semantic wikis for mathematics – a state-of-the-art survey
DESCRIPTION
Ontolog Semantic Wiki Miniseries 2008/09TRANSCRIPT
Requirements Survey Challenge Vision
Semantic Wikis for Mathematics –a State-of-the-Art SurveyOntolog Semantic Wiki Mini-Series
Christoph Lange
Jacobs University, Bremen, GermanyKWARC – Knowledge Adaptation and Reasoning for Content
January 22, 2009
Lange (Jacobs University) Semantic Wikis for Mathematics – a State-of-the-Art Survey January 22, 2009 1
Requirements Survey Challenge Vision
Lange (Jacobs University) Semantic Wikis for Mathematics – a State-of-the-Art Survey January 22, 2009 2
Requirements Survey Challenge Vision
Requirements for Managing MathematicalKnowledge on the Web
Ever-growing mathematical knowledge bases (previous slide:Mizar Mathematical Library, http://www.mizar.org)Wide acceptance of computer support in formal mathematics
automated theorem provingcomputer algebra systems
e-learning (e. g. ActiveMath: http://www.activemath.org)computer-based math publishing: LATEX, MathML
But: Hardly any systems for Math Collaboration [on the web]!
Lange (Jacobs University) Semantic Wikis for Mathematics – a State-of-the-Art Survey January 22, 2009 3
Requirements Survey Challenge Vision
Survey: Wikis for Mathematical Knowledge
Wikis for managing mathematical knowledge – some semantic,some notWiki engines with just LATEX or MathML input don’t countWiki sites with an ordinary engine and just mathematicalcontent don’t count
ExampleGoogling for “math wiki” does not help much. Same as the “unrealwiki”, which really exists ,
Lange (Jacobs University) Semantic Wikis for Mathematics – a State-of-the-Art Survey January 22, 2009 4
Requirements Survey Challenge Vision
PlanetMath – Free Math Encyclopedia
Dedicated wiki engine, mathematical metadata and keywords used forsearch and navigationhttp://www.planetmath.org
Lange (Jacobs University) Semantic Wikis for Mathematics – a State-of-the-Art Survey January 22, 2009 5
Requirements Survey Challenge Vision
vdash – Automated Theorem Proving
Integrates the automated theorem prover IsabelleNot yet released but promising roadmap: web crawling, consistencyhttp://vdash.org
Lange (Jacobs University) Semantic Wikis for Mathematics – a State-of-the-Art Survey January 22, 2009 6
Requirements Survey Challenge Vision
ProofWiki – Automated Theorem Proving
Integrates automated theorem prover Coq (future: more); prototypePrototype/mockup at http://prover.cs.ru.nl/wiki.phpDon’t confuse with non-semantic proofwiki.org
Lange (Jacobs University) Semantic Wikis for Mathematics – a State-of-the-Art Survey January 22, 2009 7
Requirements Survey Challenge Vision
ASciencePad – Personal Wiki
TiddlyWiki (local, single-user JavaScript wiki) with MathML and SVGCan calculate and graphhttp://math.chapman.edu/~jipsen/asciencepad/
Lange (Jacobs University) Semantic Wikis for Mathematics – a State-of-the-Art Survey January 22, 2009 8
Requirements Survey Challenge Vision
WebMathematica wiki – Computer Algebra
MediaWiki rewrite integrating WebMathematica CAS frontendCan do computer algebra, computations, graphing, . . .http://www.mathematica-users.org/webMathematica/wiki/
Lange (Jacobs University) Semantic Wikis for Mathematics – a State-of-the-Art Survey January 22, 2009 9
Requirements Survey Challenge Vision
SlugMath – SMW for E-Learning
Semantic MediaWiki containing formal core of math lectureshttp://slugmath.ucsc.edu/mediawiki/
Lange (Jacobs University) Semantic Wikis for Mathematics – a State-of-the-Art Survey January 22, 2009 10
Requirements Survey Challenge Vision
SWiM – Ontology-based Semantic Wiki
Ontology of math. knowledge structures at the coreEditing, RDF-powered navigation and queries, argumentationhttp://wiki.openmath.org / http://kwarc.info/projects/swim/
Lange (Jacobs University) Semantic Wikis for Mathematics – a State-of-the-Art Survey January 22, 2009 11
Requirements Survey Challenge Vision
Summary
PlanetMath
vdash ProofWiki
ASciencePad
WebMathe-matica
SlugMath
SWiM
Sem. Web n n n n n y yMetadata y n n n n (y) ySem.Formulae
n y y/n n/y y n y
Verification n y y n (y) n (n)Computation n (y) (y) y y n nGraphing n n n y y n nLearning (y) n (y) n n y (n)
Lange (Jacobs University) Semantic Wikis for Mathematics – a State-of-the-Art Survey January 22, 2009 12
Requirements Survey Challenge Vision
Formality Challenge
