Handling time in RDF Claudio Gutierrez (Joint work with C. Hurtado - PowerPoint PPT Presentation

Handling time in RDF Claudio Gutierrez (Joint work with C. Hurtado and A. Vaisman) Department of Computer Science Universidad de Chile UPM, Madrid, January 2009 Time in RDF – p. 1/15

Outline • Introducing time into RDF • Temporal RDF Graphs • Semantics of Temporal RDF Graphs • Syntax for Temporal Graphs • Querying Time in RDF Time in RDF – p. 2/15

� � � Introducing time into RDF �� Student �� subC subC � � � � � � � � �� Grad UnderGrad �� subC �� M.Sc �� type �� John �� Time in RDF – p. 3/15

� � � Introducing time into RDF �� Student �� subC subC � � � � � � � � �� Grad UnderGrad �� subC � � subC � � � � � �� Ph.D M.Sc �� type �� John �� Time in RDF – p. 3/15

� � � � Introducing time into RDF �� Student �� subC subC � � � � � � � � �� Grad UnderGrad �� subC � � subC � � � � � �� Ph.D M.Sc �� type �� John �� Time in RDF – p. 3/15

� � � � � Temporal Graph �� Student �� [0 ,Now ] [0 ,Now ] � � � � � � � � � �� Grad UnderGrad �� [3 ,Now ] � � � [0 ,Now ] � � � � �� Ph.D M.Sc �� [3 , 4] [0 , 3] �� [4 ,Now ] John �� Time in RDF – p. 4/15

General Issues • Versioning versus Labeling – Label elements subject to change – Maintain a snapshot of each state of the graph Time in RDF – p. 5/15

General Issues • Versioning versus Labeling – Label elements subject to change – Maintain a snapshot of each state of the graph • Time Points versus Time Intervals. [4 , 31] = [4] ∪ [5] ∪ · · · ∪ [30] ∪ [31] Time in RDF – p. 5/15

General Issues • Versioning versus Labeling – Label elements subject to change – Maintain a snapshot of each state of the graph • Time Points versus Time Intervals. [4 , 31] = [4] ∪ [5] ∪ · · · ∪ [30] ∪ [31] • Temporal Query Language – Point based (variables refer to point times) – Interval based (variables refer to intervals) Time in RDF – p. 5/15

� � RDF Intrinsic Issues • Notion of temporal Entailment | = τ [2 , 7] [5 , 9] �� sc � �� Ph.D Grad Stud �� sc sc [5 , 7] Time in RDF – p. 6/15

� � � � � RDF Intrinsic Issues • Notion of temporal Entailment | = τ [2 , 7] [5 , 9] �� sc � �� Ph.D Grad Stud �� sc sc [5 , 7] • Treatment of temporal Blank Nodes: ? �� | = τ Student Student �� [2 , 3] � � � [2 , 5] [3 , 5] � � � � � �� Mary X John �� Time in RDF – p. 6/15

� � � � � RDF Intrinsic Issues • Notion of temporal Entailment | = τ [2 , 7] [5 , 9] �� sc � �� Ph.D Grad Stud �� sc sc [5 , 7] • Treatment of temporal Blank Nodes: ? �� | = τ Student Student �� [2 , 3] � � � [2 , 5] [3 , 5] � � � � � �� Mary X John �� • Vocabulary for temporal labeling Time in RDF – p. 6/15

Definitions Temporal Triple: an RDF triple with a temporal label, e.g. ( a, b, c )[ t ] Temporal Graph: set of temporal triples Snapshot of graph G at time t : G ( t ) = { ( a, b, c ) : ( a, b, c )[ t ] ∈ G } Notion of temporal entailment G 1 | = τ G 2 Time in RDF – p. 7/15

Semantics Ground Case: G 1 | = τ G 2 if for each t, G 1 ( t ) | = G 2 ( t ) Time in RDF – p. 8/15

Semantics Ground Case: G 1 | = τ G 2 if for each t, G 1 ( t ) | = G 2 ( t ) Non Ground Case: G 1 | = τ G 2 if there are ground instances µ 1 ( G 1 ) and µ 2 ( G 2 ) such that for each t : µ 1 ( G 1 )( t ) | = τ µ 2 ( G 2 )( t ) Time in RDF – p. 8/15

Semantics Ground Case: G 1 | = τ G 2 if for each t, G 1 ( t ) | = G 2 ( t ) Non Ground Case: G 1 | = τ G 2 if there are ground instances µ 1 ( G 1 ) and µ 2 ( G 2 ) such that for each t : µ 1 ( G 1 )( t ) | = τ µ 2 ( G 2 )( t ) Proposition. For ground graphs, G 1 | = τ G 2 implies G 1 ( t ) | = G 2 ( t ) for all times t . Time in RDF – p. 8/15

Semantics (cont.) The temporal closure tcl ( G ) is a maximal set of temporal triples G ′ such that: – G ′ contains G – G is equivalent to G ′ Proposition. = τ G 2 iff tcl ( G 1 ) | G 1 | = τ G 2 Proposition. Deciding if G ′ is the closure of G is DP-complete. Time in RDF – p. 9/15

� � � Syntax for ( a, b, c )[4 , 5] • Point version �� Instant �� a 4 �� Y1 �� temporal � � � � � � � tsubj � � �� Instant �� c X Y2 5 �� tpred temporal tobj �� c �� Time in RDF – p. 10/15

� � � � � � � Syntax for ( a, b, c )[4 , 5] • Point version �� Instant �� a 4 �� Y1 �� temporal � � � � � � � tsubj � � �� Instant �� c X Y2 5 �� tpred temporal tobj �� c �� • Interval version �� a 4 �� initial � � � � tsubj � temporal � �� Interval �� c X Y Z �� tpred � � � � � tobj final � �� c 5 �� Time in RDF – p. 10/15

� � � Syntax (cont.): rules Rule 1-2: Equivalence betwen point and interval versions Rule 3: Normalization of point-version: �� a 4 �� Y �� Instant � � temporal � � � � � � tsubj � � �� c X Z 5 �� Instant tpred temporal tobj �� c �� Time in RDF – p. 11/15

� � � � Syntax (cont.): rules Rule 1-2: Equivalence betwen point and interval versions Rule 3: Normalization of point-version: �� a 4 �� Instant � � � � � � tsubj � � �� Instant �� c X V 5 �� tpred temporal tobj �� c �� Time in RDF – p. 11/15

� � � � � � Syntax works well ( a, b, c )[ m, n ] . ( ) ∗ ( ) ∗ �� . a m �� init � � � � � temp �� Int � �� c X Y Z �� fin � �� c n �� Time in RDF – p. 12/15

Syntax works well (cont.) Theorem. = τ G 2 implies ( G 1 ) ∗ | 1. G 1 | = ( G 2 ) ∗ 2. G 2 | = G 2 implies ( G 1 ) ∗ | = τ ( G 2 ) ∗ 3. ( G ∗ ) ∗ = G and G | = ( G ∗ ) ∗ Theorem. Let ⊢ be the deductive system formed by RDFS rules plus Temporal rules. Then: = τ G 2 iff ( G 1 ) ∗ ⊢ ( G 2 ) ∗ G 1 | Time in RDF – p. 13/15

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