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- 1. Learning Commonalities in SPARQL Sara El Hassad François Goasdoué Hélène Jaudoin IRISA, Univ. Rennes 1, Lannion, France ISWC 2017 - 21 - 26 October 2017 1/31
- 2. 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 2/31
- 3. 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 Query optimization: identify candidate views, or potiential query sharing Query approximation: a set of queries by a single query Social context: recommending users asking for enough relates things 2/31
- 4. 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 Query optimization: identify candidate views, or potiential query sharing Query approximation: a set of queries by a single query Social context: recommending users asking for enough relates things Goal To study the problem in the entire conjunctive fragment of SPARQL setting. 2/31
- 5. Outline Introduction Preliminaries Finding commonalities between SPARQL conjunctive queries Experiments Related work Conclusion 3/31
- 6. 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" ConfPaper b1 hasTitle τ hasContactAuthor 4/31
- 7. 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" ConfPaper hasContactAuthor b1 Publication hasAuthor Researcher hasTitle τ sc sp →r←d hasContactAuthor 5/31
- 8. Deriving the implicit triples b "LGG in RDF" ConfPaper hasContactAuthor b1 Publication hasAuthor Researcher hasTitle τ sc sp →r←d hasContactAuthorτ hasAuthor τ→r←d Figure: RDF graph G How to derive implicit triples of an RDF graph ? 6/31
- 9. Sample set of entailment rules Rule [W3C-RDFS, 2014] Entailment rule rdfs2 (p, ←d , o), (s1, p, o1) → (s1, τ, o) rdfs3 (p, →r , o), (s1, p, o1) → (o1, τ, o) rdfs5 (p1, sp, p2), (p2, sp, p3) → (p1, sp, p3) rdfs7 (p1, sp, p2), (s, p1, o) → (s, p2, o) rdfs9 (s, sc, o), (s1, τ, s) → (s1, τ, o) rdfs11 (s, sc, o), (o, sc, o1) → (s, sc, o1) ext1 (p, ←d , o), (o, sc, o1) → (p, ←d , o1) ext2 (p, →r , o), (o, sc, o1) → (p, →r , o1) ext3 (p, sp, p1), (p1, ←d , o) → (p, ←d , o) ext4 (p, sp, p1), (p1, →r , o) → (p, →r , o) Table: Sample RDF entailment rules R 7/31
- 10. Semantics of RDF graphs b "LGG in RDF" ConfPaper hasContactAuthor b1 Publication hasAuthor Researcher hasTitle τ sc sp →r←d hasContactAuthorτ hasAuthor τ→r←d Figure: Saturated RDF graph G∞ 8/31
- 11. Basic graph pattern queries (BGPQ) BGPQ : conjunctive fragment of SPARQL queries, is the counterpart of the select-project-join queries for databases (s, p, o) ∈ (V ∪ U) × (V ∪ U) × (V ∪ U ∪ L) 9/31
- 12. Basic graph pattern queries (BGPQ) BGPQ : conjunctive fragment of SPARQL queries, is the counterpart of the select-project-join queries for databases (s, p, o) ∈ (V ∪ U) × (V ∪ U) × (V ∪ U ∪ L) x1 ConfPaper y1 τ hasContactAuthor body(q1) Figure: Sample BGPQ q1(x1) 9/31
- 13. Entailing and answering queries Query entailment G |=R q ⇐⇒ G∞ |=R q x1 x2 τ b "LGG in RDF" ConfPaper hasContactAuthor b1 Publication hasAuthor G∞q(x1, x2) Researcher hasTitle τ sc sp →r←d hasContactAuthorτ hasAuthor τ→r←d
- 14. Entailing and answering queries Query entailment G |=R q ⇐⇒ G∞ |=R q x1 x2 τ b "LGG in RDF" ConfPaper hasContactAuthor b1 Publication hasAuthor G∞q(x1, x2) Researcher hasTitle τ sc sp →r←d hasContactAuthorτ hasAuthor τ→r←d b Publication τ 10/31
