1. Institut für Informatik Betriebliche Informationssysteme Jens Lehmann, AKSW, Universität Leipzig1 Learning OWL Class Expressions Jens Lehmann AKSW Research Group

2. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Jens Lehmann, AKSW, Universität Leipzig2 Outline AKSW Research Group  People  Projects Learning OWL Class Expressions  The Learning Problem in OWL and Description Logics (DLs)  Foundations of Refinement Operators in DLs  A Learning Algorithm for OWL  Application Scenarios

3. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Jens Lehmann, AKSW, Universität Leipzig3 AKSW Group

4. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Jens Lehmann, AKSW, Universität Leipzig4 AKSW Group Head: Dr. Sören Auer PhD Students:  Thomas Riechert  Sebastian Dietzold  Jens Lehmann  Thorsten Berger  Axel C. Ngonga Ngomo  Michael Martin  Sebastian Hellmann  Jörg Unbehauen Semantic Web combined with other research disciplines Open source, open access, open knowledge http://aksw.org

5. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Jens Lehmann, AKSW, Universität Leipzig5 AKSW Projects - DBpedia Joint work with FU Berlin and OpenLink Extract RDF/OWL from Wikipedia, e.g. From Infoboxes, categories, Geo- Coordinates, Images,... 274 million triples, 213.000 persons, 328.000 places, 57.000 music albums, 36.000 films, 20.000 companies 2500 manual mappings for infobox attributes to DBpedia Ontology (175 classes, 384 object properties, 336 data properties) http://dbpedia.or g

6. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Jens Lehmann, AKSW, Universität Leipzig6 AKSW Projects - DL-Learner Framework for Supervised Machine Learning for OWL and Description Logics (explained later in this talk) Application Areas:  “Classical” Machine Learning, e.g. predicting Carcinogenesis  Ontology Engineering  recommendation/navigation Works on OWL Files and SPARQL Endpoints Supports different reasoner interfaces Accessible via command-line, GUI, web service http://dl-learner.org

7. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Jens Lehmann, AKSW, Universität Leipzig7 AKSW Projects - OntoWiki Agile, distributed knowledge engineering Not a Wiki with semantic extensions (Semantic MediaWiki, IkeWiki), but an ontology editor using Wiki Concepts:  Make it easy to correct mistakes (ant intelligence)  Activity can be watched and reviewed  Everything can be undone http://ontowiki.ne t

8. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Jens Lehmann, AKSW, Universität Leipzig8 AKSW Projects - Triplify DB to RDF mapping using user defined SQL queries Lightweight (500 lines of code) Makes DB content available as RDF, JSON, Linked Data http://triplify.org

9. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Jens Lehmann, AKSW, Universität Leipzig9 AKSW Projects - xOperator combines advantages of social network websites with instant messaging

10. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Jens Lehmann, AKSW, Universität Leipzig10 AKSW Projects - OpenResearch Supports scientific content types: events (conferences, workshops), journals, people, groups Based on Semantic MediaWiki http://openresearch.or g

11. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme http://vakantieland.nl RDF based Dutch tourism portal Displays information about points of interest: description, address, contact information, classification, geo coordinates,... AKSW Projects - Vakantieland

12. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Jens Lehmann, AKSW, Universität Leipzig12 AKSW Projects Cofundos (http://cofundos.org):http://cofundos.org  Platform for funding of open source software  People can post software ideas and bid money for their realization SoftWiki (http://softwiki.de):http://softwiki.de  Problem: Requirements Engineering with large, spatially distributed stakeholder groups  Solution: comprehensive ontology for representing RE relevant knowledge + adapted OntoWiki application

13. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Jens Lehmann, AKSW, Universität Leipzig13 The Learning Problem in OWL and Description Logics (DLs) Foundations of Refinement Operators in DLs A Learning Algorithm for OWL Application Scenarios Learning OWL Class Expressions

14. Institut für Informatik Betriebliche Informationssysteme Jens Lehmann, AKSW, Universität Leipzig14 Learning Problem Given:  Background Knowledge Base  Positive and negative examples (example = individual in ontology) Goal:  Find an OWL Class Expression / DL concept which °covers as many positive examples as possible °covers as few negative examples as possible Concept C covers example a = a is instance of C Analogous problem can be defined for logic programs => Inductive Logic Programming (ILP) Supervised Machine Learning Task

15. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Footer15 OWL 2 – Class Expressions {Germany, France} LivingPerson u : (Teenager t Adult) boolean connectors and nominals:

16. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Footer16 OWL 2 – Class Expressions foaf:Person u 9 foaf:image 9 birthPlace.{Leipzig} 8 hasPet.Dog quantifiers :

17. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Footer17 OWL 2 – Class Expressions Exam v · 2 examiner Exam v ¸ 3 topic cardinality restrictions:

18. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Lernen von OWL-Klassen - Vorstellung nach Fragenkatalog18 Learning Problem - Example train7 train6 train1 train2

19. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Footer19 Refinement Operators Downward refinement operators map a concept to more special concepts wrt. subsumption Upward refinement operators analogous More generally refinement operators can be used on any quasi ordered space (i.e. there is a reflexive and transitive order on its elements) owl:Thing Person and (takesPartIn some Meeting) CarPerson...

20. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Footer20 Refinement Operator Properties A refinement operator ρ is... ... finite iff ρ(C) is finite for any concept C ... redundant iff there exists a refinement chain from a concept C to a concept D, which does not go through a concept E, and another one which does go through E ... proper iff for any concepts C and D, D Є ρ(C) implies C and D are not equivalent C C1C1 CnCn... C D C D ´ C

21. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Footer21 Refinement Operator Properties A downward refinement operator ρ is... ... complete iff for all concepts C and D, D subsumed by C, we can reach a concept E equivalent to D from C by ρ ... weakly complete iff for all concepts D not equivalent to Τ we can reach a concept E equivalent to D from Τ by ρ ... ideal iff it is complete, finite, and proper. C E ´ D... > E ´ D...

22. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Footer22 Refinement Operator Properties Properties indicate how suitable a refinement operator is for solving the learning problem:  Incomplete operators may miss solutions  Redundant operators may lead to duplicate concepts in the search tree  Improper operators may produce equivalent concepts (which cover the same examples)  For infinite operators it may not be possible to compute all refinements of a given concept We researched properties of refinement operators in Description Logics Key question: Which properties can be combined?

23. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Footer23 Refinement Operator Properties DL RO Properties Theorem: Considering the analysed properties and the languages ALC, ALCN, SHOIN, SROIQ, the following are maximal sets of properties: 1. {weakly complete, complete, finite} 2. {weakly complete, complete, proper} 3. {weakly complete, non-redundant, finite} 4. {weakly complete, non-redundant, proper} 5. {non-redundant, finite, proper} DL RO Properties Theorem: Considering the analysed properties and the languages ALC, ALCN, SHOIN, SROIQ, the following are maximal sets of properties: 1. {weakly complete, complete, finite} 2. {weakly complete, complete, proper} 3. {weakly complete, non-redundant, finite} 4. {weakly complete, non-redundant, proper} 5. {non-redundant, finite, proper}

24. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Footer24 Refinement Operator Properties No ideal operators for many description languages Consequence: learning in OWL is a hard task New result (unpublished): ideal operators exist for the lightweight description logic EL Goal: try to define an operator close to the theoretical limitations

25. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Footer25 An Operator for OWL (excerpt of definition)

26. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Footer26 An Operator for OWL Examples :

27. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Footer27 Operator - Completeness Proof Idea for weak completeness:  Define set S of concepts  Proof that for each concept, there is an equivalent one in S.  Show that all concepts in S can be reached from Τ by ρ. Prove completeness using the weak completeness result. ρ is complete.

28. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Footer28 Operator - Finiteness Infinitely many refinements of this form Idea: consider only refinements up to length n (= finitely many) Start with n=0 and increase n as necessary during the run of the learning algorithm ρ is not finite.

29. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Footer29 Operator - Properness Idea: Define closure operator ρ cl over ρ, which applies ρ until all reached refinements are inequivalent Ρ cl is (obviously) proper It can be shown for ρ that the closure up to a given length n can be computed in finite time for any n ρ is not proper. Example :

30. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Footer30 Operator - Redundancy Redundancy should be checked by learning algorithm Result: we can check whether a refinement is redundant in polynomial time wrt. the search tree size ρ is redundant.

31. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Footer31 Learning Algorithm

32. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Footer32 Example Demo in DL-Learner GUI

33. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Footer33 Learning – Use Cases „Classical“ Machine Learning Tasks  Carcinogenesis Ontology Engineering  Learn axioms for existing classes  PlugIns for Protégé and OntoWiki Recommendation/Navigation  Recommending music based on last songs heard  Navigation suggestions in large knowledge bases, e.g. DBpedia

34. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Footer34 Carcinogenesis Goal: predict whether chemical compounds can cause cancer Rationale:  hazard of chemical substances in many industries  1000 new substances developed each year  Cancer risk can only be estimated by expensive long term research trials on rats and mice Background Knowledge Used:  Database of US National Toxicoloy Institute (NTP)  Converted from Prolog to OWL “Obtaining accurate structural alerts for the causes of chemical cancers is a problem of great scientific and humanitarian value.” (A. Srinivasan, R.D. King, S.H. Muggleton, M.J.E. Sternberg 1997)

35. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Footer35 Carcinogenesis Human experts: 70% acc., DL-Learner 3% less Often Better than related tools Background knowledge needs to be improved and more relevant chemical features extracted (e.g. LarKC project) Example of learned definition:

36. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Footer36 Ontology Engineering Protégé-PlugIn- Screencast

37. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Footer37 Navigation/Recommendation DBpedia Navigator Prototype

38. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Jens Lehmann, AKSW, Universität Leipzig38 Use Case DBpedia Navigator Difficult to browse or navigate within DBpedia, since both TBox and ABox are large Idea: use concept learning to generate navigation suggestions Positive Examples = last articles viewed by a user DBpedia Navigator SPARQL Endpoint DL-Learner OWL Reasoner AJAX-call to web service extract relevant knowledge using SPARQL Queries and convert to OWL OWL API/DIG reasoner interface Pythagoras Philolaus Archytas Socrates Zeno of Elea Democritus navigation suggestions: “Mathematician and (Physicist or Vegatarian)” “Philosopher born in Greece”

39. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Footer39 Thanks for your attention!

40. Learning OWL Class Expressions Institut für Informatik Betriebliche Informationssysteme Jens Lehmann, AKSW, Universität Leipzig40 State of the Art Some research based on DLs in early 90s already Rising interest with the introduction of the Semantic Web and OWL Research mainly at the universities of Bari, Liverpool, Leipzig approaches:  top-down: Nienhuys-Cheng, Badea, Lehmann  bottom-up: Cohen, Hirsh  other: Iannone, Palmisano, Fanizzi, Lehmann Implemented system: YinYang, DL-Learner (+ older prototypes)