OpenGeo: An Open Geometric Knowledge Base Dongming Wang, Xiaoyu - - PowerPoint PPT Presentation
OpenGeo: An Open Geometric Knowledge Base Dongming Wang, Xiaoyu Chen, Wenya An, Lei Jiang, and Dan Song Beihang University, China August 6, 2014 X. Chen (franknewchen@gmail.com) ICMS 2014, Seoul August 6, 2014 1 / 30 Motivation Outline
Dongming Wang, Xiaoyu Chen, Wenya An, Lei Jiang, and Dan Song
Beihang University, China
August 6, 2014
ICMS 2014, Seoul August 6, 2014 1 / 30
Motivation
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Motivation
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Geometric knowledge base: design methodology
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OpenGeo: an enhanced version of GeoData
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Conclusion and future work
ICMS 2014, Seoul August 6, 2014 2 / 30
Motivation
Geometric knowledge is rich in content: definitions, axioms, theorems, proofs, problems, solutions, and algorithms; sophisticated in structure: from basic concepts to derived concepts, from simple diagrams to complicated configurations. Problem How to digitalize geometric knowledge and make it easily accessible, presentable, interoperable, and processable on advanced computing machines and communication devices?
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Motivation
A geometric knowledge base is a special database for storing and managing geometric knowledge data.
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Motivation
Resourcesµ
Association of America, Washington D.C., 1967
Society, Providence, 2008
GeoData currently includes
theorems (e.g., Simson’s theorem)
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Motivation
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Geometric knowledge base: design methodology
1
Motivation
2
Geometric knowledge base: design methodology
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OpenGeo: an enhanced version of GeoData
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Conclusion and future work
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Geometric knowledge base: design methodology
The following aspects are needed to be studied for constructing a geometric knowledge base. Geometric knowledge representation Meta-knowledge representation (the knowledge about geometric knowledge)
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Geometric knowledge base: design methodology
Natural languageµa circle with center O and radius r Algebraic expressionµ (x, y)|x2 + y2 = r2 or x = r · 1 − t2 1 + t2 y = r · 2t 1 + t2 Drawing instructionµCircle[O, r] Degeneracy conditionµr = 0 Image:
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Geometric knowledge base: design methodology
Formalization:
incident(A, m))], not(parallel(l, m)))
circumcircle(triangle(A,B,C)))], [collinear(foot(D,line(A, B)), foot(D,line(A, C)), foot(D, line(B, C)))])
Dynamic diagram: Multimedia: video, audio
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Geometric knowledge base: design methodology
A knowledge object is individual knowledge unit that can be recognized, differentiated, understood, and manipulated in the process of management. Knowledge objects are used to encapsulate interrelated geometric knowledge data. Knowledge classes are used to define the internal structure of knowledge objects.
Example, Exercise, Proof, Solution, Algorithm, Introduction, Remark.
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Geometric knowledge base: design methodology
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Geometric knowledge base: design methodology
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Geometric knowledge base: design methodology
Catalog is used to describe how knowledge objects are clustered.
Chapter: Points and Lines Connected with a Triangle Section: Points of interest Definition of orthocenter
Knowledge graph is used to describe how knowledge objects are related.
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Geometric knowledge base: design methodology
C: Points and Lines Connected with a Triangle T1: Steiner-Lehmus theorem P1: Steiner-Lehmus theorem’s proof L1, L2: Lemma used in P1 E1, E2: Exercise for T1 S1, S2: Solution to the exercises I1, R1: Introduction and remark on T1 D1: Definition of bisector T2: Theorem: the three inner bisectors of a triangle are concurrent D2: Definition of incenter of a triangle D3: Another definition of incenter of a triangle
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Geometric knowledge base: design methodology
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Geometric knowledge base: design methodology
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Geometric knowledge base: design methodology
Inclusion A →include B Inheritance A →inherit B Dependance A →contextOf B A →deriveFrom B A →imply B A →hasProperty B A →decide B A →introduce B A →remarkOn B A →complicate B A →solve B A →exerciseOf B Association A →justify B A →applyOn B A →exampleOf B A ↔associate B A ↔equal B
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OpenGeo: an enhanced version of GeoData
1
Motivation
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Geometric knowledge base: design methodology
3
OpenGeo: an enhanced version of GeoData
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Conclusion and future work
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OpenGeo: an enhanced version of GeoData
OpenGeo is an enhanced version of GeoData, which is equipped with web-based interfaces, new management facilities, and made open online.
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OpenGeo: an enhanced version of GeoData
knowledge objects can be edited or deleted; meta-information (e.g., language, format, and keyword) can be annotated for organizing and classifying knowledge objects; revisions of knowledge objects can be recorded; knowledge objects can be retrieved in meta-information-based ways; knowledge objects can be rated and commented for screening high-quality versions; new knowledge objects can be created and added to OpenGeo.
*Creative Commons Attribution-ShareAlike license is adopted as its main content license.
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OpenGeo: an enhanced version of GeoData
We adopt ontology (OWL) to formally specify geometric knowledge
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OpenGeo: an enhanced version of GeoData
knowledge object → ontology instance knowledge class → ontology class
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OpenGeo: an enhanced version of GeoData
knowledge class structure → ontology attribute knowledge graph → ontology relation
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OpenGeo: an enhanced version of GeoData
Database schema (relational data tables) can be automatically generated from the ontologies. − →
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OpenGeo: an enhanced version of GeoData
The LAMP (Linux Apache MySQL PHP/Perl/Python) framework MathEdit: editing formatted formulas in a WISIWIG style Sketchometry: drawing and exporting dynamic diagrams GeoGebra: constructing and rendering dynamic diagrams
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Conclusion and future work
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Motivation
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Geometric knowledge base: design methodology
3
OpenGeo: an enhanced version of GeoData
4
Conclusion and future work
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Conclusion and future work
OpenGeo is created for the purpose of research and education, and may serve as a public resource for users to test, for instance, geometric theorem provers and problem solvers; and an infrastructure for developing new educational applications (e.g., generation of textbooks and courses) in online learning environments. We are formalizing geometric theorems in the OpenGeo collection and developing semantic querying tools based on images of diagrams. We expect to complete these tasks and release a preliminary version of OpenGeo in early 2015.
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Conclusion and future work
Input Output If the points A, B, and C are arbitrary, the point D is on the circumcircle of the triangle ABC, F is the perpendicular foot of the line AC to the line DF, G is the perpendicular foot of the line BC to the line DG, and E is the perpendicular foot of the line BA to the line DE, then the point F is on the line EG.
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Conclusion and future work
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