClassOf
Domain-specific positionOn positionOn
argumentation
classes (partly shown) Math. Know-
withPositions ledge Item
OMDoc ontology
subClassOf
Ontology
Decision Entity
onIssue onIdea
resolvesInto
Issue Idea
responseTo
subClassOf subClassOf
Wrong Inappropriate Incomprehensible Provide Keep as Delete
for Domain Example Bad Example
Applicable Issue/Idea types depend on type of knowledge item
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 12

22. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Issues in Mathematics
50 participants, experienced in mathematical knowledge management
Survey is still open: http://tinyurl.com/5qdetd
Common granularities of knowledge: course unit, mathematical
theory, mathematical statement
Little software support for issue tracking and solving known
Knowledge item type most frequently affected by issues: definitions
Common issues: wrong, incomprehensible, truth uncertain,
underspecified, redundant
Common solutions: directly improve affected knowledge item, split it
Issues remain unresolved due to insufficient restructuring support
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 13

23. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Automated Assistance
1 Find legitimate issues
not yet decided, more agreement than disagreement
2 Find best solution proposal (idea)
highest agreement/disagreement ratio
3 Assist with implementation
system knows common idea and issue types
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 14

24. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Implementation
SWiM (Semantic Wiki for Mathematical Knowledge Management)
one page holds one mathematical statement
DILIGENT SIOC Argumentation Module (work in progress)
SPARQL queries for finding the winning ideas
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 15

25. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Structure of a Use Case
hasDiscussion
forum1 theorem
(IkeWiki ontology)
has_container exemplifies
post1: Issue
(Incomprehensible) example
responseTo
has_reply resolvesInto
post2: Idea
(ProvideExample)
positionOn knowledge
post3: Agree items
(OMDoc ontology)
onIdea on wiki pages
post4: Disagree
post5: Agree onIssue
withPositions
post6: Decision
argumentative
physical structure structure
(SIOC) discussion page (DILIGENT)
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 16

26. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Structure of a Use Case
hasDiscussion
forum1 theorem
(IkeWiki ontology)
has_container exemplifies
post1: Issue
(Incomprehensible) example
responseTo
has_reply resolvesInto
post2: Idea
(ProvideExample)
positionOn knowledge
post3: Agree items
(OMDoc ontology)
onIdea on wiki pages
post4: Disagree
post5: Agree onIssue
withPositions
post6: Decision
argumentative
physical structure structure
(SIOC) discussion page (DILIGENT)
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 16

27. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Demo (1)
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 17

28. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Demo (2)
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 18

29. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Demo (3)
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 19

30. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Critical Questions
Coverage of the model: No arguments so far (will make it harder to find
the winning idea)
Structure required: Knowledge items already need to have types (but
DILIGENT-like approach to conceptualising/formalising from
scratch would be possible)
Wicked problems? Standard problems with standard solutions are not
really wicked.
But we give the user enough freedom to discuss
non-standard problems as well.
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 20

31. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
OpenMath Case Study
OpenMath Content Dictionary Wiki: http://wiki.openmath.org
small group of knowledge engineers
adding and revising semiformal definitions of math. symbols
intensive discussions, formerly on a mailing list
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 21

32. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Practical Evaluation
Idea:
Given: a knowledge base where we intentionally break some
knowledge items
Task: fix it!
One group has argumentation feature enabled
The other group doesn’t
Find out which group is more effective
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 22

33. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Related Work
Foucault@Wiki: How to edit summaries and discussion posts relate to
changes made to Wikipedia articles?
Lekapidia: developing a new ontology with a DILIGENT-based wiki:
detect inconsistent arguments, foster consensus
Cicero: Arguing and voting on problem solutions using Semantic
MediaWiki
Collaborative Protégé: collaborative ontology editor
Drupal: Versatile Content Management System, could port our
implementation there
panta rhei: interactive and collaborative reader for mathematical
documents; discussion forums and ratings
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 23

34. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Summary
Knowledge bases need structured discussions for better problem
solving and documentation
We have integrated an argumentation ontology into a semantic wiki
. . . offering domain-specific extensions and assistance
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 24

35. Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion
Scale it to the web
Users can have accounts on multiple social media sites
SIOC allows for modeling this
There are crawlers and indexers for RDF data on the web
⇒ we can find about arguments and actions of the same user on
other sites
. . . and use it for the purpose of our own site
Example
A user on site A proposes lots of solutions to issues which get positive
feedback and are then implemented ⇒ This is a competent user!
Site B, dealing with a related topic, might be interested in him.
Lange/Hastrup/Corlosquet (Jacobs U./DERI) Arguing on Issues with Math. Knowledge Items in a Wiki October 7, 2008 25