Bringing Math to LOD

Bringing Math to LOD:A Semantic Publishing Platform Prototype for

Scientific Collections in Mathematics

Olga Nevzorova, Nikita Zhiltsov, Danila Zaikin, Olga Zhibrik,Alexander Kirillovich, Vladimir Nevzorov, Evgeniy Birialtsev

Kazan Federal UniversityRussia

October 23, 2013

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Outline

1 Introduction

2 Approach

3 Use Cases

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Our Contribution

Our prototype is geared to build a semantic graph ofmathematical knowledge objects, that

I is extracted from a collection of mathematicalscholarly papers, and

I is integrated into the LOD «cloud»

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Research OutputIVM Data Set

I LOD representation of 1 330 scholarly publications ofthe «Izvestiya Vuzov. Matematika» (IVM) journal

I Covers the semantics of:I article metadataI elements of the logical structureI terminologyI formulas

I Aligned with DBpedia, CORDISI More than 850 000 RDF triplesI SPARQL endpoint:

http://cll.niimm.ksu.ru:8890/sparql-auth∗

∗the SPARQL endpoint is secured. Please email the authors for credentials4 / 29

Related Work

I Domain-specific languages: OMDoc, MathLangI Domain models: Cambridge MathematicalThesaurus, DBpedia (math-related part),ScienceWISE Ontology

I Math-related NLP: mArachna; linguistic modules ofarXMLiv

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Outline

1 Introduction

2 Approach

3 Use Cases

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Key Research Contributions

I a thorough ontological model of the mathematicaldomain

I an ontology-based language-independent method forextraction of logical structure elements in papers

I an ontology-based method for extraction ofmathematical named entities from texts in Russian

I a method that connects mathematical named entitiesto symbolic expressions

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Prototype’s Design

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Domain Model

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Ontology of Structural Elements (1)http://cll.niimm.ksu.ru/ontologies/mocassin

I Covers 15 common structural elements:

I Defines 9 object properties and 4 datatype properties:

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Ontology of Structural Elements (2)http://cll.niimm.ksu.ru/ontologies/mocassin

I 3 cardinality axioms, e.g.Proof ∧ (= 1 proves ProvableStatement†)

I 2 transitivity axioms for hasPart and dependsOnproperties

I DL expressivity: SRIN (D)

†i.e., Claim ∨ Corollary ∨ Lemma ∨ Proposition ∨ Theorem11 / 29

Ontology of Mathematical Concepts (1)http://cll.niimm.ksu.ru/ontologies/mathematics

I Covers 3 450 mathematical conceptsI Defines commonly used terms as well as terms fromthe emerging professional vocabulary (e.g.Bitsadze-Samarsky problem)

I Supports Russian/English labels

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Ontology of Mathematical Concepts (2)http://cll.niimm.ksu.ru/ontologies/mathematics

I Includes two taxonomies:I taxonomy of mathematical theories‡:

F number theory, set theory, algebra, analysis, geometry,mathematical logic, discrete mathematics, theory ofcomputation, differential equations, numerical analysis,probability theory and statistics

I taxonomy of mathematical objects

I Covers common scientific concepts, such as Problem,Method, Statement, Formula etc.

I DL expressivity: ALCHI

‡covers just a part of the mathematical knowledge13 / 29

Ontology of Mathematical Concepts (3)Object properties

I belongsTo/contains, e.g.Barycentric Coordinates belongsTo Metric Geometry

I defines/isDefinedBy, e.g.Christoffel Symbol isDefinedBy Connectedness

I seeAlso, e.g.Chebyshev Iterative Method seeAlso Numerical Solution ofLinear Equation Systems

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Ontology of Mathematical Concepts (4)Stats

I 3 450 classesI 27% of classes are mapped onto DBpediaI 3 630 subclass-of property instancesI 1 140 other object property instancesI Common facts about the development:

I lasted for 4 monthsI 7 pro mathematicians participated as domain experts

guided by the authorsI WebProtege was used as a collaborative tool

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Semantic Annotation

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NLP Annotation

I Relies on the OntoIntegrator facilitiesI Solves some of the conventional linguistic tasks, suchas:

I tokenizationI sentence splitting (∼ 98% F-measure§)I morphological analysisI NP extraction (88% precision)

I Special handling of math symbols, abbreviations, andmath expressions as parts of NPs

I Currently supports only Russian language

§the metrics were evaluated on real math texts with the help ofdomain experts

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Mining the Logical StructureI Supports our ontology of structural elements:

elements in real texts are instances of the ontology classesI Recognizing types of structural elements:

I A string similarity based method gives 89%-100%F-measure depending on the class

I Recognizing semantic relations between them:I A decision tree learner gives 61%-95% F-measure

depending on the relation

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Mathematical Named Entity Extraction

I Supports our ontology of mathematical concepts:assigned NPs are instances of the ontology classes

I Our method employs annotations of the NP structureand Jaccard similarity

I The method gives 86% F-measure with parametersfocusing on precision/recall trade-off

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Connecting Named Entities to Formulas

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Connecting Named Entities to FormulasI Parsing mathematical expressionsI Detection of variablesI Proximity-based matching of mathematical variableswith noun phrases at 68% accuracy

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Other supported features

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Other supported features

I Article metadata extraction (title, author names,publication year etc.) according to AKT Portalschema

I Semi-manual interlinking¶ with existing LOD datasets: DBpedia, CORDIS

I Publishing the extracted data as an LOD-compliantRDF data set

¶by leveraging the Silk app23 / 29

Outline

1 Introduction

2 Approach

3 Use Cases

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Finding DBpedia Entities in Mathematical Formulashttp://cll.niimm.ksu.ru/iswc-demo

1

2

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Semantic Search of Theoretical FindingsFinding articles with theorems about finite groups

PREFIX moc: <http://cll.niimm.ksu.ru/ontologies/mocassin#>PREFIX math: <http://cll.niimm.ksu.ru/ontologies/mathematics#>SELECT ?article WHERE {?article moc:hasSegment ?theorem .?theorem moc:mentions ?entity; a moc:Theorem .?entity a math:E2183}

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Conclusion

I We have developed a holistic approach for miningLOD representation of scholarly papers inmathematics

I We applied the prototype to a collection of over1 300 real math papers

I We conducted a thorough evaluation of the proposedmethods with the help of domain experts

I We provided several use cases to illustrate the utilityof the published data

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Future Work

I Integrating all the modules into a full-fledged toolkitI Add support of English to the NLP moduleI Extend our approach to texts on other naturalscience domains

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Thanks for your attention!Questions?

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