RDF AND SPARQL. Part V: Semantics of SPARQL. Dresden, August Sebastian Rudolph ICCL Summer School

Transcription

1 RDF AND SPARQL Part V: Semantics of SPARQL Sebastian Rudolph ICCL Summer School Dresden, August 2013

2 Agenda 1 Recap 2 SPARQL Semantics 3 Transformation of Queries into Algebra Objects 4 Evaluation of the SPARQL Algebra 5 Operators for the Modifiers 6 Summary TU Dresden, August 2013 RDF and SPARQL slide 2 of 73

3 Agenda 1 Recap 2 SPARQL Semantics 3 Transformation of Queries into Algebra Objects 4 Evaluation of the SPARQL Algebra 5 Operators for the Modifiers 6 Summary TU Dresden, August 2013 RDF and SPARQL slide 3 of 73

4 Recap: Introduced SPARQL Features Basic Structure PREFIX WHERE Graph Patterns Basic Graph Patterns {... } OPTIONAL UNION Filter BOUND isuri isblank isliteral STR LANG DATATYPE sameterm langmatches REGEX Modifiers ORDER BY LIMIT OFFSET DISTINCT Output Formats SELECT CONSTRUCT ASK DESCRIBE TU Dresden, August 2013 RDF and SPARQL slide 4 of 73

5 Agenda 1 Recap 2 SPARQL Semantics 3 Transformation of Queries into Algebra Objects 4 Evaluation of the SPARQL Algebra 5 Operators for the Modifiers 6 Summary TU Dresden, August 2013 RDF and SPARQL slide 5 of 73

6 Semantics of Query Languages So far only informal presentation of SPARQL features User: Which answers can I expect for my query? Developer: Which behaviour is expected from my SPARQL implementation? Marketing: Is our product already conformant with the SPARQL standard? Formal semantics should clarify these questions... TU Dresden, August 2013 RDF and SPARQL slide 6 of 73

7 Semantics of Query Languages (1) Query Entailment Query as description of allowed results Data as set of logical assumptions (axiom set/theory) Results as logical entailment OWL DL and RDF(S) as query languages conjunctive queries TU Dresden, August 2013 RDF and SPARQL slide 7 of 73

8 Semantics of Query Languages (2) Query Algebra Query as instruction for computing the results Queried data as input Results as output Relational algebra for SQL SPARQL Algebra TU Dresden, August 2013 RDF and SPARQL slide 8 of 73

9 Agenda 1 Recap 2 SPARQL Semantics 3 Transformation of Queries into Algebra Objects 4 Evaluation of the SPARQL Algebra 5 Operators for the Modifiers 6 Summary TU Dresden, August 2013 RDF and SPARQL slide 9 of 73

10 Translation into SPARQL Algebra {?book ex:price?price. FILTER (?price < 15) OPTIONAL {?book ex:title?title } {?book ex:author ex:shakespeare } UNION {?book ex:author ex:marlowe } } Semantics of a SPARQL query: 1 Transformation of the query into an algebra expression 2 Evaluation of the algebra expression TU Dresden, August 2013 RDF and SPARQL slide 10 of 73

11 Translation into SPARQL Algebra {?book ex:price?price FILTER (?price < 15) OPTIONAL {?book ex:title?title } {?book ex:author ex:shakespeare } UNION {?book ex:author ex:marlowe } } Attention: Filters apply to the whole group in which they occur TU Dresden, August 2013 RDF and SPARQL slide 11 of 73

12 Translation into SPARQL Algebra {?book ex:price?price OPTIONAL {?book ex:title?title } {?book ex:author ex:shakespeare } UNION {?book ex:author ex:marlowe } FILTER (?price < 15) } 1 Expand abbreviated IRIs TU Dresden, August 2013 RDF and SPARQL slide 12 of 73

13 Translation into SPARQL Algebra {?book < OPTIONAL {?book < } {?book < < } UNION {?book < < } FILTER (?price < 15) } TU Dresden, August 2013 RDF and SPARQL slide 13 of 73

14 Translation into SPARQL Algebra {?book < OPTIONAL {?book < } {?book < < } UNION {?book < < } FILTER (?price < 15) } 2. Replace triple patterns with operator Bgp( ) TU Dresden, August 2013 RDF and SPARQL slide 14 of 73

