Annotating Rhetorical and Argumentative Structures in Mathematical Knowledge
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
Annotating Rhetorical and Argumentative Structures
in Mathematical Knowledge
Summary of my work at DERI (Apr–Oct 2008)
EECS Seminar
Christoph Lange
Jacobs University, Bremen, Germany
KWARC – Knowledge Adaptation and Reasoning for Content
October 14, 2008
Lange (Jacobs University) Annotating Rhetorical and Argumentative Structures in Mathematical 14, 2008 1
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
My Home: Mathematical Knowledge Management
Ph. D. student with Prof. Michael Kohlhase
Our group does “Mathematical Knowledge Management”
dealing with mathematical knowledge
formality ranges from human-friendly to computer-veriﬁable
My Project
Collaboration on semiformal knowledge
Using semantic web technologies (a semantic wiki, in particular)
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
What I Wanted to Learn About the Semantic Web
engineering ontologies for scientiﬁc documents
user interfaces for annotating and browsing
relation of social interaction to knowledge
Where?
At DERI, they do this (and more)
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
DERI (Digital Enterprise Research Institute)
Largest semantic web research institute worldwide (130 members)
Applied Research
eLearning
semantic reality (sensor networks, ubiquitous computing)
web services
industrial applications
Semantic Information Systems and Language Engineering
Social Software
Foundational Research
data intensive infrastructures
information mining and retrieval
reasoning and querying
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
Before: SWiM, a Semantic Wiki for Mathematics
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
Ontologies for Mathematical Documents (1)
Previous State
notDef
I had a basic ontology that modelled structures of
renders-
mathematical knowledge; mainly statements (deﬁnition, Symbol
theorem, proof, examples) sym
used in SWiM for navigation, queries, internal uses- uses-
Symbol Symbol
bookkeeping
fmp ex
fmp ex
fmp ex
contains contains
symDef
symDef
symDef
contains
cd
cd
cd
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
Ontologies for Mathematical Documents (1)
Previous State
notDef
I had a basic ontology that modelled structures of
renders-
mathematical knowledge; mainly statements (deﬁnition, Symbol
theorem, proof, examples) sym
used in SWiM for navigation, queries, internal uses- uses-
Symbol Symbol
bookkeeping
fmp ex
fmp ex
fmp ex
Next Challenge
contains contains
Semi-formal knowledge often comes in documents that
also contain text symDef
symDef
symDef
There is a document structure (chapter, section, contains
cross-reference), and a rhetorical structure, both of
cd
cd
cd
which can be independent from the mathematical
structure.
Lange (Jacobs University) Annotating Rhetorical and Argumentative Structures in Mathematical 14, 2008 6
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
Ontologies for Mathematical Documents (2)
Getting the Model Right
rhetorical ont.
document ont. ↔ annotation ont. ↔
mathematical ont.
(following the SALT approach)
A
SALT (Semantically Annotated LTEX)
semantic authoring framework for creating scientiﬁc publications
Implementation
Expansion of the ontology
Rules for extracting these concepts from
OMDoc documents to RDF
Krextor XML→RDF extraction library
Lange (Jacobs University) Annotating Rhetorical and Argumentative Structures in Mathematical 14, 2008 7
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
User Interfaces for Annotating and Browsing
Improved Annotation Support
More and easier annotation support in the editor
toolbars for easy selection of types of mathematical knowledge
from phrase to theory level
deleting annotations
auto-completion of link targets (prepared)
Lange (Jacobs University) Annotating Rhetorical and Argumentative Structures in Mathematical 14, 2008 8
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
User Interfaces for Annotating and Browsing
Improved Annotation Support
More and easier annotation support in the editor
toolbars for easy selection of types of mathematical knowledge
from phrase to theory level
deleting annotations
auto-completion of link targets (prepared)
Rhetorical Annotation and Visualisation
improved and extended syntax for annotating SALT-/RST-like
rhetorical structures in OMDoc
A
using the SALT ontology within the host language OMDoc, not LTEX
ideas for an editing interface
visualisation of rhetorical relations and blocks implemented
→ active documents
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
Annotation
Sections in the editor
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
Annotation
The toolbar
Sections in the editor
(Implementation by Gordan Ristovski)
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
Visualisation of Rhetorical Structures
Rhetorical Blocks (SALT)
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
Visualisation of Rhetorical Structures
Rhetorical Blocks (SALT)
Rhetorical Relations
(SALT, implementing RST)
(Implementation by Jana Giceva)
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
Argumentation about Mathematical Knowledge
Idea
Need for structured wiki discussions, well-deﬁned workﬂow for solving
problems with knowledge in a wiki
My Case
a wiki page is an item of mathematical knowledge, e. g. a theorem
issues discussed will be quite speciﬁc: e. g. “This theorem is hard to
understand” (or wrong, or inadequately presented, . . . )
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
Argumentation about Mathematical Knowledge
Idea
Need for structured wiki discussions, well-deﬁned workﬂow for solving
problems with knowledge in a wiki
My Case
a wiki page is an item of mathematical knowledge, e. g. a theorem
issues discussed will be quite speciﬁc: e. g. “This theorem is hard to
understand” (or wrong, or inadequately presented, . . . )
Related Topic
There is also argumentation within artifacts of scientiﬁc knowledge, but so
far I focused more on argumentation about them.