- 15. Entailing and answering queries Query answering x1 x2 τ b "LGG in RDF" ConfPaper hasContactAuthor b1 Publication hasAuthor G∞q(x1, x2) Researcher hasTitle τ sc sp →r←d hasContactAuthorτ hasAuthor τ→r←d
- 16. Entailing and answering queries Query answering x1 x2 τ b "LGG in RDF" ConfPaper hasContactAuthor b1 Publication hasAuthor G∞q(x1, x2) Researcher hasTitle τ sc sp →r←d hasContactAuthorτ hasAuthor τ→r←d b Publication τ ConfPaper τ Researcher τ b1 11/31
- 17. Entailing between BGPQs q |=R q ⇐⇒ q∞ |= q x1 Publication y1 τ hasAuthor SA z1 hasContactAuthor title x2 Publication y2 τ hasAuthor q∞ (x1) q (x2)
- 18. Entailing between BGPQs q |=R q ⇐⇒ q∞ |= q x1 Publication y1 τ hasAuthor SA z1 hasContactAuthor title x2 Publication y2 τ hasAuthor q∞ (x1) q (x2) x2 Publication y2 τ hasAuthor x1 Publication y1 τ hasAuthor 12/31
- 19. Outline Introduction Preliminaries Finding commonalities between SPARQL conjunctive queries Experiments Related work Conclusion 13/31
- 20. Towards defining lgg in SPARQL conjunctive fragment 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 our SPARQL setting descriptions are BGP Queries relation generalization/specialization is entailment between queries 14/31
- 21. Defining the lgg of queries lgg of BGPQs Let q1, . . . , qn be BGPQs with the same arity and R a set of RDF entailment rules. A generalization of q1, . . . , qn is a BGPQ qg such that qi |=R qg for 1 ≤ i ≤ n. A least general generalization of q1, . . . , qn is a generalization qlgg of q1, . . . , qn such that for any other generalization qg of q1, . . . , qn: qlgg |=R qg . 15/31
- 22. Defining the lgg of queries lgg of BGPQs Let q1, . . . , qn be BGPQs with the same arity and R a set of RDF entailment rules. A generalization of q1, . . . , qn is a BGPQ qg such that qi |=R qg for 1 ≤ i ≤ n. A least general generalization of q1, . . . , qn is a generalization qlgg of q1, . . . , qn such that for any other generalization qg of q1, . . . , qn: qlgg |=R qg . x1 ConfPaper y1 τ hasContactAuthor x2 JourPaper y2 τ hasAuthor bx1x2 bCPJP τ q1(x1) q2(x2) qlgg (bx1x2 )
- 23. Defining the lgg of queries lgg of BGPQs Let q1, . . . , qn be BGPQs with the same arity and R a set of RDF entailment rules. A generalization of q1, . . . , qn is a BGPQ qg such that qi |=R qg for 1 ≤ i ≤ n. A least general generalization of q1, . . . , qn is a generalization qlgg of q1, . . . , qn such that for any other generalization qg of q1, . . . , qn: qlgg |=R qg . x1 ConfPaper y1 τ hasContactAuthor x2 JourPaper y2 τ hasAuthor bx1x2 bCPJP τ bx1x2 Publication by1y2 Researcher τ hasAuthor τ q1(x1) q2(x2) qlgg (bx1x2 ) qlggO(bx1x2 ) 15/31
- 24. Entailment relation between BGPQs w.r.t. background knowledge Entailment between BGPQs w.r.t. R, O Given a set R of RDF entailment rules, a set O of RDFS statements, and two BGPQs q1 and q2 with the same arity, q1 entails q2 w.r.t. O, denoted q1 |=R,O q2, iff q1 ∞ O |= q2 holds. Well-founded relation : q1 |=R,O q2 Query entailment: if G |=R q1 holds then G |=R q2 holds, Query answering: q1(G) ⊆ q2(G) holds. 16/31