15 Translation into SPARQL Algebra { Bgp(?book < OPTIONAL {Bgp(?book < {Bgp(?book < < UNION {Bgp(?book < < FILTER (?price < 15) } TU Dresden, August 2013 RDF and SPARQL slide 15 of 73

16 Translation into SPARQL Algebra { Bgp(?book < OPTIONAL {Bgp(?book < {Bgp(?book < < UNION {Bgp(?book < < FILTER (?price < 15) } 3. Introduce the LeftJoin( ) operator for optional parts TU Dresden, August 2013 RDF and SPARQL slide 16 of 73

17 Translation into SPARQL Algebra { LeftJoin(Bgp(?book < Bgp(?book < true) {Bgp(?book < < UNION {Bgp(?book < < FILTER (?price < 15) } TU Dresden, August 2013 RDF and SPARQL slide 17 of 73

18 Translation into SPARQL Algebra { LeftJoin(Bgp(?book < Bgp(?book < true) {Bgp(?book < < UNION {Bgp(?book < < FILTER (?price < 15) } 4. Combine alternative graph patterns with Union( ) operator Refers to neighbouring patterns and has higher precedence than conjunction (left associative) TU Dresden, August 2013 RDF and SPARQL slide 18 of 73

19 Translation into SPARQL Algebra { LeftJoin(Bgp(?book < Bgp(?book < true) Union(Bgp(?book < < Bgp(?book < < FILTER (?price < 15) } TU Dresden, August 2013 RDF and SPARQL slide 19 of 73

20 Translation into SPARQL Algebra { LeftJoin(Bgp(?book < Bgp(?book < true) Union(Bgp(?book < < Bgp(?book < < FILTER (?price < 15) } 5. Apply Join( ) operator to join non-filter elements TU Dresden, August 2013 RDF and SPARQL slide 20 of 73

21 Translation into SPARQL Algebra { Join( LeftJoin(Bgp(?book < Bgp(?book < true), Union(Bgp(?book < < Bgp(?book < < FILTER (?price < 15) } TU Dresden, August 2013 RDF and SPARQL slide 21 of 73

22 Translation into SPARQL Algebra { Join( LeftJoin(Bgp(?book < Bgp(?book < true), Union(Bgp(?book < < Bgp(?book < < FILTER (?price < 15) } 6. Translate a group with filters with the Filter( ) operator TU Dresden, August 2013 RDF and SPARQL slide 22 of 73

23 Translation into SPARQL Algebra Filter(?price < 15, Join( LeftJoin(Bgp(?book < Bgp(?book < true), Union(Bgp(?book < < Bgp(?book < < TU Dresden, August 2013 RDF and SPARQL slide 23 of 73

24 Translation into SPARQL Algebra Filter(?price < 15, Join( LeftJoin(Bgp(?book < Bgp(?book < true), Union(Bgp(?book < < Bgp(?book < < Online translation tool: TU Dresden, August 2013 RDF and SPARQL slide 24 of 73

25 Agenda 1 Recap 2 SPARQL Semantics 3 Transformation of Queries into Algebra Objects 4 Evaluation of the SPARQL Algebra 5 Operators for the Modifiers 6 Summary TU Dresden, August 2013 RDF and SPARQL slide 25 of 73

26 Semantics of the SPARQL Algebra Operations Now we have an algebra object, but what do the algebra operations mean? Bgp(P) match/evaluate pattern P Join(M 1, M 2 ) conjunctive join of solutions M 1 and M 2 Union(M 1, M 2 ) union of solutions M 1 with M 2 LeftJoin(M 1, M 2, F) optional join of M 1 with M 2 with filter constraint F (true if no filter given) Filter(F, M) filter solutions M with constraint F Z empty pattern (identity for join) TU Dresden, August 2013 RDF and SPARQL slide 26 of 73

27 Semantics of the SPARQL Algebra Operations Now we have an algebra object, but what do the algebra operations mean? Bgp(P) match/evaluate pattern P Join(M 1, M 2 ) conjunctive join of solutions M 1 and M 2 Union(M 1, M 2 ) union of solutions M 1 with M 2 LeftJoin(M 1, M 2, F) optional join of M 1 with M 2 with filter constraint F (true if no filter given) Filter(F, M) filter solutions M with constraint F Z empty pattern (identity for join) Only Bgp( ) matches or evaluates graph patterns We can use entailment checking rather than graph matching TU Dresden, August 2013 RDF and SPARQL slide 27 of 73

