1. On Provenance of Queries on Linked Web Data
1,2Yannis Theoharis, 2Irini Fundulaki, 3,2Grigoris Karvounarakis and 1,2Vassilis Christophides
1Institute of Computer Science, FORTH and
2Computer Science Department, University of Crete
3LogicBox, USA

2. What is “Linked Data” W3C Linking Open Data
publish various open datasets as RDF on the Web
set RDF typed links between data items from different data sources. 2

3. Motivation: Linked Data Processing
Data is:
fetched from heterogeneous sources
integrated
materialized in RDF
made available via SPARQL
Range of computations
SPARQL queries
Complex programs (logic or procedular) 3

4. Provenance Aware Applications
Trust assessment
trustworthiness
Access control
confidentiality level
Data cleaning
validity
Curated databases
source data origin
All these applications need to represent and store the relation of the input with the output of data processes
gain efficiency
impossible without
provenance 4

5. Data Provenance Models
Annotation Models:
annotation computation coupled with a particular application and a particular assignment of source data annotations R1 R2
R1 R2 X Y
Annot. a b t c d Y Z
Annot. b e X Y Z
Annot. a b e
t: trusted
f: untrusted t f f t
query recomputation!
Abstract Provenance Models:
abstract provenance tokens and operators are substituted by appropriate concrete tokens for a particular application and assignment R1 R2
R1 R2 X Y
Annot. a b c1 c d c2 Y Z
Annot. b e c3 X Y Z
Annot. a b e
c1 * c3 t t f
t Λ f
t Λ t 5

6. This Talk
“Can previous work on abstract provenance models be leveraged for SPARQL” ?
NO: due to the OPTIONAL (similar to the SQL left outer join) operator
YES: for the positive (without OPTIONAL) fragment of SPARQL
We present our ongoing work on a SPARQL abstract provenance model.
Challenge: to capture the form of negation that OPTIONAL introduces 6

7. Outline SPARQL algebra Abstract Provenance Models for Positive SPARQL
Limitations of Previous Models
Towards a SPARQL Provenance Model 7

8. Outline SPARQL algebra Abstract Provenance Models for Positive SPARQL
Limitations of Previous Models
Towards a SPARQL Provenance Model 8

9. SPARQL (1/2) SPARQL: W3C Recommendation language to Query RDF data.
triple patterns
(?x, ?y, e)
mappings
{(?x,d),(?y,b)}
{(?x,f),(?y,g)}
Compose
Filter
{ … }
Select
Construct/
Describe
(?x, ?y, e)
constant
variables
Triple Set S P O a b c d e f g Ω1 ?x ?y d b f g μ1 μ2 9

10. SPARQL (2/2) SPARQL algebra defines 5 operators on mapping bags
Unary ops:
π (projection),
σ (selection, also called filtering)
Binary ops:
U (union)
(join)
(optional)
Positive SPARQL (SPARQL+)
μ and μ’ are compatible (μ ~ μ’),
if they agree
in their common variables
μ1 ~ μ4
μ3 ~ μ4
μ2 ~ μ4 Ω1 Ω1 Ω Ω2 Ω2
Ω1 Ω2
Ω Ω2
σ?x=a (Ω)
π?x (Ω) ?x ?y a b c d e - ?x ?y a b c d Ω1 ?x ?y a b c d e ?y ?z b f ?y ?z b f Ω2
Ω1 U Ω2 ?x ?y ?z a b f e ?x ?y ?z a b f c d - ?x ?y a b c μ1 μ2 μ3 μ1 μ2 μ4 μ3
μ4 = μ1 U μ3 μ2
μ5 = μ1 U μ4
μ6 = μ3 U μ4 ?x ?y a b ?x ?z c d
Ω1 \ Ω2
Ω Ω2 ?x ?y ?z a b - c d ?x a d μ1 μ2 μ1 μ2
card(μ1) = 2
card(μ2) = 1 μ1 μ2
?z is unbound in μ1 10

11. Outline SPARQL algebra Abstract Provenance Models for Positive SPARQL
Limitations of Previous Models
Towards a SPARQL Provenance Model 11

12. Abstract Provenance Models
triple patterns
(?x, ?y, e)
mappings
{(?x,d),(?y,b)}
{(?x,f),(?y,g)}
Compose
Filter
{ … }
Select
Provenance
Most
informative
How
Trio
Why
Lineage
Abstract provenance models encode the query operators in different level of detail
Expressiveness vs efficiency (annotation storage and computation time)
Less
informative 12

13. Abstract Provenance Models for SPARQL+
Previous models are defined for positive relational algebra
Positive relational operators are monotonic
The addition (removal) of a tuple can only result in additional (removed) tuples in the output
This also holds for SPARQL+ (projection, union, join)
Previous models suffice for SPARQL+ 13