- 25. Saturation of queries BGPQ saturation w.r.t. RDFS constraints Publication hasAuthor Researcher ConfPaper JourPaper hasContactAuthor ←d →r sp←d →r scsc O x1 ConfPaper y1 Researcher Publication τ τ hasContactAuthor τ hasAuthor x2 JourPaper y2 Researcher Publication τ τ hasAuthor τ (body(q) ∪ O)∞ q1 ∞ O (x1) q2 ∞ O (x2) 17/31
- 26. Defining the lgg of queries w.r.t. background knowledge Definition (lgg of BGPQs w.r.t. RDFS constraints) Let R be a set of RDF entailment rules, O a set of RDFS statements, and q1, . . . , qn n BGPQs with the same arity. A generalization of q1, . . . , qn w.r.t. O is a BGPQ qg such that qi |=R,Oqg for 1 ≤ i ≤ n. A least general generalization of q1, . . . , qn w.r.t. O is a generalization qlgg of q1, . . . , qn w.r.t. O such that for any other generalization qg of q1, . . . , qn w.r.t. O: qlgg|=R,Oqg . Theorem An lgg of BGPQs w.r.t. RDFS statements may not exist for some set of RDF entailment rules; when it exists, it is unique up to entailment (|=R,O). 18/31
- 27. Defining the lgg of queries w.r.t. background knowledge Definition (lgg of BGPQs w.r.t. RDFS constraints) Let R be a set of RDF entailment rules, O a set of RDFS statements, and q1, . . . , qn n BGPQs with the same arity. A generalization of q1, . . . , qn w.r.t. O is a BGPQ qg such that qi |=R,Oqg for 1 ≤ i ≤ n. A least general generalization of q1, . . . , qn w.r.t. O is a generalization qlgg of q1, . . . , qn w.r.t. O such that for any other generalization qg of q1, . . . , qn w.r.t. O: qlgg|=R,Oqg . Result : lgg of n BGPQ queries vs lgg of two BGPQ queries 3(q1, q2, q3) ≡R,O 2( 2(q1, q2), q3) · · · · · · n(q1, . . . , qn) ≡R,O 2( n−1(q1, . . . , qn−1), qn) ≡R,O 2( 2(· · · 2( 2(q1, q2), q3) · · · , qn−1), qn) 19/31
- 28. Defining the lgg of queries w.r.t. background knowledge Definition (lgg of BGPQs w.r.t. RDFS constraints) Let R be a set of RDF entailment rules, O a set of RDFS statements, and q1, . . . , qn n BGPQs with the same arity. A generalization of q1, . . . , qn w.r.t. O is a BGPQ qg such that qi |=R,Oqg for 1 ≤ i ≤ n. A least general generalization of q1, . . . , qn w.r.t. O is a generalization qlgg of q1, . . . , qn w.r.t. O such that for any other generalization qg of q1, . . . , qn w.r.t. O: qlgg|=R,Oqg . Result : lgg of n BGPQ queries vs lgg of two BGPQ queries 3(q1, q2, q3) ≡R,O 2( 2(q1, q2), q3) · · · · · · n(q1, . . . , qn) ≡R,O 2( n−1(q1, . . . , qn−1), qn) ≡R,O 2( 2(· · · 2( 2(q1, q2), q3) · · · , qn−1), qn) We focus on computing lgg of two BGPQ queries 19/31
- 29. Defining the lgg of queries x1 ConfPaper y1 τ hasContactAuthor x2 JourPaper y2 τ hasAuthor Publication hasAuthor Researcher ConfPaper JourPaper hasContactAuthor ←d →r sp←d →r scsc q1(x1) q2(x2) O
- 30. Defining the lgg of queries x1 ConfPaper y1 τ hasContactAuthor x2 JourPaper y2 τ hasAuthor Publication hasAuthor Researcher ConfPaper JourPaper hasContactAuthor ←d →r sp←d →r scsc q1(x1) q2(x2) O bx1x2 Publication by1y2 Researcher τ hasAuthor τ qlggO 20/31
- 31. Defining the lgg of queries x1 ConfPaper y1 τ hasContactAuthor x2 JourPaper y2 τ hasAuthor Publication hasAuthor Researcher ConfPaper JourPaper hasContactAuthor ←d →r sp←d →r scsc q1(x1) q2(x2) O bx1x2 Publication by1y2 Researcher τ hasAuthor τ qlggO How to compute this query ? 20/31