28 Definition of the SPARQL Operators How can we define that more formally? Output: solution set (formatting irrelevant) Input: Queried (active) graph Partial results from previous evaluation steps Different parameters according to the operation How can we formally describe the results? TU Dresden, August 2013 RDF and SPARQL slide 28 of 73

29 SPARQL Results Intuition: Results coded as tables of variable assignments Result: List of solutions (solution sequence) each solution corresponds to one table row TU Dresden, August 2013 RDF and SPARQL slide 29 of 73

30 SPARQL Results Intuition: Results coded as tables of variable assignments Result: List of solutions (solution sequence) each solution corresponds to one table row Solution: Partial function Domain: relevant variables Range: IRIs blank nodes RDF literals Unbound variables are those that have no assigned value (partial function) TU Dresden, August 2013 RDF and SPARQL slide 30 of 73

31 Evaluation of Basic Graph Patterns Definition (Solution) Let P be a basic graph pattern. A partial function µ is a solution for Bgp(P) over the queried (active) graph G if: 1 the domain of µ is exactly the set of variables in P, 2 there exists an assignment σ from blank nodes in P to IRIs, blank nodes, or RDF literals such that: 3 the RDF graph µ(σ(p)) is a subgraph of G. TU Dresden, August 2013 RDF and SPARQL slide 31 of 73

32 Evaluation of Basic Graph Patterns The result of evaluating Bgp(P) over G is written Bgp(P) G The result is a multi set of solutions µ The multiplicity of each solution µ corresponds to the number of different assignments σ TU Dresden, August 2013 RDF and SPARQL slide 32 of 73

33 Multi Sets Definition (Multi Set) A multi set over a set S is a total function M : S IN + {ω} IN + denotes the positive natural numbers ω > n for all n IN + M(s) is the multiplicity of s S ω: countably infinite number of occurrences We represent a multi se over the set S also with the set {(s, M(s)) s S} We write (s, n) M if M(s) = n We assume that M(s) = 0 if s / S Alternative notation: {a, b, b } corresponds to the multi set M over the set {a, b} with M(a) = 1 and M(b) = 2 TU Dresden, August 2013 RDF and SPARQL slide 33 of 73

34 Solution Mapping Example ex:birte ex:gives [ a ex:lecture ; ex:hastopic "SPARQL" ]. ex:sebastian ex:gives [ a ex:lecture ; ex:hastopic "DLs and OWL" ]. Bgp(?who ex:gives _ :x. _ :x ex:hastopic?what) TU Dresden, August 2013 RDF and SPARQL slide 34 of 73

35 Solution Mapping Example ex:birte ex:gives _ :a. _ :a rdf:type ex:lecture. _ :a ex:hastopic "SPARQL". ex:sebastian ex:gives _ :b. _ :b rdf:type ex:lecture. _ :b ex:hastopic "DLs and OWL". Bgp(?who ex:gives _ :x. _ :x ex:hastopic?what) TU Dresden, August 2013 RDF and SPARQL slide 35 of 73

36 Solution Mapping Example ex:birte ex:gives _ :a. _ :a rdf:type ex:lecture. _ :a ex:hastopic "SPARQL". ex:sebastian ex:gives _ :b. _ :b rdf:type ex:lecture. _ :b ex:hastopic "DLs and OWL". Bgp(?who ex:gives _ :x. _ :x ex:hastopic?what) µ 1 :?who ex : Birte,?what "SPARQL" σ 1 : _ :x _ :a TU Dresden, August 2013 RDF and SPARQL slide 36 of 73

37 Solution Mapping Example ex:birte ex:gives _ :a. _ :a rdf:type ex:lecture. _ :a ex:hastopic "SPARQL". ex:sebastian ex:gives _ :b. _ :b rdf:type ex:lecture. _ :b ex:hastopic "DLs and OWL". Bgp(?who ex:gives _ :x. _ :x ex:hastopic?what) µ 1 :?who ex : Birte,?what "SPARQL" σ 1 : _ :x _ :a µ 2 :?who ex : Sebastian,?what "DLs and OWL" σ 2 : _ :x _ :b TU Dresden, August 2013 RDF and SPARQL slide 37 of 73

