The document discusses using RDFS and OWL reasoning to integrate heterogeneous linked data by addressing issues like terminology and naming heterogeneity. It presents an approach using a subset of OWL 2 RL rules to reason over a billion triple corpus in a scalable way, handling the TBox separately from the ABox to avoid quadratic inferences. It also describes augmenting the reasoning with annotations to track trustworthiness and using this to filter inferences, detect inconsistencies and perform a light repair of the data. Consolidation is discussed as rewriting URIs to canonical identifiers based on owl:sameAs relations. Performance results show the different techniques taking between 1-20 hours to run over the corpus distributed across 9 machines.

1. Exploiting RDFS and OWL for Integrating Heterogeneous, Large-Scale, Linked Data Corpora Aidan Hogan PhD Viva

2. Cold Open Figure 1: Web of Data explicit data implicit data Topic of thesis: How can consumers tap into the implicit data

3. PRELUDE The Area… The Problem… The Hypothesis…

4. The Area… … Linked Data / Linking Open Data

5. Bottom-up Approach to Semantic Web Individual Publishers should: Use URIs to name things (not just documents) Use HTTP URIs that can be looked up Return information in a common structured data model ( RDF ) Use external URIs in your data so as to link to related data … the micro … Linked Data Principles

6. … the macro … A Web of Data Images from: http://richard.cyganiak.de/2007/10/lod/ ; Cyganiak, Jentzsch September 2010 August 2007 November 2007 February 2008 March 2008 September 2008 March 2009 July 2009

7. … so what’s The Problem ? … … heterogeneity

8. Take Query Answering … SPARQL endpoints over Web data such as YARS2 , Virtuoso, FactForge, etc. Search engines such as SWSE , Sindice, Falcons, Swoogle, Watson, etc.

9. Take Query Answering … Gimme webpages relating to Tim Berners-Lee foaf:page timbl:i timbl:i foaf:page ?pages .

10. Hetereogenity in terminology … webpage: properties foaf:page foaf:homepage foaf:isPrimaryTopicOf foaf:weblog doap:homepage foaf:topic foaf:primaryTopic mo:musicBrainz mo:myspace … = rdfs:subPropertyOf = owl:inverseOf

11. Linked Data, RDFS and OWL: Linked Vocabularies … … Image from http://blog.dbtune.org/public/.081005_lod_constellation_m.jpg : ; Giasson, Bergman

12. Hetereogenity in naming … Tim Berners-Lee: URIs … timbl:i dblp:100007 identica:45563 adv:timbl fb:en.tim_berners-lee db:Tim-Berners_Lee = owl:sameAs

13. Returning to our Query … Gimme webpages relating to Tim Berners-Lee foaf:page timbl:i timbl:i foaf:page ?pages . ... 7 x 6 = 42 possible patterns foaf:homepage foaf:isPrimaryTopicOf doap:homepage foaf:topic foaf:primaryTopic mo:myspace dblp:100007 identica:45563 adv:timbl fb:en.tim_berners-lee db:Tim-Berners_Lee

14. … The Hypothesis ? … … we can use the OWL and RDFS inherent in Linked Data to attenuate the problem of heterogeneity for consumers

15. Scenario… … take a static corpus crawled from Linked Data… … about a billion triples or so… … and tackle the problem (s) of heterogeneity … ( without domain-specific “cheats” ).

16. Setup… hardware … 9 machines … ~6 years old… 4Gb RAM, 2.2GHz, Ethernet

17. Setup… corpus … crawl ( 9 machines: 52.5 hr ) … took random seed URIs from Billion Triple Challenge 2009 dataset … crawled ~4 million RDF/XML documents … from arbitrary domains (e.g., dbpedia.org) Only found 785 domains providing RDF/XML … 1.118 billion quadruples … 947 million unique triples

18. Setup… ranking ( 9 machines: 30.3 hr ) … applied PageRank over interlinked source docs. … source A links to source B if A uses a URI which “dereferences” (points) to B

19. Challenges… … what (OWL) reasoning is feasible for Linked Data?

20. Linked Data Reasoning: Challenges Scalable Expressive Robust Domain-Agnostic

21. CORE 1. Reasoning… 2. Annotated Reasoning… 3. Consolidation…

22. 1. Reasoning

23. High Level Approach… … apply a subset of OWL 2 RL/RDF rules over the data

24. Forward Chaining materialisation: Avoid runtime expense of backward-chaining Users taught impatience by Google Pre-compute answers for quick retrieval Web-scale systems should be scalable! More data = more disk-space/machines Web Reasoning: Forward Chaining! One size does not fit all! Don't materialise too much!