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
Resource Edit Discussion History
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
Resource Edit Discussion History
Issue Alice 2008–05–30 [Idea][Argument][Agree][Disagree][Decision]
It’s hard to ﬁnd out how to improve content (= resources) in wikis
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
Resource Edit Discussion History
Issue Alice 2008–05–30 [Idea][Argument][Agree][Disagree][Decision]
It’s hard to ﬁnd out how to improve content (= resources) in wikis
Agree Bob 2008–05–31
Indeed, besides automated approaches it’s hard to get focused feedback from users.
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
Resource Edit Discussion History
Issue Alice 2008–05–30 [Idea][Argument][Agree][Disagree][Decision]
It’s hard to ﬁnd out how to improve content (= resources) in wikis
Agree Bob 2008–05–31
Indeed, besides automated approaches it’s hard to get focused feedback from users.
Idea Claire 2008–06–01 [Argument][Agree][Disagree][Decision]
So let’s make wiki discussions semantic!
Lange (Jacobs University) Annotating Rhetorical and Argumentative Structures in Mathematical 14, 2008 12
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
Resource Edit Discussion History
Issue Alice 2008–05–30 [Idea][Argument][Agree][Disagree][Decision]
It’s hard to ﬁnd out how to improve content (= resources) in wikis
Agree Bob 2008–05–31
Indeed, besides automated approaches it’s hard to get focused feedback from users.
Idea Claire 2008–06–01 [Argument][Agree][Disagree][Decision]
So let’s make wiki discussions semantic!
Argument Dave 2008–06–02 [Agree][Disagree]
We could take types from an argumentation ontology for the posts.
Lange (Jacobs University) Annotating Rhetorical and Argumentative Structures in Mathematical 14, 2008 12
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
Resource Edit Discussion History
Issue Alice 2008–05–30 [Idea][Argument][Agree][Disagree][Decision]
It’s hard to ﬁnd out how to improve content (= resources) in wikis
Agree Bob 2008–05–31
Indeed, besides automated approaches it’s hard to get focused feedback from users.
Idea Claire 2008–06–01 [Argument][Agree][Disagree][Decision]
So let’s make wiki discussions semantic!
Argument Dave 2008–06–02 [Agree][Disagree]
We could take types from an argumentation ontology for the posts.
Argument Eric 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 (Jacobs University) Annotating Rhetorical and Argumentative Structures in Mathematical 14, 2008 12
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23.
Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
Resource Edit Discussion History
Issue Alice 2008–05–30 [Idea][Argument][Agree][Disagree][Decision]
It’s hard to ﬁnd out how to improve content (= resources) in wikis
Agree Bob 2008–05–31
Indeed, besides automated approaches it’s hard to get focused feedback from users.
Idea Claire 2008–06–01 [Argument][Agree][Disagree][Decision]
So let’s make wiki discussions semantic!
Argument Dave 2008–06–02 [Agree][Disagree]
We could take types from an argumentation ontology for the posts.
Argument Eric 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 (Jacobs University) Annotating Rhetorical and Argumentative Structures in Mathematical 14, 2008 12
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
Resource Edit Discussion History
Issue Alice 2008–05–30 [Idea][Argument][Agree][Disagree][Decision]
It’s hard to ﬁnd out how to improve content (= resources) in wikis
Agree Bob 2008–05–31
Indeed, besides automated approaches it’s hard to get focused feedback from users.