38 Solution Mapping Example ex:birte ex:gives _ :a. _ :a rdf:type ex:lecture. _ :a ex:hastopic "SPARQL". ex:sebastian ex:gives _ :b. _ :b rdf:type ex:lecture. _ :b ex:hastopic "DLs and OWL". Bgp(?who ex:gives _ :x. _ :x ex:hastopic?what) µ 1 :?who ex : Birte,?what "SPARQL" σ 1 : _ :x _ :a µ 2 :?who ex : Sebastian,?what "DLs and OWL" σ 2 : _ :x _ :b Two solutions each with multiplicity 1 TU Dresden, August 2013 RDF and SPARQL slide 38 of 73

39 Exercise Solution Sets ex:birte ex:gives [ a ex:lecture ; ex:hastopic "SPARQL" ]. ex:birte ex:gives [ a ex:lecture ; ex:hastopic "SPARQL Algebra" ]. Bgp(?who ex:gives _ :x. _ :x ex:hastopic _ :y) TU Dresden, August 2013 RDF and SPARQL slide 39 of 73

40 Solution TU Dresden, August 2013 RDF and SPARQL slide 40 of 73

41 Solution ex:birte ex:gives _ :a. _ :a rdf:type ex:lecture. _ :a ex:hastopic "SPARQL". ex:birte ex:gives _ :b. _ :b rdf:type ex:lecture. _ :b ex:hastopic "SPARQL Algebra". Bgp(?who ex:gives _ :x. _ :x ex:hastopic _ :y) TU Dresden, August 2013 RDF and SPARQL slide 41 of 73

42 Solution ex:birte ex:gives _ :a. _ :a rdf:type ex:lecture. _ :a ex:hastopic "SPARQL". ex:birte ex:gives _ :b. _ :b rdf:type ex:lecture. _ :b ex:hastopic "SPARQL Algebra". Bgp(?who ex:gives _ :x. _ :x ex:hastopic _ :y) µ 1 :?who ex : Birte, σ 1 : _ :x _ :a _ :y "SPARQL" TU Dresden, August 2013 RDF and SPARQL slide 42 of 73

43 Solution ex:birte ex:gives _ :a. _ :a rdf:type ex:lecture. _ :a ex:hastopic "SPARQL". ex:birte ex:gives _ :b. _ :b rdf:type ex:lecture. _ :b ex:hastopic "SPARQL Algebra". Bgp(?who ex:gives _ :x. _ :x ex:hastopic _ :y) µ 1 :?who ex : Birte, σ 1 : _ :x _ :a _ :y "SPARQL" µ 2 :?who ex : Birte, σ 2 : _ :x _ :b _ :y "SPARQL Algebra" TU Dresden, August 2013 RDF and SPARQL slide 43 of 73

44 Solution ex:birte ex:gives _ :a. _ :a rdf:type ex:lecture. _ :a ex:hastopic "SPARQL". ex:birte ex:gives _ :b. _ :b rdf:type ex:lecture. _ :b ex:hastopic "SPARQL Algebra". Bgp(?who ex:gives _ :x. _ :x ex:hastopic _ :y) µ 1 :?who ex : Birte, σ 1 : _ :x _ :a _ :y "SPARQL" µ 2 :?who ex : Birte, σ 2 : _ :x _ :b _ :y "SPARQL Algebra" One solution with multiplicity 2 TU Dresden, August 2013 RDF and SPARQL slide 44 of 73

45 Union of Solutions (1) Definition (Compatibility) Two solutions µ 1 and µ 2 are compatible if µ 1 (x) = µ 2 (x) for all x, for which µ 1 and µ 2 are defined TU Dresden, August 2013 RDF and SPARQL slide 45 of 73

46 Union of Solutions (1) Definition (Compatibility) Two solutions µ 1 and µ 2 are compatible if µ 1 (x) = µ 2 (x) for all x, for which µ 1 and µ 2 are defined µ 1 :?x ex : a,?y ex : b µ 2 :?y ex : b,?z ex : c TU Dresden, August 2013 RDF and SPARQL slide 46 of 73