25. Scalable Authoritative OWL Reasoner Our Approach

26. Our Approach… INPUT: Flat file of triples (quads) OUTPUT: Flat file of (partial) inferred triples (quads)

27. Scalable Reasoning: In-mem T-Box Main optimisation: Store T-Box in memory T-Box: (loosely) data describing classes and properties. Aka. schemata/vocabularies/ontologies/terminologies. E.g., foaf:topic owl:inverseOf foaf:page . sioc:UserAccount rdfs:subClassOf foaf:OnlineAccount . Most commonly accessed data for reasoning Quite small (~0.1% for our Linked Data corpus) High selectivity (if you prefer) A-Box: Lots ?s foaf:page ?o . vs. T-Box: Few foaf:page ?p ?o . + ?s ?p foaf:page .

28. Scan 1: Scan input data separate T-Box statements, load T-Box statements into memory Do T-Box level reasoning if required (semi-naïve) Scan 2: Scan all on-disk data, join with in-memory T-Box. Scalable Reasoning: Two Scans

29. ... ex:me foaf:homepage ex:hp . ... ... ex:hp rdf:type foaf:Document . ex:me foaf:page ex:hp . ex:hp foaf:topic ex:me . ... IN-MEM T-BOX ON-DISK A-BOX ON-DISK OUTPUT Execution of three rules: OWL 2 RL rule prp-inv1 ?p 1 owl:inverseOf ?p 2 . ?x ?p 1 ?y . ⇒ ?y ?p 2 ?x . OWL 2 RL rule prp-rng ?p rdfs:range ?c . ?x ?p ?y . ⇒ ?y a ?c . OWL 2 RL rule prp-spo1 ?p 1 rdfs:subPropertyOf ?p 2 . ?x ?p 1 ?y. ⇒ ?x ?p 2 ?y . Scalable Reasoning: No A-Box Joins

30. However: some rules do require A-Box joins ?p a owl:TransitiveProperty . ?x ?p ?y . ?y ?p z . ⇒ ?x ?p ?z . Difficult to engineer a scalable solution (which reaches a fixpoint) for Linked Data(?) Can lead to quadratic inferences A lot of useful reasoning still possible without A-Box joins… Scalable Reasoning: A-Box joins?

31. Consider source of T-Box (schemata) data Class/property URIs dereference to their authoritative document FOAF spec authoritative for foaf:Person ✓ MY spec not authoritative for foaf:Person ✘ Allow “extension” in authoritative documents my:Person rdfs:subClassOf foaf:Person . (MY spec) ✓ BUT: Reduce obscure memberships foaf:Person rdfs:subClassOf my:Person . (MY spec) ✘ ALSO: Protect specifications foaf:knows a owl:SymmetricProperty . (MY spec) ✘ Authoritative Reasoning

32. Survey of terminology: counts Looked at use of RDFS and OWL in our corpus rdfs:subClassOf ~307k axioms ~51k docs ✓ owl:equivalentClass ~23k axioms ~23k docs ✓ rdfs:domain ~16k axioms 623 docs ✓ rdfs:range ~14k axioms 717 docs ✓ owl:unionOf ~13k axioms 109 docs ✓ rdfs:subPropertyOf ~9k axioms 227 docs ✓ owl:inverseOf ~1k axioms 98 docs ✓ owl:disjointWith 917 axioms 60 docs ✘ owl:someValuesFrom 465 axioms 48 docs ✓ owl:intersectionOf 325 axioms 12 docs ✓ / ✘ …

33. ...summary please? Our “cheap rules” cover 99% of RDFS/OWL axioms in our corpus 82.3% of such axioms have an authoritative version - 78.3% of all non-authoritative axioms come from one doc - (without which, ~96% of axioms have auth. version) 9.1% of documents have non-authoritative axioms Authoritative reasoning for cheap rules fully support 90.6% of the “vocabulary documents” Survey of terminology: counts

