SPARQL: Un Lenguaje de Consulta para la Web

Transcription

1 SPARQL: Un Lenguaje de Consulta para la Web Semántica Marcelo Arenas Pontificia Universidad Católica de Chile y Centro de Investigación de la Web M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 1 / 54

2 Outline RDF model Querying RDF data Conjunctive queries Entailment of RDF graphs Graphs with RDFS vocabulary Inference rules Querying RDFS data: Closure, Core. Querying RDF Data in practice: SPARQL Formal semantics for SPARQL Complexity of the SPARQL evaluation problem A procedural semantics: Well designed patterns M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 2 / 54

3 Semantic Web The Semantic Web is an extension of the current web in which information is given well-defined meaning, better enabling computers and people to work in cooperation. Specific Goals: [Tim Berners-Lee et al ] Build a description language with standard semantics. Make semantics machine-processable and understandable. Incorporate logical infrastructure to reason about resources. W3C Proposal: Resource Description Framework (RDF). M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 3 / 54

4 RDF in a nutshell RDF is the W3C proposal framework for representing information in the Web. Abstract syntax based on directed labeled graph. Schema definition language (RDFS): Define new vocabulary (typing, inheritance of classes and properties). Extensible URI-based vocabulary. Support use of XML schema datatypes. Formal semantics. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 4 / 54

5 RDF formal model U Subject Predicate Object U = set of Uris B = set of Blank nodes U B U B L L = set of Literals M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 5 / 54

6 RDF formal model U Subject Predicate Object U = set of Uris B = set of Blank nodes U B U B L L = set of Literals (s,p,o) (U B) U (U B L) is called an RDF triple M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 5 / 54

7 RDF formal model U Subject Predicate Object U = set of Uris B = set of Blank nodes U B U B L L = set of Literals (s,p,o) (U B) U (U B L) is called an RDF triple A set of RDF triples is called an RDF graph M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 5 / 54

8 RDFS: An example person rdf:dom works in rdf:range company rdf:sc sportman rdf:sp rdf:sc rdf:sc soccer player rdf:dom plays in rdf:range soccer team rdf:type rdf:type Ronaldinho plays in Barcelona lives in Spain M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 6 / 54

9 RDFS: An example person rdf:dom works in rdf:range company rdf:sc sportman rdf:sp rdf:sc rdf:sc soccer player rdf:dom plays in rdf:range soccer team rdf:type rdf:type Ronaldinho plays in Barcelona lives in Spain M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 6 / 54

10 RDF model Some difficulties: Existential variables as datavalues Built-in vocabulary with fixed semantics (RDFS) Graph model where nodes may also be edge labels RDF data processing can take advantage of database techniques: Query processing Storing Indexing M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 7 / 54

11 RDF model Some difficulties: Existential variables as datavalues Built-in vocabulary with fixed semantics (RDFS) Graph model where nodes may also be edge labels RDF data processing can take advantage of database techniques: Query processing Storing Indexing M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 7 / 54

12 Querying RDF data Conjunctive query: Q(X) = Y t 1 t 2 t k Some examples: M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 8 / 54

13 Querying RDF data Conjunctive query: Q(X) = Y t 1 t 2 t k Some examples: (Ronaldinho, plays in, Barcelona) M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 8 / 54

14 Querying RDF data Conjunctive query: Q(X) = Y t 1 t 2 t k Some examples: (Ronaldinho, plays in, Barcelona) (Ronaldinho, plays in, X) M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 8 / 54

15 Querying RDF data Conjunctive query: Q(X) = Y t 1 t 2 t k Some examples: Y (Ronaldinho, plays in, Barcelona) (Ronaldinho, plays in, X) (X, plays in, Y ) (X, lives in,spain) M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 8 / 54

16 Semantics of conjunctive queries Given an RDF graph G, a conjunctive query Q(X) and a tuple ā of values in U B L: Notation: G = Q(ā) Is ā an answer to Q(X) in G? Notice that Q(X) and ā may include blank nodes. Blank nodes play a similar role as existential variables. (Ronaldinho, plays in, B) and X (Ronaldinho, plays in, X) are equivalent. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 9 / 54

17 Conjunctive queries and entailment of RDF graphs Q(ā) can be transformed into an RDF graph G. Notion to define: G = G Entailment of RDF graphs: M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 10 / 54

18 Conjunctive queries and entailment of RDF graphs Q(ā) can be transformed into an RDF graph G. Notion to define: G = G Entailment of RDF graphs: Can be defined in terms of classical notions such model, interpretation, etc M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 10 / 54

19 Conjunctive queries and entailment of RDF graphs Q(ā) can be transformed into an RDF graph G. Notion to define: G = G Entailment of RDF graphs: Can be defined in terms of classical notions such model, interpretation, etc As for the case of first order logic M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 10 / 54

20 Conjunctive queries and entailment of RDF graphs Q(ā) can be transformed into an RDF graph G. Notion to define: G = G Entailment of RDF graphs: Can be defined in terms of classical notions such model, interpretation, etc As for the case of first order logic Has a graph characterization via homomorphisms. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 10 / 54

