The document discusses finding commonalities between RDF graphs by computing their least general generalization (lgg). It defines the lgg of RDF graphs as a generalization that entails all input graphs based on RDF entailment rules, and is entailed by any other generalization. The document focuses on computing the lgg of two RDF graphs, which can be used to iteratively find the lgg of multiple graphs. An example is provided to illustrate defining the lgg of two sample RDF graphs.
1. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Learning Commonalities in RDF
Sara El Hassad François Goasdoué Hélène Jaudoin
IRISA, Univ. Rennes 1, Lannion, France
ESWC 2017 28th May - 1st June 2017
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2. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Introduction
Least general generalization (lgg)
• Machine Learning in the early 70’s by Gordon Plotkin
• Knowledge representation domain in the early 90’s
• Recently in semantic web
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3. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Introduction
Least general generalization (lgg)
• Machine Learning in the early 70’s by Gordon Plotkin
• Knowledge representation domain in the early 90’s
• Recently in semantic web
Applications of lgg
• Social context : lgg of users descriptions (profiles)
• Research common graph patterns between of datasets
• Linked Data Cloud : links between datasets
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4. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Introduction
Least general generalization (lgg)
• Machine Learning in the early 70’s by Gordon Plotkin
• Knowledge representation domain in the early 90’s
• Recently in semantic web
Applications of lgg
• Social context : lgg of users descriptions (profiles)
• Research common graph patterns between of datasets
• Linked Data Cloud : links between datasets
Goal
To study the problem in the setting of the entire RDF standard
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5. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Outline
Introduction
The Resource Description Framework
Finding commonalities between RDF graphs
Related work
Conclusion
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6. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
RDF graphs
• Specification of RDF graphs with triples :
(s, p, o) ∈ (U ∪ B) × U × (U ∪ L ∪ B) s op
• Built-in property URIs to state RDF statements
RDF statement Triple
Class assertion (s, rdf:type, o)
Property assertion (s, p, o) with
p = rdf:type
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7. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
RDF graphs
• Specification of RDF graphs with triples :
(s, p, o) ∈ (U ∪ B) × U × (U ∪ L ∪ B) s op
• Built-in property URIs to state RDF statements
RDF statement Triple
Class assertion (s, rdf:type, o)
Property assertion (s, p, o) with
p = rdf:type
b "LGG in RDF"
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8. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Adding ontological knowledge to RDF graphs
• Built-in property URIs to state RDF Schema statements, i.e.,
ontological constraints.
RDFS statement Triple
Subclass (s, sc, o)
Subproperty (s, sp, o)
Domain typing (s, ←d , o)
Range typing (s, →r , o)
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9. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Adding ontological knowledge to RDF graphs
• Built-in property URIs to state RDF Schema statements, i.e.,
ontological constraints.
RDFS statement Triple
Subclass (s, sc, o)
Subproperty (s, sp, o)
Domain typing (s, ←d , o)
Range typing (s, →r , o)
b "LGG in RDF"
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10. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Deriving the implicit triples
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Figure: RDF graph G
11. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Deriving the implicit triples
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Figure: RDF graph G
12. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Deriving the implicit triples
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Figure: RDF graph G
13. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Deriving the implicit triples
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Figure: RDF graph G
14. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Deriving the implicit triples
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Figure: RDF graph G
15. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Deriving the implicit triples
b "LGG in RDF"
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Figure: RDF graph G
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16. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Deriving the implicit triples
b "LGG in RDF"
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Figure: RDF graph G
How to derive implicit triples of an RDF graph ?
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18. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Semantics of RDF graphs
b "LGG in RDF"
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Figure: RDF graph G
19. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Semantics of RDF graphs
b "LGG in RDF"
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rdfs9 : (s, sc, o), (s1, τ, s) → (s1, τ, o)
Figure: RDF graph G
20. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Semantics of RDF graphs
b "LGG in RDF"
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rdfs7 : (p1, sp, p2), (s, p1, o) → (s, p2, o)
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Figure: RDF graph G
21. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Semantics of RDF graphs
b "LGG in RDF"
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rdfs3 : (p, →r , o), (s1, p, o1) → (o1, τ, o)
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Figure: RDF graph G
22. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Semantics of RDF graphs
b "LGG in RDF"
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ext4 : (p, sp, p1), (p1, →r , o) → (p, →r , o)
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Figure: RDF graph G
23. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Semantics of RDF graphs
b "LGG in RDF"
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ext3 : (p, sp, p1), (p1, ←d , o) → (p, ←d , o)
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Figure: RDF graph G
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24. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Semantics of RDF graphs
b "LGG in RDF"
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Figure: Saturated RDF graph G∞
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25. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Entailment between RDF graphs
Let G and G be two graphs RDF and R a set of RDF entailment rules.