47 Union of Solutions (1) Definition (Compatibility) Two solutions µ 1 and µ 2 are compatible if µ 1 (x) = µ 2 (x) for all x, for which µ 1 and µ 2 are defined µ 1 :?x ex : a,?y ex : b µ 2 :?y ex : b,?z ex : c TU Dresden, August 2013 RDF and SPARQL slide 47 of 73

48 Union of Solutions (1) Definition (Compatibility) Two solutions µ 1 and µ 2 are compatible if µ 1 (x) = µ 2 (x) for all x, for which µ 1 and µ 2 are defined µ 1 :?x ex : a,?y ex : b µ 2 :?y ex : b,?z ex : c µ 1 :?x ex : a,?y ex : b µ 2 :?x ex : b,?z ex : c TU Dresden, August 2013 RDF and SPARQL slide 48 of 73

49 Union of Solutions (1) Definition (Compatibility) Two solutions µ 1 and µ 2 are compatible if µ 1 (x) = µ 2 (x) for all x, for which µ 1 and µ 2 are defined µ 1 :?x ex : a,?y ex : b µ 2 :?y ex : b,?z ex : c µ 1 :?x ex : a,?y ex : b µ 2 :?x ex : b,?z ex : c TU Dresden, August 2013 RDF and SPARQL slide 49 of 73

50 Union of Solutions (1) Definition (Compatibility) Two solutions µ 1 and µ 2 are compatible if µ 1 (x) = µ 2 (x) for all x, for which µ 1 and µ 2 are defined µ 1 :?x ex : a,?y ex : b µ 2 :?y ex : b,?z ex : c µ 1 :?x ex : a,?y ex : b µ 2 :?x ex : b,?z ex : c µ 1 :?x ex : a µ 2 :?y ex : b TU Dresden, August 2013 RDF and SPARQL slide 50 of 73

51 Union of Solutions (1) Definition (Compatibility) Two solutions µ 1 and µ 2 are compatible if µ 1 (x) = µ 2 (x) for all x, for which µ 1 and µ 2 are defined µ 1 :?x ex : a,?y ex : b µ 2 :?y ex : b,?z ex : c µ 1 :?x ex : a,?y ex : b µ 2 :?x ex : b,?z ex : c µ 1 :?x ex : a µ 2 :?y ex : b TU Dresden, August 2013 RDF and SPARQL slide 51 of 73

52 Union of Solutions (2) Union of two compatible solutions µ 1 and µ 2 : { µ1 (x) if x dom(µ (µ 1 µ 2 )(x) = 1 ) µ 2 (x) otherwise simple intuition: union of matching table rows TU Dresden, August 2013 RDF and SPARQL slide 52 of 73

53 Evaluation of Join( ) For the evaluation of Join(A 1, A 2 ) over a graph G with A 1, A 2 algebra objects, we define: Let M 1 = A 1 G Let M 2 = A 2 G Let J(µ) = { (µ 1, µ 2 ) M 1 (µ 1 ) > 0, M 2 (µ 2 ) > 0, µ 1 and µ 2 are compatible and µ = µ 1 µ 2 } J defines compatible pairs of solutions from M 1 and M 2 The evaluation Join(A 1, A 2 ) G results in { (µ, n ) n = ( M1 (µ 1 ) M 2 (µ 2 ) ) > 0} (µ 1,µ 2 ) J(µ) TU Dresden, August 2013 RDF and SPARQL slide 53 of 73

54 Example to Join( ) We consider Join(A 1, A 2 ) over a graph G with A 1 G = M 1, A 2 G = M 2 and: M 1 ={((µ 1 :?x ex : a,?y ex : b), 2), ((µ 2 :?x ex : a, 1)} M 2 ={((µ 3 :?y ex : b,?z ex : c, 3)} µ =?x ex : a,?y ex : b,?z ex : c J(µ) ={(µ 1, µ 3 ), (µ 2, µ 3 )} { (µ, ) ( Join(M 1, M 2 ) = n n = M1 (µ 1 ) M 2 (µ 2 ) ) > 0} (µ 1,µ 2 ) J(µ) ={(µ, 9)} n = = = 9 TU Dresden, August 2013 RDF and SPARQL slide 54 of 73