21 Homomorphism A function h : U B L U B L is a homomorphism h from G 1 to G 2 if: h(c) = c for every c U L; for every (a,b,c) G 1, (h(a),h(b),h(c)) G 2 Notation: G 1 G 2 Example: h = {B b} a p B a p p b b M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 11 / 54

22 Entailment Theorem (CM77) G 1 = G 2 if and only if there is a homomorphism G 2 G 1. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 12 / 54

23 Entailment Theorem (CM77) G 1 = G 2 if and only if there is a homomorphism G 2 G 1. a a p B p = p b b M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 12 / 54

24 Entailment Theorem (CM77) G 1 = G 2 if and only if there is a homomorphism G 2 G 1. a a p B p = p b b p M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 12 / 54

25 Entailment Theorem (CM77) G 1 = G 2 if and only if there is a homomorphism G 2 G 1. a a p B p = p b b p Complexity Entailment for RDF is NP-complete M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 12 / 54

26 Graphs with RDFS vocabulary Previous characterization of entailment is not enough to deal with RDFS vocabulary: M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 13 / 54

27 Graphs with RDFS vocabulary Previous characterization of entailment is not enough to deal with RDFS vocabulary: (Ronaldinho, rdf : type, person) person rdf:dom works in rdf:range company rdf:sc sportman rdf:sp rdf:sc rdf:sc soccer player rdf:dom plays in rdf:range soccer team rdf:type rdf:type Ronaldinho plays in Barcelona lives in Spain M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 13 / 54

28 Graphs with RDFS vocabulary Built-in predicates have pre-defined semantics: M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 14 / 54

29 Graphs with RDFS vocabulary Built-in predicates have pre-defined semantics: rdf:sc: transitive M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 14 / 54

30 Graphs with RDFS vocabulary Built-in predicates have pre-defined semantics: rdf:sc: transitive rdf:sp: transitive M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 14 / 54

31 Graphs with RDFS vocabulary Built-in predicates have pre-defined semantics: rdf:sc: transitive rdf:sp: transitive More complicated interactions: (p,rdf:dom, c) (a, p, b) (a, rdf:type, c) M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 14 / 54

32 Graphs with RDFS vocabulary Built-in predicates have pre-defined semantics: rdf:sc: transitive rdf:sp: transitive More complicated interactions: (p,rdf:dom, c) (a, p, b) (a, rdf:type, c) RDFS-entailment can be characterized by a set of rules An Existential rule Subproperty rules Subclass rules Typing rules Implicit typing M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 14 / 54

33 Graphs with RDFS vocabulary: Inference rules Inference system in [MPG07] has 14 rules: Existential rule : Subproperty rules : Subclass rules : Typing rules : Implicit typing : M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 15 / 54

34 Graphs with RDFS vocabulary: Inference rules Inference system in [MPG07] has 14 rules: Existential rule : G 1 G 2 if G 2 G 1 Subproperty rules : Subclass rules : Typing rules : Implicit typing : M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 15 / 54

35 Graphs with RDFS vocabulary: Inference rules Inference system in [MPG07] has 14 rules: Existential rule : Subproperty rules : G 1 G 2 if G 2 G 1 (p,rdf:sp, q) (a, p, b) (a, q, b) Subclass rules : Typing rules : Implicit typing : M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 15 / 54

36 Graphs with RDFS vocabulary: Inference rules Inference system in [MPG07] has 14 rules: Existential rule : Subproperty rules : Subclass rules : G 1 G 2 if G 2 G 1 (p,rdf:sp, q) (a, p, b) (a, q, b) (a, rdf:sc, b) (b, rdf:sc, c) (a, rdf:sc, c) Typing rules : Implicit typing : M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 15 / 54

37 Graphs with RDFS vocabulary: Inference rules Inference system in [MPG07] has 14 rules: Existential rule : Subproperty rules : Subclass rules : Typing rules : G 1 G 2 if G 2 G 1 (p,rdf:sp, q) (a, p, b) (a, q, b) (a, rdf:sc, b) (b, rdf:sc, c) (a, rdf:sc, c) (p,rdf:dom, c) (a, p, b) (a, rdf:type, c) Implicit typing : M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 15 / 54

38 Graphs with RDFS vocabulary: Inference rules Inference system in [MPG07] has 14 rules: Existential rule : Subproperty rules : Subclass rules : Typing rules : Implicit typing : G 1 G 2 if G 2 G 1 (p,rdf:sp, q) (a, p, b) (a, q, b) (a, rdf:sc, b) (b, rdf:sc, c) (a, rdf:sc, c) (p,rdf:dom, c) (a, p, b) (a, rdf:type, c) (q, rdf:dom, a) (p, rdf:sp, q) (b, p, c) (b, rdf:type, a) M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 15 / 54

39 Graphs with RDFS vocabulary: Inference rules Inference system in [MPG07] has 14 rules: Existential rule : Subproperty rules : (p,rdf:sp, q) (a, p, b) (a, q, b) Subclass rules : Typing rules : Implicit typing : (p,rdf:dom, c) (a, p, b) (a, rdf:type, c) (q, rdf:dom, a) (p, rdf:sp, q) (b, p, c) (b, rdf:type, a) M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 15 / 54

