A Context-Based Semantics for SPARQL Property Paths over the Web

A Context-Based Semanticsfor SPARQL Property Paths

over the Web

Olaf Hartig and Giuseppe Pirrò

A Context-Based Semantics for SPARQL Property Paths over the Web - Olaf Hartig and Giuseppe Pirrò 2

Puzzle

Give me the URL of every Web document that mentions its own URL somewhere in its text.

A Context-Based Semanticsfor SPARQL Property Paths

over the Web

Olaf Hartig and Giuseppe Pirrò

Disclaimer:

This work is not about reasoning.


Property Path Pattern (PP Pattern)

(α, path, β)

variable, IRI, literal (orbnode), respectively

property path expression


Property Path Expression

(α, path, β)

variable, IRI, literal (orbnode), respectively

path := p | (IRI)

^path | (inverse)

path / path | (concatenation)

(path | path) | (alternative)

(path)* (recursive concatenation)


path := p | (IRI)

^path | (inverse)

path / path | (concatenation)

(path | path) | (alternative)

(path)* (recursive concatenation)

Example

( ex:bob , foaf:knows / (foaf:made | ^foaf:maker) , ?x )

( ex:bob , foaf:knows , ex:alice )( ex:alice , foaf:made , a:doc1 )

( e:objA , foaf:maker , ex:alice )

Data:

μ1 = { ?x → a:doc1 }

μ2 = { ?x → e:objA }


Example



( e:objA , foaf:maker , ex:alice )G =

⟦P⟧G = { μ1, μ2 }

P =

μ1 = { ?x → a:doc1 }

μ2 = { ?x → e:objA }


Example




P =


Example

( ex:bob , foaf:knows / (foaf:made | ^foaf:maker) , ?x )P =

( ex:alice , foaf:made , a:doc1 )

( ex:bob , foaf:knows , ex:alice )



Example

( ex:bob , foaf:knows / (foaf:made | ^foaf:maker) , ?x )P =

⟦P⟧W = ??

What is the expected result of executing Pas a query over the Web of Linked Data?

Can this expected result be computed in practice?


Contributions

● Formal definition of a context-based query semantics to use PP patterns (and SPARQL patterns constructed thereof) as queries over Linked Data in a well-defined manner.

● Web-safeness property of such queries (i.e., the fundamental feasibility of executing such a query in practice over the WWW)

● Decidable syntactic property to identify queries that are Web safe


⟦( u1, p, ?x )⟧W =

Context-Based Query Semantics

…( u1, p, u2 )( u1, p, u3 )

...

{ μ1, μ2 } μ1 = { ?x → u2 } μ2 = { ?x → u3 }


⟦( u1, p / q , ?x )⟧W =


…( u1, p, u2 )( u1, p, u3 )

...

{ μ1, μ2 }

μ1 = { ?x → b } μ2 = { ?x → a }

…( u3, q, a )

...

…( u2, q, b )

...



= { μ={ ?x → u } | for every URI u s.t. ( u, p, a ) in ctxt(u) }⟦( ?x, p, a )⟧W


Main Result

Theorem: A PP-based SPARQL pattern P is Web-safe if cbvars( P | Ø ) = vars(P),

...where cbvars( P | X ) denotes the set ofconditionally bounded variables of P for agiven set X of variables (see paper).

● Open problem:

– Note that the condition is sufficient only.

– Is there an alternative condition that is sufficient and also necessary (and decidable)?


Summary

● Formal definition of a context-based query semantics to use PP patterns (and SPARQL patterns constructed thereof) as queries over Linked Data in a well-defined manner.

● Web-safeness property of such queries (i.e., the fundamental feasibility of executing such a query in practice over the WWW)

● Decidable syntactic property to identify queries that are Web safe


Backup Slides


Web-Safeness

A PP-based SPARQL pattern P is Web-safe if there exists an algorithm that, for any Web of Linked Data W = (D, adoc), computes ⟦P⟧W without assuming an a-priori availability of information about the sets D and dom(adoc).


Conditionally Bounded Variables

● cbvars( P | X ) denotes the set of conditionally bounded variables of P for a given set X of variables

● Defined recursively for all types of patterns

– If P is ( P1 AND P2 ) s.t. cbvars( P1 | X ) = vars(P1)and cbvars( P2 | X U sbvars(P1) ) = vars(P2), thencbvars( P | X ) = vars(P).

– If P is (u, p, β), then cbvars( P | X ) = vars(P).

– If P is (?x, p, β) s.t. ?x in X, then cbvars( P | X ) = vars(P).

– If P is (?x, p, β) s.t. ?x not in X, then cbvars( P | X ) = Ø.

– etc.









– etc.

Pex = ( ( u1, p, ?x ) AND ( ?x, q, ?y ) )

cbvars( Pex | Ø ) = ?

Example









– etc.

Pex = ( ( u1, p, ?x ) AND ( ?x, q, ?y ) )

cbvars( P1 | Ø ) = {?x} cbvars( P2 | Ø ) = Ø

Example









– etc.

Pex = ( ( u1, p, ?x ) AND ( ?x, q, ?y ) )

cbvars( P1 | Ø ) = {?x} cbvars( P2 | sbvars(P1) )

Example









– etc.

Pex = ( ( u1, p, ?x ) AND ( ?x, q, ?y ) )

cbvars( P1 | Ø ) = {?x} cbvars( P2 | {?x} ) = {?x,?y}

Example









– etc.

Pex = ( ( u1, p, ?x ) AND ( ?x, q, ?y ) )

cbvars( Pex | Ø ) = vars(Pex) = {?x,?y}

Example

A Context-Based Semantics for SPARQL Property Paths over the Web

Science