Handling time in RDF

Transcription

1 Time in RDF p. 1/15 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

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

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

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

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

6 Time in RDF p. 4/15 Temporal Graph [3,N ow] Student [0,N ow] [0,N ow] Grad UnderGrad [0,N ow] Ph.D M.Sc [3,4] [0,3] [4,N ow] John

7 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

8 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]

9 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)

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

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

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

13 Time in RDF p. 7/15 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

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

15 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)

16 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.

17 Time in RDF p. 9/15 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. G 1 = τ G 2 iff tcl(g 1 ) = τ G 2 Proposition. Deciding if G is the closure of G is DP-complete.

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

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

20 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 Y 4 Instant temporal tsubj c X Z 5 tpred temporal Instant tobj c

21 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 tsubj c X tpred tobj c temporal 4 Instant V Instant 5

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

23 Time in RDF p. 13/15 Syntax works well (cont.) Theorem. 1. G 1 = τ G 2 implies (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: G 1 = τ G 2 iff (G 1 ) (G 2 )

24 Time in RDF p. 14/15 Querying Temporal RDF Proposal: Conjunctive fragment with interval and point variables aggregate functions constructor of graphs for answers

25 Time in RDF p. 14/15 Querying Temporal RDF Proposal: Conjunctive fragment with interval and point variables aggregate functions constructor of graphs for answers Students who have taken a Master course between year 2000 Students taking Ph.D courses together and the time when this occurred Time intervals when the IT Master program was offered Students applying for jobs at time t after finishing their Ph.D program in no more than 4 years

26 Time in RDF p. 15/15 What we have: 1. Semantics for Temporal RDF graphs 2. Syntax to incorporate the framework into standard RDF 3. Sound and complete inference rules for temporal graphs 4. Complexity bounds showing temporal RDF preserves complexity of RDF 5. Sketch of Temporal RDF query language