40 Graphs with RDFS vocabulary: Inference rules Inference system in [MPG07] has 14 rules: Existential rule : Subproperty rules : (p,rdf:sp, q) (a, p, b) (a, q, b) Subclass rules : Typing rules : Implicit typing : (p,rdf:dom, c) (a, p, b) (a, rdf:type, c) (B, rdf:dom, a) (p, rdf:sp, B) (b, p, c) (b, rdf:type, a) M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 15 / 54

41 RDFS Entailment Theorem (H03,GHM04,MPG07) G 1 = G 2 iff there is a proof of G 2 from G 1 using the system of 14 inference rules. Complexity RDFS-entailment is NP-complete. Proof idea Membership in NP: If G 1 = G 2, then there exists a polynomial-size proof of this fact. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 16 / 54

42 Querying RDFS data System of inference rules can be used as a mechanism for evaluating queries. It is difficult to implement. Is there any practical mechanism for evaluating queries? M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 17 / 54

43 Querying RDFS data System of inference rules can be used as a mechanism for evaluating queries. It is difficult to implement. Is there any practical mechanism for evaluating queries? Making explicit the implicit information. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 17 / 54

44 Closure of an RDF Graph Notation: ground(g) : Graph obtained by replacing every blank B in G by a constant c B. ground 1 (G) : Graph obtained by replacing every constant c B in G by B. Closure of an RDF graph G (denoted by closure(g)): M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 18 / 54

45 Closure of an RDF Graph Notation: ground(g) : Graph obtained by replacing every blank B in G by a constant c B. ground 1 (G) : Graph obtained by replacing every constant c B in G by B. Closure of an RDF graph G (denoted by closure(g)): G {t (U B) U (U B L) there exists a ground tuple t such that ground(g) = t and t = ground 1 (t )} M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 18 / 54

46 Closure of an RDF Graph: Example c c rdf : sc rdf : sc b b rdf : sc rdf : sc rdf : sc a a M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 19 / 54

47 Closure of an RDF Graph: Example c c rdf : sc rdf : sc b b rdf : sc rdf : sc rdf : sc a a M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 19 / 54

48 Querying RDFS data: Using the closure of a graph Proposition (H03,GHM04,MPG07) G 1 = G 2 iff G 2 closure(g 1 ) Complexity The closure of G can be computed in time O( G 4 log G ). M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 20 / 54

49 Querying RDFS data: Using the closure of a graph Proposition (H03,GHM04,MPG07) G 1 = G 2 iff G 2 closure(g 1 ) Complexity The closure of G can be computed in time O( G 4 log G ). Can the closure be used in practice? M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 20 / 54

50 Querying RDFS data: Using the closure of a graph Proposition (H03,GHM04,MPG07) G 1 = G 2 iff G 2 closure(g 1 ) Complexity The closure of G can be computed in time O( G 4 log G ). Can the closure be used in practice? Can we use an alternative materialization? M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 20 / 54

51 Querying RDFS data: Using the closure of a graph Proposition (H03,GHM04,MPG07) G 1 = G 2 iff G 2 closure(g 1 ) Complexity The closure of G can be computed in time O( G 4 log G ). Can the closure be used in practice? Can we use an alternative materialization? Can we materialize a small part of the closure? M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 20 / 54

52 Core of an RDF Graph An RDF Graph G is a core if there is no homomorphism from G to a proper subgraph of it. Theorem (HN92,FKP03,GHM04) Each RDF graph G has a unique core (denoted by core(g)). Deciding if G is a core is conp-complete. Deciding if G = core(g ) is DP-complete. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 21 / 54

53 Core and RDFS For RDF graphs with RDFS vocabulary, the core of G may contain redundant information: d d rdf : sc rdf : sc rdf : sc c c rdf : sc rdf : sc B rdf : sc b b rdf : sc rdf : sc rdf : sc a a M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 22 / 54

56 A normal form for RDF graphs To reduce the size of the materialization, we can combine both core and closure. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 23 / 54

57 A normal form for RDF graphs To reduce the size of the materialization, we can combine both core and closure. nf(g) = core(closure(g)) M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 23 / 54

58 A normal form for RDF graphs To reduce the size of the materialization, we can combine both core and closure. nf(g) = core(closure(g)) Theorem (GHM04) G 1 is equivalent to G 2 iff nf(g 1 ) = nf(g 2 ). G 1 = G 2 iff G 2 nf(g 1 ) M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 23 / 54

59 A normal form for RDF graphs To reduce the size of the materialization, we can combine both core and closure. nf(g) = core(closure(g)) Theorem (GHM04) G 1 is equivalent to G 2 iff nf(g 1 ) = nf(g 2 ). G 1 = G 2 iff G 2 nf(g 1 ) Complexity The problem of deciding if G 1 = nf(g 2 ) is DP-complete. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 23 / 54

60 Querying RDF Data in practice SPARQL is the W3C candidate recommendation query language for RDF. SPARQL is a graph-matching query language. A SPARQL query consists of three parts: Pattern matching: optional, union, nesting, filtering. Solution modifiers: projection, distinct, order, limit, offset. Output part: construction of new triples,.... M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 24 / 54