34. Survey of terminology: ranks Looked at use of RDFS and OWL wrt. ranks of documents… rdfs:subClassOf 0.295 ✓ rdfs:range 0.294 ✓ rdfs:domain 0.292 ✓ rdfs:subPropertyOf 0.090 ✓ owl:FunctionalProperty 0.063 ✘ owl:disjointWith 0.049 ✘ owl:inverseOf 0.047 ✓ owl:unionOf 0.035 ✓ owl:SymmetricProperty 0.033 ✓ owl:equivalentClass 0.021 ✓ owl:InverseFunctionalProperty 0.030 ✘ owl:equivalentProperty 0.030 ✓ owl:someValuesFrom 0.030 ✓ / ✘

35. ...summary please? Adding up the ranks of all vocabularies our rules fully support gives 77% of the total rank of all vocabularies Adding up the ranks of all vocabularies our authoritative rules fully support gives 70% of the total rank of all vocabularies The highest ranked document our rules do not fully support was 5 th overall: SKOS The highest ranked document with non-authoritative axioms was 7 th overall: FOAF Survey of terminology: ranks

36. ...let’s stick to the simple rules

37. Scalable Distributed Reasoning ... ... ex:me ex:presented ex:ThisTalk ... SAME T-BOX SAME T-BOX SAME T-BOX SAME T-BOX SAME T-BOX DIFF. A-BOX DIFF. A-BOX DIFF. A-BOX DIFF. A-BOX DIFF. A-BOX ... ... ex:me ex:presented ex:ThisTalk ... ... ... ex:me ex:presented ex:ThisTalk ... ... ... ex:me ex:presented ex:ThisTalk ... ... ... ex:me ex:presented ex:ThisTalk ... LOCAL OUTPUT ... ... ex:me ex:presented ex:ThisTalk ... LOCAL OUTPUT LOCAL OUTPUT LOCAL OUTPUT LOCAL OUTPUT ... ... ex:me ex:presented ex:ThisTal ... ... ex:me ex:presented ex:ThisTalk ... ... ex:me ex:presented ex:ThisTalk ... ... ex:me rdf:type ex:Awesome . ... ... ... ... ... ... ... ex:me ex:presented ex:ThisTalk ... ... ... ex:me ex:presented ex:ThisTalk ... ... ... ex:me ex:presented ex:ThisTalk ... ... ... ex:me ex:presented ex:ThisTalk ... ... ... ex:me ex:presented ex:ThisTalk ... EXTRACT T-BOX EXTRACT T-BOX EXTRACT T-BOX EXTRACT T-BOX EXTRACT T-BOX COLLECT T-BOX COLLECT T-BOX COLLECT T-BOX COLLECT T-BOX COLLECT T-BOX ... ...

38. Reasoning Performance (1 machine)

39. Reasoning Performance: Distrib. 9 machines: Total 3.35 hours

40. Reasoning: Results 962 million unique/novel triples 947 million unique triples

41. 2. Annotated Reasoning

42. Annotated Reasoning Let’s try track some meta-information during the reasoning process Annotate input triples with information Use annotated reasoning framework for transforming annotations on input triples into annotations on output triples

43. Each input triple is assigned the sum of the ranks of the documents in which it appears… foaf:Person rdfs:subClassOf foaf:Agent 0.3 . timbl:i rdf:type foaf:Person 0.04 . aidan:me rdf:type foaf:Person 0.0001 . Annotated Reasoning: ranks

44. During reasoning, inferences are assigned the least-trustworthy triple involved in their “proof” foaf:Person rdfs:subClassOf foaf:Agent 0.3 . timbl:i rdf:type foaf:Person 0.04 . ⇒ timbl:i rdf:type foaf:Agent 0.04 . Annotated Reasoning

45. Can do top- k materialisation Only give me inferences above a certain rank threshold Only give me top- k inferences Can fix inconsistencies in the data… … aka. logical contradictions … interpreting the rank values as denoting “trustworthy” data Why?

46. foaf:Person owl:disjointWith foaf:Document . Inconsistencies: aka. Contradictions

47. ?c 1 owl:disjointWith ?c 2 . ?x rdf:type ?c 1 . ?x rdf:type ?c 2 . ⇒ false foaf:Person owl:disjointWith foaf:Document . ex:sleepygirl rdf:type foaf:Person . ex:sleepygirl rdf:type foaf:Document . ⇒ false Cannot compute…

48. Considered two approaches: Find the “consistency threshold” of the input + inferred data: The largest rank such that all data above that rank are consistent Unfortunately, the 22 nd ranked document had an ill-typed literal, and so was inconsistent… So we would keep the data of ~22 documents And throw away the data of nearly four million Fixing inconsistencies