- 32. The cover of SPARQL queries Definition (Cover query) Let q1, q2 be two BGPQs with the same arity n. If there exists the BGPQ q such that head(q1) = q(x1 1 , . . . , xn 1 ) and head(q2) = q(x1 2 , . . . , xn 2 ) iff head(q) = q(vx1 1 x1 2 , . . . , vxn 1 xn 2 ) (t1, t2, t3) ∈ body(q1) and (t4, t5, t6) ∈ body(q2) iff (t7, t8, t9) ∈ body(q) with, for 1 ≤ i ≤ 3, ti+6 = ti if ti = ti+3 and ti ∈ U ∪ L, otherwise ti+6 is the variable vti ti+3 then q is the cover query of q1, q2. 21/31
- 33. The cover of SPARQL queries x1 ConfPaper y1 Researcher Publication τ τ hasContactAuthor τ hasAuthor x2 JourPaper y2 Researcher Publication τ τ hasAuthor τ q1 ∞ O (x1) q2 ∞ O (x2) vx1x2 vPJP vy1PvPy2 vy1JP vy1y2 vCPy2 vCPPvCPJP Researcher Publication vx1y2 vy1R vPRvCPR vy1x2 vRy2vRJP vRP τ vτhA τ τ τ vτhA vhCAτ vhAτ vhAτ vhCAτ τ vhCAhA hasAuthor τ τvτhA τ τ vhCAτ vhAτ q(Vx1x2) 22/31
- 34. The cover of SPARQL queries x1 ConfPaper y1 Researcher Publication τ τ hasContactAuthor τ hasAuthor x1 ConfPaper τ x2 JourPaper y2 Researcher Publication τ τ hasAuthor τ x2 JourPaper τ q1 ∞ O (x1) q2 ∞ O (x2) vx1x2 vPJP vy1PvPy2 vy1JP vy1y2 vCPy2 vCPPvCPJP Researcher Publication vx1y2 vy1R vPRvCPR vy1x2 vRy2vRJP vRP τ vτhA ττ τ τ vτhA vhCAτ vhAτ vhAτ vhCAτ τ vhCAhA hasAuthor τ τvτhA τ τ vhCAτ vhAτ q(Vx1x2) 22/31
- 35. The cover of SPARQL queries x1 ConfPaper y1 Researcher Publication τ τ hasContactAuthor τ hasAuthor x1 ConfPaper τ Publication τ x2 JourPaper y2 Researcher Publication τ τ hasAuthor τ x2 JourPaper τ Publication τ q1 ∞ O (x1) q2 ∞ O (x2) vx1x2 vPJP vy1PvPy2 vy1JP vy1y2 vCPy2 vCPPvCPJP Researcher PublicationPublication vx1y2 vy1R vPRvCPR vy1x2 vRy2vRJP vRP τ vτhA ττ τ ττ vτhA vhCAτ vhAτ vhAτ vhCAτ τ vhCAhA hasAuthor τ τvτhA τ τ vhCAτ vhAτ q(Vx1x2) 22/31
- 36. The cover of SPARQL queries x1 ConfPaper y1 Researcher Publication τ τ hasContactAuthor τ hasAuthor x1 Publication τ x2 JourPaper y2 Researcher Publication τ τ hasAuthor τ x2 Publication τ q1 ∞ O (x1) q2 ∞ O (x2) vx1x2 vPJP vy1PvPy2 vy1JP vy1y2 vCPy2 vCPPvCPJP Researcher Publication vx1y2 vy1R vPRvCPR vy1x2 vRy2vRJP vRP τ vτhA τ τ τ vτhA vhCAτ vhAτ vhAτ vhCAτ τ vhCAhA hasAuthor τ τvτhA τ τ vhCAτ vhAτ q(Vx1x2) 22/31
- 37. Cover graph vs lgg Theorem Given a set R of RDF entailment rules, a set O of RDFS statements and two BGPQs q1, q2 with the same arity, 1. the cover query q of q1 ∞ O , q2 ∞ O exists iff an lgg of q1, q2 w.r.t. O exists; 2. the cover query q of q1 ∞ O , q2 ∞ O is an lgg of q1, q2 w.r.t. O. Corollary A cover query-based lgg of two BGPQs q1 and q2 is computed in O(|body(q1 ∞ O )| × |body(q2 ∞ O )|) and its size is |body(q1 ∞ O )| × |body(q2 ∞ O )|. 23/31
- 38. Outline Introduction Preliminaries Finding commonalities between SPARQL conjunctive queries Experiments Related work Conclusion 24/31