61 A simple RDF query language SELECT?Name? WHERE {?X :name?name?x : ? } M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 25 / 54

65 A simple RDF query language SELECT?Name? WHERE {?X :name?name?x : ? } In general, in a query we have: H Head: processing of some variables. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 25 / 54

66 A simple RDF query language SELECT?Name? WHERE {?X :name?name?x : ? } In general, in a query we have: H P Head: processing of some variables. Body: pattern matching expression. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 25 / 54

67 A simple RDF query language SELECT?Name? WHERE {?X :name?name?x : ? } In general, in a query we have: H P Head: processing of some variables. Body: pattern matching expression. We focus on P. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 25 / 54

68 But things can become more complex... Interesting features of pattern matching on graphs Grouping Optional parts Nesting Union of patterns Filtering... { P1 P2 } M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 26 / 54

69 But things can become more complex... Interesting features of pattern matching on graphs Grouping Optional parts Nesting Union of patterns Filtering... { { P1 P2 } } { P3 P4 } M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 26 / 54

70 But things can become more complex... Interesting features of pattern matching on graphs Grouping Optional parts Nesting Union of patterns Filtering... { { P1 P2 OPTIONAL { P5 } } } { P3 P4 OPTIONAL { P7 } } M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 26 / 54

71 But things can become more complex... Interesting features of pattern matching on graphs Grouping Optional parts Nesting Union of patterns Filtering... { { P1 P2 OPTIONAL { P5 } } } { P3 P4 OPTIONAL { P7 OPTIONAL { P8 } } } M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 26 / 54

72 But things can become more complex... Interesting features of pattern matching on graphs Grouping Optional parts Nesting Union of patterns Filtering... { { P1 P2 OPTIONAL { P5 } } { P3 P4 OPTIONAL { P7 OPTIONAL { P8 } } } } UNION { P9 } M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 26 / 54

73 But things can become more complex... Interesting features of pattern matching on graphs Grouping Optional parts Nesting Union of patterns Filtering... { { P1 P2 OPTIONAL { P5 } } { P3 P4 OPTIONAL { P7 OPTIONAL { P8 } } } } UNION { P9 FILTER ( R ) } M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 26 / 54

74 But things can become more complex... Interesting features of pattern matching on graphs Grouping Optional parts Nesting Union of patterns Filtering... { { P1 P2 OPTIONAL { P5 } } { P3 P4 OPTIONAL { P7 OPTIONAL { P8 } } } } UNION { P9 FILTER ( R ) } M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 26 / 54

75 A formal semantics for SPARQL is needed. A formal approach would be beneficial for: Clarifying corner cases Helping in the implementation process Providing sound foundations M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 27 / 54

76 A formal semantics for SPARQL is needed. A formal approach would be beneficial for: Clarifying corner cases Helping in the implementation process Providing sound foundations Our primary interest M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 27 / 54

77 A formal semantics for SPARQL is needed. A formal approach would be beneficial for: Clarifying corner cases Helping in the implementation process Providing sound foundations Our primary interest In our work: A formal compositional semantics (for simple RDF) Complexity bounds Optimization procedures M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 27 / 54

78 A standard algebraic syntax Triple patterns: just triples + variables, without blanks?x :name "john" (?X, name, john) Graph patterns: full parenthesized algebra { P1 P2 } (P 1 AND P 2 ) { P1 OPTIONAL { P2 }} (P 1 OPT P 2 ) { P1 } UNION { P2 } (P 1 UNION P 2 ) { P1 FILTER ( R ) } (P 1 FILTER R ) original SPARQL syntax algebraic syntax M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 28 / 54

79 A standard algebraic syntax Explicit precedence/association Example { t1 t2 OPTIONAL { t3 } OPTIONAL { t4 } t5 } ((((t 1 AND t 2 ) OPT t 3 ) OPT t 4 ) AND t 5 ) M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 29 / 54

80 Mappings: building block for the semantics Definition A mapping is a partial function from variables to RDF terms. The evaluation of a pattern results in a set of mappings. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 30 / 54

81 Mappings: building block for the semantics Definition A mapping is a partial function from variables to RDF terms. The evaluation of a pattern results in a set of mappings. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 30 / 54

82 The semantics of triple patterns Given an RDF graph and a triple pattern t Definition The evaluation of t is the set of mappings that M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 31 / 54

83 The semantics of triple patterns Given an RDF graph and a triple pattern t Definition The evaluation of t is the set of mappings that make t to match the graph M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 31 / 54

84 The semantics of triple patterns Given an RDF graph and a triple pattern t Definition The evaluation of t is the set of mappings that make t to match the graph have as domain the variables in t. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 31 / 54

85 The semantics of triple patterns Given an RDF graph and a triple pattern t Definition The evaluation of t is the set of mappings that make t to match the graph have as domain the variables in t. Example graph triple evaluation (R 1, name, john)?x?y (R 1, , [email protected]) (?X, name,?y ) µ 1 : R 1 john (R 2, name, paul) µ 2 : R 2 paul M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 31 / 54