49. Time for Plan B: 2. Perform a “granular” repair of the data Remove the weakest triple causing each contradiction foaf:Person owl:disjointWith foaf:Document 0.3 . ex:sleepygirl rdf:type foaf:Person 0.007 . ex:sleepygirl rdf:type foaf:Document 0.002 . Fixing inconsistencies

50. ~294k ill-typed datatypes ~7k members of disjoint classes Inconsistencies found

51. Performance 9 machines Annotated Reasoning: 14.6 hrs (vs. 3.35hrs w/o annotations: need to do a distributed sort to remove non-optimal triples ) Detect/Extract Inconsistencies: 2.9 hrs Diagnosis/Repair 2.8 hrs Total ~20.3 hours

52. 3. Consolidation

53. Consolidation for Linked Data

54. Baseline Approach… … use the explicit owl:sameAs relations given in the data…

55. Scan the data and extract all owl:sameAs triples timbl:i owl:sameas identica:45563 . dbpedia:Berners-Lee owl:sameas identica:45563 . Load into memory Use a map to store equivalences: timbl:i -> identica:45563 -> dbpedia:Berners-Lee -> Consolidation: Baseline timbl:i identica:45563 dbpedia:Berners-Lee

56. For each set of equivalent identifiers, choose a canonical term Consolidation: Baseline timbl:i identica:45563 dbpedia:Berners-Lee

57. Scan data a second time: Rewrite identifiers to their canonical version Skip predicates and values of rdf:type Canonicalisation timbl:i rdf:type foaf:Person . identica:48404 foaf:knows identica:45563 . dbpedia:Berners-Lee dpo:birthDate “ 1955-06-08”^^xsd:date . dbpedia:Berners-Lee rdf:type foaf:Person . identica:48404 foaf:knows dbpedia:Berners-Lee . dbpedia:Berners-Lee dpo:birthDate “ 1955-06-08”^^xsd:date . timbl:i identica:45563 dbpedia:Berners-Lee

58. Baseline Consolidation: Performance 9 machines Extract owl:sameAs : 0.2 hr Gather owl:sameAs : 0.1 hr Canonicalise data 0.7 hr Total ~1.1 hours

59. Applied over raw input data ~12 million owl:sameAs triples ~2.2 million sets of equivalent identifiers ~5.8 million identifiers involved ~2.65 identifiers per set ~99.99% of terms were URIs ~6.25% of all URIs Baseline Consolidation: Results

60. Extended Approach… … use the owl:sameAs relations inferable through reasoning…

61. Infer owl:sameAs through reasoning (OWL 2 RL/RDF) explicit owl:sameAs (again) owl:InverseFunctionalProperty owl:FunctionalProperty owl:cardinality 1 / owl:maxCardinality 1 foaf:homepage a owl:InverseFunctionalProperty . timbl:i foaf:homepage w3c:timblhomepage . adv:timbl foaf:homepage w3c:timblhomepage . ⇒ timbl:i owl:sameas adv:timbl . … then apply consolidation as before Extended Consolidation

62. OWL 2 RL/RDF consolidation rules require A-Box joins! Might not be able to fit owl:sameAs index in memory ( 4 Gb ) ! ⇒ Use on-disk batch-processing Distributed sorts, scans and merge-joins Derive owl:sameAs on-disk

63. Extended Consolidation: Performance 9 machines Inferring owl:sameAs ~7.4 hr Canonicalise data ~4.9 hr Total ~12.3 hours (11X baseline)

64. ~12 million explicit owl:sameAs triples (as before) ~8.7 million thru. owl:InverseFunctionalProperty ~106 thousand thru. owl:FunctionalProperty none thru. owl:cardinality / owl:maxCardinality ~2.8 million sets of equivalent identifiers (1.31x baseline) ~14.86 million identifiers involved (2.58x baseline) ~5.8 million URIs (1.014x baseline) Extended Consolidation: Results

65. CONCLUSION

66. timbl:i foaf:page ?pages . timbl:i identica:45563 dbpedia:Berners-Lee dbpedia:Berners-Lee foaf:page ?pages .

67. Heterogeneity poses a significant problem for consuming Linked Data Lightweight reasoning can go a long way Simple/authoritative rules have reasonable coverage Deceit/Noise ≠ End Of World Inconsistency ≠ End Of World Useful for finding noise in fact! Explicit owl:sameAs vs. extended consolidation: Extended consolidation mostly for consolidating blank-nodes from older FOAF exporters Conclusions