Idea Claire 2008–06–01 [Argument][Agree][Disagree][Decision]
So let’s make wiki discussions semantic!
Argument Dave 2008–06–02 [Agree][Disagree]
We could take types from an argumentation ontology for the posts.
Argument Eric 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 SWiM)
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
Domain-Speciﬁc Argumentation
Assumptions
Possible problems depend on the type of knowledge item
Possible solutions depend on the type of knowledge item and the type
of problem
Standard problems have standard solutions, with which software can
assist
Lange (Jacobs University) Annotating Rhetorical and Argumentative Structures in Mathematical 14, 2008 13
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26.
Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
Domain-Speciﬁc Argumentation
Assumptions
Possible problems depend on the type of knowledge item
Possible solutions depend on the type of knowledge item and the type
of problem
Standard problems have standard solutions, with which software can
assist
Survey (tinyurl.com/5qdetd)
Common issues: wrong, incomprehensible, uncommon style,
underspeciﬁed, redundant, truth uncertain
Common solutions: directly improve aﬀected knowledge item, split it
When issues remain unresolved, it’s mostly due to insuﬃcient
restructuring support
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
Domain-Speciﬁc Argumentation (Example)
User Interface
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
Domain-Speciﬁc Argumentation (Example)
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)
on wiki pages
post4: Disagree onIdea
post5: Agree onIssue
withPositions
post6: Decision
physical structure argumentative
(SIOC) discussion page structure
RDF Graph
User Interface
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
General Argumentation on Social Media Sites
developing an argumentation module for SIOC
(ontology for Semantically Interlinking Online Communities)
joint work with Uldis Boj¯rs (SIOC) and Tudor Groza (SALT)
a
use cases, model, guidelines for usage
implementation and evaluation to be done
refers_to
supports/
Statement Argument
challenges
agrees_with/
subClassOf disagrees_with/ subClassOf
neutral_towards
arises_from
Issue Idea Elaboration Example Evaluation Justification
proposes_solution_for elaborates_on
decides Position
supported_by
Decision
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
OpenMath Case Study
lightweight mathematical ontology engineering
(http://wiki.openmath.org)
no rhetorical structures, no documents
but still a lot of structures to annotate!
deﬁnitions, formal properties, examples, notations
local argumentation
small group of knowledge engineers (domain experts)
specialised editors: structured deﬁnitions, formulas, metadata
evaluation needed
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
Summary
What I hope(d) to learn – to use it for mathematical knowledge
management:
engineering ontologies for scientiﬁc documents !
user interfaces for annotating and browsing !
relation of social interaction to knowledge !
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32.
Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
Summary
What I hope(d) to learn – to use it for mathematical knowledge
management:
engineering ontologies for scientiﬁc documents !
user interfaces for annotating and browsing !
relation of social interaction to knowledge !
What I hope to contribute to the semantic web:
mathematics as a complex use case pointing out limits of the
semantic web
an ontology for a complex domain, with document structure,
mathematical structure, and rhetorical structure
domain-speciﬁc argumentation
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
Further Work
Active Documents
Interactive editing and previewing of notations
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
Further Work
Active Documents
Interactive editing and previewing of notations
Argumentation
Study relationship between argumentation within and about documents
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Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
Further Work
Active Documents
Interactive editing and previewing of notations
Argumentation
Study relationship between argumentation within and about documents
Ontologies
1 Scalable metadata syntax and semantics for OMDoc
→ import metadata vocabularies as theories
2 Document these vocabularies in OMDoc
3 Model them in OMDoc
4 Export them back to the semantic web
Lange (Jacobs University) Annotating Rhetorical and Argumentative Structures in Mathematical 14, 2008 18
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36.
Introduction Ontologies/Annotation Argumentation Case Study Summary Outlook
Further Work
Active Documents
Interactive editing and previewing of notations
Argumentation
Study relationship between argumentation within and about documents
Ontologies
1 Scalable metadata syntax and semantics for OMDoc
→ import metadata vocabularies as theories
2 Document these vocabularies in OMDoc
3 Model them in OMDoc
4 Export them back to the semantic web
Semantic Web Empowering MKM
Lange (Jacobs University) Annotating Rhetorical and Argumentative Structures in Mathematical 14, 2008 18
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