88 Compatible mappings Definition Two mappings are compatible if they agree in their shared variables. Example?X?Y?Z?V µ 1 : R 1 john µ 2 : R 1 [email protected] µ 3 : [email protected] R 2 M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 32 / 54

89 Compatible mappings Definition Two mappings are compatible if they agree in their shared variables. Example?X?Y?Z?V µ 1 : R 1 john µ 2 : R 1 [email protected] µ 3 : [email protected] R 2 M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 32 / 54

90 Compatible mappings Definition Two mappings are compatible if they agree in their shared variables. Example?X?Y?Z?V µ 1 : R 1 john µ 2 : R 1 [email protected] µ 3 : [email protected] R 2 µ 1 µ 2 : R 1 john [email protected] M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 32 / 54

91 Compatible mappings Definition Two mappings are compatible if they agree in their shared variables. Example?X?Y?Z?V µ 1 : R 1 john µ 2 : R 1 [email protected] µ 3 : [email protected] R 2 µ 1 µ 2 : R 1 john [email protected] M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 32 / 54

92 Compatible mappings Definition Two mappings are compatible if they agree in their shared variables. Example?X?Y?Z?V µ 1 : R 1 john µ 2 : R 1 [email protected] µ 3 : [email protected] R 2 µ 1 µ 2 : R 1 john [email protected] µ 1 µ 3 : R 1 john [email protected] R 2 M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 32 / 54

93 Compatible mappings Definition Two mappings are compatible if they agree in their shared variables. Example?X?Y?Z?V µ 1 : R 1 john µ 2 : R 1 [email protected] µ 3 : [email protected] R 2 µ 1 µ 2 : R 1 john [email protected] µ 1 µ 3 : R 1 john [email protected] R 2 µ 2 and µ 3 are not compatible M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 32 / 54

94 Sets of mappings and operations Let M 1 and M 2 be sets of mappings: Definition M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 33 / 54

95 Sets of mappings and operations Let M 1 and M 2 be sets of mappings: Definition Join: M 1 M 2 extending mappings in M 1 with compatible mappings in M 2 M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 33 / 54

96 Sets of mappings and operations Let M 1 and M 2 be sets of mappings: Definition Join: M 1 M 2 extending mappings in M 1 with compatible mappings in M 2 Difference: M 1 M 2 mappings in M 1 that cannot be extended with mappings in M 2 M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 33 / 54

97 Sets of mappings and operations Let M 1 and M 2 be sets of mappings: Definition Join: M 1 M 2 extending mappings in M 1 with compatible mappings in M 2 Difference: M 1 M 2 mappings in M 1 that cannot be extended with mappings in M 2 Union: M 1 M 2 mappings in M 1 plus mappings in M 2 (set theoretical union) M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 33 / 54

98 Sets of mappings and operations Let M 1 and M 2 be sets of mappings: Definition Join: M 1 M 2 extending mappings in M 1 with compatible mappings in M 2 Difference: M 1 M 2 mappings in M 1 that cannot be extended with mappings in M 2 Union: M 1 M 2 mappings in M 1 plus mappings in M 2 (set theoretical union) Definition Left Outer Join: M 1 M 2 = (M 1 M 2 ) (M 1 M 2 ) M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 33 / 54

99 Semantics of SPARQL operators Let M 1 and M 2 be the result of evaluating P 1 and P 2. Definition The evaluation of: (P 1 AND P 2 ) (P 1 UNION P 2 ) (P 1 OPT P 2 ) M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 34 / 54

100 Semantics of SPARQL operators Let M 1 and M 2 be the result of evaluating P 1 and P 2. Definition The evaluation of: (P 1 AND P 2 ) M 1 M 2 (P 1 UNION P 2 ) (P 1 OPT P 2 ) M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 34 / 54

101 Semantics of SPARQL operators Let M 1 and M 2 be the result of evaluating P 1 and P 2. Definition The evaluation of: (P 1 AND P 2 ) M 1 M 2 (P 1 UNION P 2 ) M 1 M 2 (P 1 OPT P 2 ) M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 34 / 54

102 Semantics of SPARQL operators Let M 1 and M 2 be the result of evaluating P 1 and P 2. Definition The evaluation of: (P 1 AND P 2 ) M 1 M 2 (P 1 UNION P 2 ) M 1 M 2 (P 1 OPT P 2 ) M 1 M 2 M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 34 / 54

103 Simple example Example (R 1, name, john) (R 1, , (R 2, name, paul) ((?X, name,?y ) OPT (?X, ,?e)) M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 35 / 54

104 Simple example Example (R 1, name, john) (R 1, , (R 2, name, paul) ((?X, name,?y ) OPT (?X, ,?e)) M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 35 / 54

105 Simple example Example (R 1, name, john) (R 1, , (R 2, name, paul) ((?X, name,?y ) OPT (?X, ,?e))?x?y R 1 john paul R 2 M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 35 / 54

106 Simple example Example (R 1, name, john) (R 1, , (R 2, name, paul) ((?X, name,?y ) OPT (?X, ,?e))?x?y R 1 john paul R 2 M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 35 / 54

107 Simple example Example (R 1, name, john) (R 1, , (R 2, name, paul) ((?X, name,?y ) OPT (?X, ,?e))?x?y R 1 john paul R 2?X?E R 1 [email protected] M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 35 / 54