55 Evaluation of Union( ) The evaluation of Union(A 1, A 2 ) over a graph G, written Union(A 1, A 2 ) G, with A 1, A 2 algebra objects results in: { } (µ, n) M 1 = A 1 G, M 2 = A 2 G, n = M 1 (µ) + M 2 (µ) > 0 TU Dresden, August 2013 RDF and SPARQL slide 55 of 73

56 Evaluation of Filter( ) The evaluation of Filter(F, A) over a graph G, written Filter(F, A) G, with F a filter condition and A an algebra object results in: { } (µ, n) M = A G, M(µ) = n > 0 and µ(f) = true µ(f) is the Boolean result of evaluating the filter condition TU Dresden, August 2013 RDF and SPARQL slide 56 of 73

57 Evaluation of LeftJoin( ) The evaluation of LeftJoin(A 1, A 2, F) over a graph G with F a filter condition and A 1, A 2 algebra objects is defined as: M 1 = A 1 G M 2 = A 2 G The evaluation LeftJoin(A 1, A 2, F) G of LeftJoin(A 1, A 2, F) over G results in Filter(F, Join(A 1, A 2 )) G { (µ1, M 1 (µ 1 ) ) for all µ 2 with M 2 (µ 2 ) > 0 : µ 1 and µ 2 are } incompatible or (µ 1 µ 2 )(F) = false TU Dresden, August 2013 RDF and SPARQL slide 57 of 73

58 ex: xsd: < ex:hamlet ex:author ex:shakespeare ; ex:price "10.50"^^xsd:decimal. ex:macbeth ex:author ex:shakespeare. ex:tamburlaine ex:author ex:marlowe ; ex:price "17"^^xsd:integer. ex:doctorfaustus ex:author ex:marlowe ; ex:price "12"^^xsd:integer ; ex:title "The Tragical History of Doctor Faustus". ex:romeojulia ex:author ex:brooke ; ex:price "9"^^xsd:integer. {?book ex:price?price. FILTER (?price < 15) OPTIONAL {?book ex:title?title. } {?book ex:author ex:shakespeare. } UNION {?book ex:author ex:marlowe. } } TU Dresden, August 2013 RDF and SPARQL slide 58 of 73

59 @prefix ex: xsd: < ex:hamlet ex:author ex:shakespeare ; ex:price "10.50"^^xsd:decimal. ex:macbeth ex:author ex:shakespeare. ex:tamburlaine ex:author ex:marlowe ; ex:price "17"^^xsd:integer. ex:doctorfaustus ex:author ex:marlowe ; ex:price "12"^^xsd:integer ; ex:title "The Tragical History of Doctor Faustus". ex:romeojulia ex:author ex:brooke ; ex:price "9"^^xsd:integer. Filter(?price < 15, Join(LeftJoin(Bgp(?book < Bgp(?book < true), Union(Bgp(?book < < Bgp(?book < < TU Dresden, August 2013 RDF and SPARQL slide 59 of 73

60 Example Evaluation (1) Filter(?price < 15, Join( LeftJoin(Bgp(?book < Bgp(?book < true), Union(Bgp(?book < < Bgp(?book < < book ex:tamburlaine ex:doctorfaustus TU Dresden, August 2013 RDF and SPARQL slide 60 of 73

61 Example Evaluation (1) Filter(?price < 15, Join( LeftJoin(Bgp(?book < Bgp(?book < true), Union(Bgp(?book < < Bgp(?book < < book ex:tamburlaine ex:doctorfaustus book ex:macbeth ex:hamlet TU Dresden, August 2013 RDF and SPARQL slide 61 of 73

62 Example Evaluation (2) Filter(?price < 15, Join( LeftJoin(Bgp(?book < Bgp(?book < true), Union(Bgp(?book < < Bgp(?book < < book ex:hamlet ex:macbeth ex:tamburlaine ex:doctorfaustus TU Dresden, August 2013 RDF and SPARQL slide 62 of 73