There exists relationship to compare G and G called entailment between
graphs
G is more specific than G :
• G |=R G ⇐⇒ G∞
|= G
There must exist an embedding of G in G∞
.
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26. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Entailment between RDF graphs
G
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27. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Entailment between RDF graphs
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28. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Entailment between RDF graphs
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RDF graph G is more specific than RDF graph G
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29. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Outline
Introduction
The Resource Description Framework
Finding commonalities between RDF graphs
Related work
Conclusion
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30. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Towards defining lgg in RDF
A least general generalization (lgg) of n descriptions d1, . . . , dn is a most
specific description d generalizing every d1≤i≤n for some
generalization/specialization relation between descriptions (G.Plotkin).
lgg in RDF
• descriptions are RDF graphs
• relation generalization/specialization is entailment between RDF
graphs
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31. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Defining the lgg of RDF graphs
Definition (lgg of RDF graphs)
Let G1, . . . , Gn be RDF graphs and R a set of RDF entailment rules.
• A generalization of G1, . . . , Gn is an RDF graph Gg such that
Gi |=R Gg holds for 1 ≤ i ≤ n.
• A least general generalization (lgg) of G1, . . . , Gn is a generalization
Glgg of G1, . . . , Gn such that for any other generalization Gg of
G1, . . . , Gn, Glgg |=R Gg holds.
Result : lgg of n RDF graphs vs lgg of two RDF graphs
3(G1, G2, G3) ≡R 2( 2(G1, G2), G3)
· · · · · ·
n(G1, . . . , Gn) ≡R 2( n−1(G1, . . . , Gn−1), Gn)
≡R 2( 2(· · · 2( 2(G1, G2), G3) · · · , Gn−1), Gn)
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32. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Defining the lgg of RDF graphs
Definition (lgg of RDF graphs)
Let G1, . . . , Gn be RDF graphs and R a set of RDF entailment rules.
• A generalization of G1, . . . , Gn is an RDF graph Gg such that
Gi |=R Gg holds for 1 ≤ i ≤ n.
• A least general generalization (lgg) of G1, . . . , Gn is a generalization
Glgg of G1, . . . , Gn such that for any other generalization Gg of
G1, . . . , Gn, Glgg |=R Gg holds.
Result : lgg of n RDF graphs vs lgg of two RDF graphs
3(G1, G2, G3) ≡R 2( 2(G1, G2), G3)
· · · · · ·
n(G1, . . . , Gn) ≡R 2( n−1(G1, . . . , Gn−1), Gn)
≡R 2( 2(· · · 2( 2(G1, G2), G3) · · · , Gn−1), Gn)
We focus on computing lgg of two RDF graphs
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33. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Defining the lgg of RDF graphs
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34. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Defining the lgg of RDF graphs
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35. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Defining the lgg of RDF graphs
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36. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
The cover graph of RDF graphs
Definition (Cover graph)
The cover graph G of two RDF graph G1 and G2 is the RDF graph such
that for every property p in both G1 and G2 :
(t1, p, t2) ∈ G1 and (t3, p, t4) ∈ G2 iff (t5, p, t6) ∈ G
with t5 = t1 if t1 = t3 and t1 ∈ U ∪ L, else t5 is the blank node bt1t3
, and,
similarly t6 = t2 if t2 = t4 and t2 ∈ U ∪ L, else t6 is the blank node bt2t4
.
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37. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
The cover graph of RDF graphs
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38. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
The cover graph of RDF graphs
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39. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
The cover graph of RDF graphs
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40. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
The cover graph of RDF graphs
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41. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
The cover graph of RDF graphs
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42. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
The cover graph of RDF graphs
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43. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Cover graph vs lgg
Theorem (R = ∅)
The cover graph G of the RDF graphs G1 and G2 is an lgg of them for
the empty set R of RDF entailment rules (i.e., R = ∅).