108 Simple example Example (R 1, name, john) (R 1, , (R 2, name, paul) ((?X, name,?y ) OPT (?X, ,?e))?x?y R 1 john paul R 2?X?E R 1 [email protected] M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 35 / 54

109 Simple example Example (R 1, name, john) (R 1, , (R 2, name, paul) ((?X, name,?y ) OPT (?X, ,?e))?x?y R 1 john paul R 2?X?Y?E R 1 john [email protected] R 2 paul?x?e R 1 [email protected] M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 35 / 54

110 Simple example Example (R 1, name, john) (R 1, , (R 2, name, paul) ((?X, name,?y ) OPT (?X, ,?e))?x?y R 1 john paul R 2?X?Y?E R 1 john [email protected] R 2 paul?x?e R 1 [email protected] from the Join M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 35 / 54

111 Simple example Example (R 1, name, john) (R 1, , (R 2, name, paul) ((?X, name,?y ) OPT (?X, ,?e))?x?y R 1 john paul R 2?X?Y?E R 1 john [email protected] R 2 paul?x?e R 1 [email protected] from the Difference M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 35 / 54

112 Simple example Example (R 1, name, john) (R 1, , (R 2, name, paul) ((?X, name,?y ) OPT (?X, ,?e))?x?y R 1 john paul R 2?X?Y?E R 1 john [email protected] R 2 paul?x?e R 1 [email protected] from the Union M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 35 / 54

113 Boolean filter expressions (value constraints) In filter expressions we consider equality = among variables and RDF terms unary predicate bound boolean combinations (,, ) M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 36 / 54

114 Satisfaction of value constraints A mapping satisfies?x = c if it gives the value c to variable?x?x =?Y if it gives the same value to?x and?y bound(?x) if it is defined for?x Definition Evaluation of (P FILTER R): Set of mappings in the evaluation of P that satisfy R. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 37 / 54

115 Natural algebraic properties: A simple normal from AND and UNION are commutative and associative. AND, OPT, and FILTER distribute over UNION. Theorem (UNION Normal Form) Every graph pattern is equivalent to one of the form P 1 UNION P 2 UNION UNION P n where each P i is UNION free. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 38 / 54

116 The evaluation problem Input: A mapping, a graph pattern, and an RDF graph. Question: Is the mapping in the evaluation of the pattern against the graph? M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 39 / 54

117 Evaluation of simple patterns is polynomial. Theorem (PAG06) For patterns using only AND and FILTER operators, the evaluation problem is polynomial: O(size of the pattern size of the graph). M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 40 / 54

118 Evaluation of simple patterns is polynomial. Theorem (PAG06) For patterns using only AND and FILTER operators, the evaluation problem is polynomial: O(size of the pattern size of the graph). Proof idea Check that the mapping makes every triple to match. Then check that the mapping satisfies the FILTERs. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 40 / 54

119 Evaluation including UNION is NP-complete. Theorem (PAG06) For patterns using only AND, FILTER and UNION operators, the evaluation problem is NP-complete. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 41 / 54

120 Evaluation including UNION is NP-complete. Theorem (PAG06) For patterns using only AND, FILTER and UNION operators, the evaluation problem is NP-complete. Proof idea Reduction from 3SAT. A pattern encodes the propositional formula. bound is used to encode negation. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 41 / 54

121 Evaluation including UNION is NP-complete. Theorem (PAG06) For patterns using only AND, FILTER and UNION operators, the evaluation problem is NP-complete. Proof idea Reduction from 3SAT. A pattern encodes the propositional formula. bound is used to encode negation. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 41 / 54

122 In general: Evaluation problem is PSPACE-complete. Theorem (PAG06) For general patterns that include OPT operator, the evaluation problem is PSPACE-complete. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 42 / 54

123 In general: Evaluation problem is PSPACE-complete. Theorem (PAG06) For general patterns that include OPT operator, the evaluation problem is PSPACE-complete. Proof idea Reduction from QBF A pattern encodes a quantified propositional formula: x 1 y 1 x 2 y 2 ψ. nested OPTs are used to encode quantifier alternation. (This time, we do not need bound.) M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 42 / 54

124 In general: Evaluation problem is PSPACE-complete. Theorem (PAG06) For general patterns that include OPT operator, the evaluation problem is PSPACE-complete. Proof idea Reduction from QBF A pattern encodes a quantified propositional formula: x 1 y 1 x 2 y 2 ψ. nested OPTs are used to encode quantifier alternation. (This time, we do not need bound.) M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 42 / 54

125 PSPACE-hardness: A closer look Assume ϕ = x 1 y 1 ψ, where ψ = (x 1 y 1 ) ( x 1 y 1 ). We generate G, P ϕ and µ 0 such that µ 0 belongs to the answer of P ϕ over G iff ϕ is valid: G : P ψ : P ϕ : µ 0 : M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 43 / 54