63 Example Evaluation (3) Filter(?price < 15, Join( LeftJoin(Bgp(?book < Bgp(?book < true), Union(Bgp(?book < < Bgp(?book < < book price ex:hamlet 10.5 ex:tamburlaine 17 ex:doctorfaustus 12 ex:romeojulia 9 TU Dresden, August 2013 RDF and SPARQL slide 63 of 73

64 Example Evaluation (3) Filter(?price < 15, Join( LeftJoin(Bgp(?book < Bgp(?book < true), Union(Bgp(?book < < Bgp(?book < < book price ex:hamlet 10.5 ex:tamburlaine 17 ex:doctorfaustus 12 ex:romeojulia 9 book title ex:doctorfaustus "The Tragical History of Doctor Faustus" TU Dresden, August 2013 RDF and SPARQL slide 64 of 73

65 Example Evaluation (4) Filter(?price < 15, Join( LeftJoin(Bgp(?book < Bgp(?book < true), Union(Bgp(?book < < Bgp(?book < < book price title ex:hamlet 10.5 ex:tamburlaine 17 ex:doctorfaustus 12 "The Tragical History of Doctor Faustus" ex:romeojulia 9 TU Dresden, August 2013 RDF and SPARQL slide 65 of 73

66 Example Evaluation (5) Filter(?price < 15, Join( LeftJoin(Bgp(?book < Bgp(?book < true), Union(Bgp(?book < < Bgp(?book < < book price title ex:hamlet 10.5 ex:tamburlaine 17 ex:doctorfaustus 12 "The Tragical History of Doctor Faustus" TU Dresden, August 2013 RDF and SPARQL slide 66 of 73

67 Example Evaluation (6) Filter(?price < 15, Join( LeftJoin(Bgp(?book < Bgp(?book < true), Union(Bgp(?book < < Bgp(?book < < book price title ex:hamlet 10.5 ex:doctorfaustus 12 "The Tragical History of Doctor Faustus" TU Dresden, August 2013 RDF and SPARQL slide 67 of 73

68 Agenda 1 Recap 2 SPARQL Semantics 3 Transformation of Queries into Algebra Objects 4 Evaluation of the SPARQL Algebra 5 Operators for the Modifiers 6 Summary TU Dresden, August 2013 RDF and SPARQL slide 68 of 73

69 Operators for Representing the Modifiers ToList(M) OrderBy(M, comparators) Distinct(M) Reduced(M) Slice(M, o, l) Project(M, vars) Constructs from a multi set a sequence with the same elements and multiplicity (arbitrary order, duplicates not necessarily adjacent) sorts the solutions removes the duplicates may remove duplicates cuts the solutions to a list of length l starting from position o projects out the mentioned variables TU Dresden, August 2013 RDF and SPARQL slide 69 of 73

70 Transformation of the Modifiers Let q be a SPARQL query with pattern P and corresponding algebra object A P. We construct an algebra object A q for q as follows: 1 A q := ToList(A P ) 2 A q := OrderBy(A q, (c 1,..., c n)) if q contains an ORDER BY clause with comparators c 1,..., c n 3 A q := Project(A q, vars) if the result format is SELECT with vars the selected variables (* all variables in scope) 4 A q := Distinct(A q) is the result format is SELECT and q contains DISTINCT 5 A q := Reduced(A q) if the result format is SELECT and q contains REDUCED 6 A q := Slice(A q, start, length) if the query contains OFFSET start or LIMIT length where start defaults to 0 and length defaults to ( A q G start) TU Dresden, August 2013 RDF and SPARQL slide 70 of 73

71 Evaluation of the Modifiers The algebra objects for the modifiers are recursively evaluated Evaluate the algebra expression of the operator Apply the operations for the solution modifiers to the obtained solutions TU Dresden, August 2013 RDF and SPARQL slide 71 of 73

72 Agenda 1 Recap 2 SPARQL Semantics 3 Transformation of Queries into Algebra Objects 4 Evaluation of the SPARQL Algebra 5 Operators for the Modifiers 6 Summary TU Dresden, August 2013 RDF and SPARQL slide 72 of 73

73 Summary We learned how to evaluate SPARQL queries The query is transformed into an algebra object The query basic graph patterns generate solutions The other operators combine solutions The result format determines how the solutions are presented TU Dresden, August 2013 RDF and SPARQL slide 73 of 73