- 39. lgg of DBPedia queries q ODBpedia lgg |= qlgg lgg of: Q1Q2 Q1Q3 Q1Q4 Q2Q3 Q4Q5 Q5Q6 Q5Q7 Q7Q8 Time to compute qlgg 3 3 5 4 4 5 6 5 |qlgg(GDBpedia)| 477,455 34,747,102 34,901,117 34,747,102 1,977 1,221 35 70 Time to compute q ODBpedia lgg 13 14 14 15 15 14 17 18 |q ODBpedia lgg (GDBpedia)| 10,637 7,874,768 456,690 4,537,824 1,701 780 34 36 Gain in precision 97.77 77.33 98.69 86.94 13.96 36.11 2.85 48.57 Table: Characteristics of cover query-based lggs of test queries, w/ or w/o using the DBpedia RDFS constraints. lgg3 of : Q1Q2Q3 Q1Q2Q4 Q1Q3Q4 Q2Q3Q4 Q4Q7Q8 Q5Q7Q8 Q6Q7Q8 Time to compute qlgg 5 4 5 6 10 11 12 |qlgg(GDBpedia)| 34,747,102 34,901,117 34,901,117 34,901,117 70 1,977 4,969 Time to compute q ODBpedia lgg 19 20 20 24 27 27 33 |q ODBpedia lgg (GDBpedia)| 7,874,768 615,339 7,874,779 4,537,824 36 1,701 335 Gain in precision 77.33 98.23 77.43 86.99 48.57 13.96 93.25 Table: Characteristics of cover query-based lggs of 3 test queries, w/ or w/o using the DBpedia RDFS constraints; times are in ms. 25/31
- 40. Outline Introduction Preliminaries Finding commonalities between SPARQL conjunctive queries Experiments Related work Conclusion 26/31
- 41. Related work Structural approaches RDF Rooted graphs, ignore RDF entailment : - [Colucci et al., 2016]. SPARQL : tree queries - [Lehmann and Bühmann, 2011]. Description Logics - [Zarrieß and Turhan, 2013]. - [Baader et al., 1999]. Approaches independent of the structure RDF - [Hassad et al., 2017]. - [Petrova et al., 2017]. Conceptual Graphs - [Chein and Mugnier, 2009]. First Order Clauses - [Nienhuys-Cheng and de Wolf, 1996]. - [Plotkin, 1970]. 27/31
- 42. Conclusion We revisited the problem of computing a least general generalization of general BGPQs w.r.t. background knowledge. We defined new entailment relationship between BGPQs w.r.t. background knowledge. We studied the added-value of considering background knowledge when learning lggs. Perspective: Heuristics in order to compute lgg without redundants triples. 28/31
- 44. References I [Baader et al., 1999] Baader, F., Kiisters, R., and Molitor, R. (1999). Computing least common subsumers in description logics with existential restrictions. In IJCAI. [Chein and Mugnier, 2009] Chein, M. and Mugnier, M. (2009). Graph-based Knowledge Representation - Computational Foundations of Conceptual Graphs. Springer. [Colucci et al., 2016] Colucci, S., Donini, F., Giannini, S., and Sciascio, E. D. (2016). Defining and computing least common subsumers in RDF. J. Web Semantics, 39(0). [Hassad et al., 2017] Hassad, S. E., Goasdoué, F., and Jaudoin, H. (2017). Learning commonalities in RDF. In The 14th Extended Semantic Web Conference, ESWC 2017, Portorož, Slovenia, May 28 - June 1, 2017, Proceedings, Part I, pages 502–517. [Lehmann and Bühmann, 2011] Lehmann, J. and Bühmann, L. (2011). Autosparql: Let users query your knowledge base. In ESWC. [Nienhuys-Cheng and de Wolf, 1996] Nienhuys-Cheng, S. and de Wolf, R. (1996). Least generalizations and greatest specializations of sets of clauses. J. Artif. Intell. Res. [Petrova et al., 2017] Petrova, A., Sherkhonov, E., Grau, B. C., and Horrocks, I. (2017). Entity comparison in RDF graphs. In International Semantic Web Conference (ISWC). Springer. [Plotkin, 1970] Plotkin, G. D. (1970). A note on inductive generalization. Machine Intelligence, 5. [W3C-RDFS, 2014] W3C-RDFS (2014). RDF 1.1 semantics. https://www.w3.org/TR/rdf11-mt/. 30/31
- 45. References II [Zarrieß and Turhan, 2013] Zarrieß, B. and Turhan, A. (2013). Most specific generalizations w.r.t. general EL-TBoxes. In IJCAI. 31/31