126 PSPACE-hardness: A closer look Assume ϕ = x 1 y 1 ψ, where ψ = (x 1 y 1 ) ( x 1 y 1 ). We generate G, P ϕ and µ 0 such that µ 0 belongs to the answer of P ϕ over G iff ϕ is valid: G : {(a,tv,0), (a,tv,1), (a,false,0), (a,true,1)} P ψ : P ϕ : µ 0 : M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 43 / 54

127 PSPACE-hardness: A closer look Assume ϕ = x 1 y 1 ψ, where ψ = (x 1 y 1 ) ( x 1 y 1 ). We generate G, P ϕ and µ 0 such that µ 0 belongs to the answer of P ϕ over G iff ϕ is valid: G : {(a,tv,0), (a,tv,1), (a,false,0), (a,true,1)} P ψ : ((a,true,?x 1 ) UNION (a,false,?y 1 )) AND ((a,false,?x 1 ) UNION (a,true,?y 1 )) P ϕ : µ 0 : M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 43 / 54

128 PSPACE-hardness: A closer look Assume ϕ = x 1 y 1 ψ, where ψ = (x 1 y 1 ) ( x 1 y 1 ). We generate G, P ϕ and µ 0 such that µ 0 belongs to the answer of P ϕ over G iff ϕ is valid: G : {(a,tv,0), (a,tv,1), (a,false,0), (a,true,1)} P ψ : ((a,true,?x 1 ) UNION (a,false,?y 1 )) AND ((a,false,?x 1 ) UNION (a,true,?y 1 )) P ϕ : (a,true,?b 0 ) OPT (P 1 OPT (Q 1 AND P ψ )) µ 0 : M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 43 / 54

129 PSPACE-hardness: A closer look Assume ϕ = x 1 y 1 ψ, where ψ = (x 1 y 1 ) ( x 1 y 1 ). We generate G, P ϕ and µ 0 such that µ 0 belongs to the answer of P ϕ over G iff ϕ is valid: G : {(a,tv,0), (a,tv,1), (a,false,0), (a,true,1)} P ψ : ((a,true,?x 1 ) UNION (a,false,?y 1 )) AND ((a,false,?x 1 ) UNION (a,true,?y 1 )) P ϕ : (a,true,?b 0 ) OPT (P 1 OPT (Q 1 AND P ψ )) µ 0 : {?B 0 1} M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 43 / 54

130 PSPACE-hardness: A closer look P ϕ : (a,true,?b 0 ) OPT (P 1 OPT (Q 1 AND P ψ )) P 1 : (a,tv,?x 1 ) Q 1 : (a,tv,?x 1 ) AND (a,tv,?y 1 ) AND (a,false,?b 0 ) M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 44 / 54

131 PSPACE-hardness: A closer look P ϕ : (a,true,?b 0 ) OPT (P 1 OPT (Q 1 AND P ψ )) P 1 : (a,tv,?x 1 ) Q 1 : (a,tv,?x 1 ) AND (a,tv,?y 1 ) AND (a,false,?b 0 ) P 1?X 1 0 Q 1?X 1 0?Y 1 i?b 0 0?B 0 1?X 1 1?X 1 1?Y 1 j?b 0 0 M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 44 / 54

136 Data complexity is polynomial Theorem (PAG06) When patterns are consider to be fixed (data complexity), the evaluation problem is in LOGSPACE. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 45 / 54

137 Data complexity is polynomial Theorem (PAG06) When patterns are consider to be fixed (data complexity), the evaluation problem is in LOGSPACE. Proof idea From data complexity of first order logic. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 45 / 54

138 A procedural semantics Suggestion of the W3C to evaluate query A OPT(B OPTC): First compute the mappings that match A, then check which of these mappings match B, and for those who match B check whether they also match C. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 46 / 54

139 A procedural semantics Suggestion of the W3C to evaluate query A OPT(B OPTC): First compute the mappings that match A, then check which of these mappings match B, and for those who match B check whether they also match C. Depth first traversal of queries parse trees. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 46 / 54

140 A procedural semantics Suggestion of the W3C to evaluate query A OPT(B OPTC): First compute the mappings that match A, then check which of these mappings match B, and for those who match B check whether they also match C. Depth first traversal of queries parse trees. As opposed to the bottom-up evaluation induced by the compositional semantics. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 46 / 54

141 A procedural semantics Consider: (A AND (B OPT (C OPT D))) AND A OPT B OPT C Algebraic semantics: induces the usual bottom up evaluation. Alternative semantics: depth first traversal of the parse tree. Similar to the procedural semantics of Jena/ARQ Navigational semantics of nested OPTs in official SPARQL (April 2006) These two evaluation algorithms do not always coincide. D M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 47 / 54

154 A procedural semantics Depth first traversal evaluation: Efficient (greedy): uses intermediate results to avoid some computations. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 48 / 54

155 A procedural semantics Depth first traversal evaluation: Efficient (greedy): uses intermediate results to avoid some computations. non-compositional AND of patterns is non-commutative M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 48 / 54

156 Well designed patterns Definition A graph pattern is well designed iff for every OPT in the pattern ( ( A OPT B ) ) if a variable occurs inside B and anywhere outside the OPT, then the variable must also occur inside A. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 49 / 54