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44. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Cover graph vs lgg
Theorem (R = ∅)
The cover graph G of the RDF graphs G1 and G2 is an lgg of them for
the empty set R of RDF entailment rules (i.e., R = ∅).
Proposition (R = ∅)
The cover graph of two RDF graphs G1 and G2 can be computed in
O(|G1| × |G2|) ; its size is bounded by |G1| × |G2|.
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45. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Cover graph vs lgg
Theorem (R = ∅)
The cover graph G of the RDF graphs G1 and G2 is an lgg of them for
the empty set R of RDF entailment rules (i.e., R = ∅).
Proposition (R = ∅)
The cover graph of two RDF graphs G1 and G2 can be computed in
O(|G1| × |G2|) ; its size is bounded by |G1| × |G2|.
Theorem (R = ∅)
Let G1 and G2 be two RDF graphs, and R a set of RDF entailment rules.
The cover graph G of G∞
1 and G∞
2 is an lgg of G1 and G2.
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46. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Cover graph vs lgg
Theorem (R = ∅)
The cover graph G of the RDF graphs G1 and G2 is an lgg of them for
the empty set R of RDF entailment rules (i.e., R = ∅).
Proposition (R = ∅)
The cover graph of two RDF graphs G1 and G2 can be computed in
O(|G1| × |G2|) ; its size is bounded by |G1| × |G2|.
Theorem (R = ∅)
Let G1 and G2 be two RDF graphs, and R a set of RDF entailment rules.
The cover graph G of G∞
1 and G∞
2 is an lgg of G1 and G2.
Corollary (R = ∅)
An lgg of two RDF graphs G1 and G2 can be computed in
O(|G∞
1 | × |G∞
2 |) and its size is bounded by |G∞
1 | × |G∞
2 |.
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47. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Cover graph vs lgg
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48. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Outline
Introduction
The Resource Description Framework
Finding commonalities between RDF graphs
Related work
Conclusion
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49. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Related work
Structural based approach
• Description Logics EL
- F. Baader and al. :Computing least common subsumers in
description logics with existential restrictions.In IJCAI, 1999.
- B. ZarrieB and al. :Most specific generalizations w.r.t. general
EL-TBoxes.In IJCAI, 2013.
• RDF
• SPARQL : tree queries
- J. Lehmann and L. Buhmann. Autosparql : Let users query your
knowledge base. In ESWC, 2011.
• Rooted graphs, ignore RDF entailment :
- S. Colucci and al. :Defining and computing least common subsumers
in RDF.J. Web Semantics, 39(0), 2016.
Independent structure approach
• Conceptual Graphs
- M. Chein and M. Mugnier.Graph-based Knowledge Representation -
Computational Foundations of Conceptual Graphs.Springer, 2009.
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50. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Conclusion
• Revisit the problem of computing a least general generalization in
the entire setting of RDF.
• Algorithms to compute lggs of small-to-huge RDF graphs.
• Memory
• Data management system
• MapReduce
• Perspective : Heuristics in order to compute lgg without redundants
triples.
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51. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
Thank you !
Questions ?
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52. Introduction The Resource Description Framework Finding commonalities between RDF graphs Related work Conclusion
References I
[1] F. Baader, R. Kiisters, and R. Molitor.
Computing least common subsumers in description logics with existential restrictions.
In IJCAI, 1999.
[2] F. Baader, B. Sertkaya, and A.-Y. Turhan.
Computing the least common subsumer w.r.t. a background terminology.
Journal of Applied Logic, 5(3), 2007.
[3] M. Chein and M. Mugnier.
Graph-based Knowledge Representation - Computational Foundations of Conceptual Graphs.
Springer, 2009.
[4] S. Colucci, F. Donini, S. Giannini, and E. D. Sciascio.
Defining and computing least common subsumers in RDF.
J. Web Semantics, 39(0), 2016.
[5] S. Colucci, F. M. Donini, and E. D. Sciascio.
Common subsumbers in RDF.
In AI*IA, 2013.
[6] J. Lehmann and L. Bühmann.
Autosparql : Let users query your knowledge base.
In ESWC, 2011.
[7] RDF 1.1 semantics.
https://www.w3.org/TR/rdf11-mt/.
[8] B. Zarrieß and A. Turhan.
Most specific generalizations w.r.t. general EL-TBoxes.
In IJCAI, 2013.
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