Wiki is informal and agileMathematical knowledge should be correctCurrently different wikis for different formality levelsUltimate goal: one wiki for formal and informal mathematics
evolving an informal proof sketch into a formal proofexplaining a formal definition informallycombining formal and informal data (e. g. for search)multi-level validation: syntax, link structure, theory structure,proofsOMDoc (SWiM’s language) has the potential, but it’s a longway
Lange (Jacobs University) Semantic Wikis for Mathematics – a State-of-the-Art Survey January 22, 2009 13
Requirements Survey Challenge Vision
Vision: Active Mathematical DocumentsMathematical documents that you can adapt, edit, and interactwith like spreadsheetsAdapt symbols:
Select different notations: Ckn ;
(nk)
Edit notation on the flyGive natural-language explanation
Explain the structure of a formula:Show all brackets:(5 · (x + y)(n+3)) ≤ ((a · b)!)) ∨ ((¬p) ∧ (¬(q ≤ π)))Fold/unfold/abbreviate subterms: Wpot(R)↔ −e2
4πε0R/2 .Interlink symbols and their definitions:
Expand a definitionFill concrete values into an expressionGuided tour: explain all definitions and their definitions
more . . . −→
Lange (Jacobs University) Semantic Wikis for Mathematics – a State-of-the-Art Survey January 22, 2009 14
Requirements Survey Challenge Vision
Vision: Active Mathematical DocumentsMathematical documents that you can adapt, edit, and interactwith like spreadsheetsAdapt symbols:
Select different notations: Ckn ;
(nk)
Edit notation on the flyGive natural-language explanation
Explain the structure of a formula:Show all brackets:(5 · (x + y)(n+3)) ≤ ((a · b)!)) ∨ ((¬p) ∧ (¬(q ≤ π)))Fold/unfold/abbreviate subterms: Wpot(R)↔ −e2
4πε0R/2 .
Interlink symbols and their definitions:Expand a definitionFill concrete values into an expressionGuided tour: explain all definitions and their definitions
more . . . −→
Lange (Jacobs University) Semantic Wikis for Mathematics – a State-of-the-Art Survey January 22, 2009 14
Requirements Survey Challenge Vision
Vision: Active Mathematical DocumentsMathematical documents that you can adapt, edit, and interactwith like spreadsheetsAdapt symbols:
Select different notations: Ckn ;
(nk)
Edit notation on the flyGive natural-language explanation
Explain the structure of a formula:Show all brackets:(5 · (x + y)(n+3)) ≤ ((a · b)!)) ∨ ((¬p) ∧ (¬(q ≤ π)))Fold/unfold/abbreviate subterms: Wpot(R)↔ −e2
4πε0R/2 .Interlink symbols and their definitions:
Expand a definitionFill concrete values into an expressionGuided tour: explain all definitions and their definitions
more . . . −→Lange (Jacobs University) Semantic Wikis for Mathematics – a State-of-the-Art Survey January 22, 2009 14
Requirements Survey Challenge Vision
Vision: Active Mathematical Documents (2)cont’d:
Select term and then:Search this (→ MathWebSearch,http://search.mathweb.org)Simplify/solve thisProve thisGraph this
Beyond formulas, browse . . .structured proofsrhetorical structures of informal math content
Some services possible inside single document, others needclient/server connectionFirst examples and core of a JavaScript framework:https://jomdoc.omdoc.org/wiki/JOBADSWiM integration to be done
Lange (Jacobs University) Semantic Wikis for Mathematics – a State-of-the-Art Survey January 22, 2009 15
Requirements Survey Challenge Vision
Vision: Active Mathematical Documents (2)cont’d:
Select term and then:Search this (→ MathWebSearch,http://search.mathweb.org)Simplify/solve thisProve thisGraph this
Beyond formulas, browse . . .structured proofsrhetorical structures of informal math content
Some services possible inside single document, others needclient/server connectionFirst examples and core of a JavaScript framework:https://jomdoc.omdoc.org/wiki/JOBADSWiM integration to be done
Lange (Jacobs University) Semantic Wikis for Mathematics – a State-of-the-Art Survey January 22, 2009 15
Requirements Survey Challenge Vision
Vision: Active Mathematical Documents (2)cont’d:
Select term and then:Search this (→ MathWebSearch,http://search.mathweb.org)Simplify/solve thisProve thisGraph this
Beyond formulas, browse . . .structured proofsrhetorical structures of informal math content
Some services possible inside single document, others needclient/server connectionFirst examples and core of a JavaScript framework:https://jomdoc.omdoc.org/wiki/JOBADSWiM integration to be done
Lange (Jacobs University) Semantic Wikis for Mathematics – a State-of-the-Art Survey January 22, 2009 15