160 Well designed patterns Definition A graph pattern is well designed iff for every OPT in the pattern ( ( A OPT B ) ) if a variable occurs inside B and anywhere outside the OPT, then the variable must also occur inside A. Example ( ( (?Y, name, paul) OPT (?X, ,?z) ) AND (?X, name, john) ) M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 49 / 54

164 Well designed patterns and PSPACE-hardness In the PSPACE-hardness reduction we use this formula: P ϕ : (a,true,?b 0 ) OPT (P 1 OPT (Q 1 AND P ψ )) P 1 : (a,tv,?x 1 ) Q 1 : (a,tv,?x 1 ) AND (a,tv,?y 1 ) AND (a,false,?b 0 ) M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 50 / 54

165 Well designed patterns and PSPACE-hardness In the PSPACE-hardness reduction we use this formula: P ϕ : (a,true,?b 0 ) OPT (P 1 OPT (Q 1 AND P ψ )) P 1 : (a,tv,?x 1 ) Q 1 : (a,tv,?x 1 ) AND (a,tv,?y 1 ) AND (a,false,?b 0 ) It is not well-designed: B 0 M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 50 / 54

166 Well designed patterns Theorem (PAG06) For well designed graph patterns: depth first traversal evaluation = compositional semantics M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 51 / 54

167 Classical optimization is not directly applicable. Classical optimization assumes null rejection. null rejection: the join/outer join condition must fail in the presence of null. SPARQL operations are not null rejecting. by definition of compatible mappings. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 52 / 54

170 Well designed graph patterns and optimization Well designed patterns are suitable for reordering optimization: Theorem (OPT Normal Form) Every well designed pattern is equivalent to one of the form ( (t 1 AND AND t k ) OPT O 1 ) ) OPT O n ) where each t i is a triple pattern, and each O j is a pattern of the same form. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 53 / 54

171 Well designed graph patterns and optimization Well designed patterns are suitable for reordering optimization: Theorem (OPT Normal Form) Every well designed pattern is equivalent to one of the form ( (t 1 AND AND t k ) OPT O 1 ) ) OPT O n ) where each t i is a triple pattern, and each O j is a pattern of the same form. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 53 / 54

172 Final remarks RDFS can be considered a new data model. It is the W3C s recommendation for describing Web metadata. RDFS can definitely benefit from database technology. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 54 / 54

173 Final remarks RDFS can be considered a new data model. It is the W3C s recommendation for describing Web metadata. RDFS can definitely benefit from database technology. RDFS: M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 54 / 54

174 Final remarks RDFS can be considered a new data model. It is the W3C s recommendation for describing Web metadata. RDFS can definitely benefit from database technology. RDFS: Formal semantics, M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 54 / 54

175 Final remarks RDFS can be considered a new data model. It is the W3C s recommendation for describing Web metadata. RDFS can definitely benefit from database technology. RDFS: Formal semantics, entailment of RDFS graphs, M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 54 / 54

176 Final remarks RDFS can be considered a new data model. It is the W3C s recommendation for describing Web metadata. RDFS can definitely benefit from database technology. RDFS: Formal semantics, entailment of RDFS graphs, normal forms for RDFS graphs (closure and core). M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 54 / 54

177 Final remarks RDFS can be considered a new data model. It is the W3C s recommendation for describing Web metadata. RDFS can definitely benefit from database technology. RDFS: Formal semantics, entailment of RDFS graphs, normal forms for RDFS graphs (closure and core). SPARQL: M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 54 / 54

178 Final remarks RDFS can be considered a new data model. It is the W3C s recommendation for describing Web metadata. RDFS can definitely benefit from database technology. RDFS: Formal semantics, entailment of RDFS graphs, normal forms for RDFS graphs (closure and core). SPARQL: Formal semantics, M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 54 / 54

179 Final remarks RDFS can be considered a new data model. It is the W3C s recommendation for describing Web metadata. RDFS can definitely benefit from database technology. RDFS: Formal semantics, entailment of RDFS graphs, normal forms for RDFS graphs (closure and core). SPARQL: Formal semantics, complexity of query evaluation, M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 54 / 54

180 Final remarks RDFS can be considered a new data model. It is the W3C s recommendation for describing Web metadata. RDFS can definitely benefit from database technology. RDFS: Formal semantics, entailment of RDFS graphs, normal forms for RDFS graphs (closure and core). SPARQL: Formal semantics, complexity of query evaluation, query optimization. M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 54 / 54

181 Final remarks RDFS can be considered a new data model. It is the W3C s recommendation for describing Web metadata. RDFS can definitely benefit from database technology. RDFS: Formal semantics, entailment of RDFS graphs, normal forms for RDFS graphs (closure and core). SPARQL: Formal semantics, complexity of query evaluation, query optimization. Updating M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 54 / 54

182 Final remarks RDFS can be considered a new data model. It is the W3C s recommendation for describing Web metadata. RDFS can definitely benefit from database technology. RDFS: Formal semantics, entailment of RDFS graphs, normal forms for RDFS graphs (closure and core). SPARQL: Formal semantics, complexity of query evaluation, query optimization. Updating... M. Arenas SPARQL: Un Lenguaje de Consulta para la Web Semántica 54 / 54