Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion

Arguing on Issues with Mathematical Knowledge Itemsin a Semantic Wiki

LWA/FGWM 2008

Christoph Lange, Tuukka Hastrup, Stéphane Corlosquet

Jacobs University, Bremen, GermanyKWARC – Knowledge Adaptation and Reasoning for Content

Digital Enterprise Research Institute, National University of Ireland, GalwayThis 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

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 wikipage, 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 extensionfor 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

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 wikipage, 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 extensionfor 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

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 wikipage, 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 extensionfor 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

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 wikipage, 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 extensionfor 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

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 wikipage, 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 extensionfor 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

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 wikipage, 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 extensionfor 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

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 wikipage, 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 extensionfor 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

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 wikipage, 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 extensionfor 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

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

ExampleA Wikipedia article is not written from a neutral point of viewA mathematical theorem is hard to understand or wrong

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Resolving Issues

1 Report: What is affected by what issue2 Propose a solution3 Argue about the solution4 Vote on the solution or on the arguments5 Take a decision6 Implement the decision

BenefitAfterwards, anybody can retrace these steps. Argumentations are partof the collective experience of the community.

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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

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.

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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 Weltkulturerbeschreiben? --[[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

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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 Weltkulturerbeschreiben? --[[Benutzer:Bernd|Bernd]] 13:47, 27. Aug.2008 (CEST)

::Bin ich sehr dafür. --~~~~

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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!

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Semantic Wikis

Generally: wikis that employ semantic web technologies like RDF orontologiesMost commonly: 1 article = 1 knowledge itemArticles and links have types (taken from ontologies)

ApplicationsIn Würzburg: Problem solving using expert knowledge (KnowWE)In Karlsruhe: Semantic MediaWiki ; Semantic Wikipedia

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Semantic Discussions

SIOC (Semantically Interlinked Online Communities)ontology for user-generated content, particularly online discussionsapplied 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 /

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Wicked Problems

WarningIssues can be wicked problems

A wicked problemdoes not allow for a definitive formulationhas solutions that are not true-or-false but good-or-badThere is no immediate and ultimate test of a solution

IBIS: model for structured argumentation about wicked problems

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Argumentation Ontologies

DILIGENT: IBIS applied to ontology engineering

DILIGENT workflow1 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 ideas4 Positions: opinions/votes on ideas5 Decision: points to Issue, Idea, and supporting votes

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Domain-Specific Argumentation Ontology

Agree

Position

Disagree

Decision

subClassOf

Issue

Inappropriatefor Domain

Wrong Incomprehensible

subClassOf

Idea

ProvideExample

Keep asBad Example

Delete

subClassOfresponseTo

positionOn positionOn

onIssue onIdea

withPositions

OntologyEntity

resolvesInto

Math. Know-ledge Item

Theorem Example

subClassOf

subClassOf

DILIGENTargumentationontology

Domain-specificargumentationclasses (partly shown)

OMDoc ontology

……

Applicable Issue/Idea types depend on type of knowledge item

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Issues in Mathematics

50 participants, experienced in mathematical knowledge managementSurvey is still open: http://tinyurl.com/5qdetd

Common granularities of knowledge: course unit, mathematicaltheory, mathematical statementLittle software support for issue tracking and solving knownKnowledge item type most frequently affected by issues: definitionsCommon issues: wrong, incomprehensible, truth uncertain,underspecified, redundantCommon solutions: directly improve affected knowledge item, split itIssues remain unresolved due to insufficient restructuring support

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Automated Assistance

1 Find legitimate issuesnot yet decided, more agreement than disagreement

2 Find best solution proposal (idea)highest agreement/disagreement ratio

3 Assist with implementationsystem knows common idea and issue types

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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

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Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion

Structure of a Use Case

discussion page

knowledgeitems

(OMDoc ontology)on wiki pages

theoremforum1

example

post1: Issue(Incomprehensible)

post6: Decision

post3: Agree

post2: Idea(ProvideExample)

post4: Disagree

post5: Agree

exemplifies

hasDiscussion(IkeWiki ontology)

has_container

has_replyresponseTo

resolvesInto

positionOn

onIdea

withPositionsonIssue

physical structure(SIOC)

argumentativestructure

(DILIGENT)

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Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion

Structure of a Use Case

discussion page

knowledgeitems

(OMDoc ontology)on wiki pages

theoremforum1

example

post1: Issue(Incomprehensible)

post6: Decision

post3: Agree

post2: Idea(ProvideExample)

post4: Disagree

post5: Agree

exemplifies

hasDiscussion(IkeWiki ontology)

has_container

has_replyresponseTo

resolvesInto

positionOn

onIdea

withPositionsonIssue

physical structure(SIOC)

argumentativestructure

(DILIGENT)

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Demo (1)

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Demo (2)

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Demo (3)

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Critical Questions

Coverage of the model: No arguments so far (will make it harder to findthe winning idea)

Structure required: Knowledge items already need to have types (butDILIGENT-like approach to conceptualising/formalising fromscratch would be possible)

Wicked problems? Standard problems with standard solutions are notreally wicked.But we give the user enough freedom to discussnon-standard problems as well.

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OpenMath Case Study

OpenMath Content Dictionary Wiki: http://wiki.openmath.orgsmall group of knowledge engineersadding and revising semiformal definitions of math. symbolsintensive discussions, formerly on a mailing list

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Practical Evaluation

Idea:Given: a knowledge base where we intentionally break someknowledge itemsTask: fix it!One group has argumentation feature enabledThe other group doesn’tFind out which group is more effective

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Related Work

Foucault@Wiki: How to edit summaries and discussion posts relate tochanges 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 SemanticMediaWiki

Collaborative Protégé: collaborative ontology editorDrupal: Versatile Content Management System, could port our

implementation therepanta rhei: interactive and collaborative reader for mathematical

documents; discussion forums and ratings

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Summary

Knowledge bases need structured discussions for better problemsolving and documentationWe have integrated an argumentation ontology into a semantic wiki. . . offering domain-specific extensions and assistance

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Introduction Motivation Foundations Approach Implementation Evaluation Related Conclusion

Scale it to the web

Users can have accounts on multiple social media sitesSIOC allows for modeling thisThere are crawlers and indexers for RDF data on the web⇒ we can find about arguments and actions of the same user onother sites. . . and use it for the purpose of our own site

ExampleA user on site A proposes lots of solutions to issues which get positivefeedback 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