14. Outline SPARQL algebra Abstract Provenance Models for Positive SPARQL
Limitations of Previous Models
Towards a SPARQL Provenance Model 14

15. Boolean trust assessment (SPARQL)
Trusted:
μ1, μ2, μ3, μ4
Trusted:
μ1, μ2, μ4 Ω1 Ω2
Ω1 \ Ω2 ?x ?y d b f g ?y ?z b c e h
Ω1 \ Ω2 μ1 μ2
μ3μ4 ?x ?y ?z d b - f g ?x ?y f g
μ1μ2 μ2
boolean trust semantics
set semantics on trusted mappings
Ω Ω2
Ω Ω2 ?x ?y ?z d b c f g - ?x ?y ?z d b - f g
μ5μ2
μ1 μ2
and \ are not monotonic:
μ3 becomes untrusted
μ5 becomes untrusted
and
μ1 becomes trusted
in Ω Ω2 15

16. Perm μ1 μ2 μ3μ4 Ω1 Ω1 \ Ω2 Ω1 Ω2 Ω2 Intuitively, (f, g) is in Ω1 \ Ω2
Ω Ω2 ?x ?y d b f g ?x ?y
?y2
?z2 f g b c e h ?x ?y ?z
?x1
?y1
?y2
?z2 d b c f g - e h μ1 μ2 Ω2 ?y ?z b c e h
Intuitively, (f, g) is in Ω1 \ Ω2
because it is not compatible
with neither μ3 nor μ4
μ3μ4
(d, b, c) is in Ω1 \ Ω2
due to the join
between μ1 and μ3
If μ3 becomes untrusted, Perm
infers that (d, b, c) becomes untrusted, but
cannot infer that (d, b, -) should become trusted 16

17. RDF Meta Knowledge & M-semiringsΩ1
Ω1 \ Ω2 ?x ?y d b c1 f g c2 ?x ?y
RDF MK
M-semirings f g
c2 Λ (c3Vc4)
c = c2 μ1 μ2 μ2 t t t Ω2
Ω Ω2 ?y ?z b c c3 e h c4
μ3μ4 ?x ?y ?z
RDF MK
M-semirings d b c
c1 Λ c3
c1 * c3 f g -
c2 Λ (c3Vc4) c2 f t
μ5μ2 f f t t
Like Perm, RDF Meta Knowledge and M-semirings infer that μ5 is untrusted but can not infer that μ1: (d, b, -) is trusted. 17

18. Outline SPARQL algebra Abstract Provenance Models for Positive SPARQL
Limitations of Previous Models
Towards a SPARQL Provenance Model 18

19. A Third Operation for Compatibility (1/2)
Take care about compatible mappings
Only one between μ1, μ5 can appear in the result
Keep provenance information for both of them ! Ω1
Ω Ω2 = (Ω Ω2) U (Ω1 \ Ω2) ?x ?y d b c1 f g c2 ?x ?y ?z
How
SPARQL Prov. d b c
c1*c3 -
No Info
c1*A(μ1, μ3) f g c2 μ1 μ2 t
μ5μ1μ2
(t Λ t) = t
(t Λ f) = f t f ? Ω2 t ?y ?z b c c3 e h c4
μ3μ4 t f t
A(μ1, μ3) =
f, if μ1 ~ μ3 and c3 = t
t, else 19

20. A Third Operation for Compatibility (2/2)
Ω Ω2 = (Ω Ω2) U (Ω1 \ Ω2) ?x ?y ?z
How
SPARQL Prov. d b c
c1*c3 -
No Info
c1*A(μ1, μ3) f g c2
μ5μ1μ2
A is a binary operator on mappings
Determines whether the mapping exist in the result or not
If yes, its provenance equals the positive provenance part, e.g. c1 for c1*A(μ1, μ3)
In general,
A(μ1, μ3) =
0, if μ1 ~ μ3 and c3 ≠ 0
1, else
0: the neutral element for +
1: the neutral element for * 20

21. SPARQL Provenance Operators
Two types of operators
on provenance tokens, i.e. + and * (for SPARQL+)
on mappings, i.e. A (for and \)
Good news:
Every triple of the dataset is uniquely annotated.
Why not to use annotations as mapping identifiers in A?
Due to the projection operator… 21

22. Enrich Tokens with Schema Information
A( (c1, S1), (c2, S2) ) =
0, if πS1 (μ1) ~ πS2 (μ2) and c2 ≠ 0
1, else
A(c1, c2) =
0, if μ1 ~ μ2 and c2 ≠ 0
1, else
Use tokens (c1, c2…) as mapping ids in A expressions
But, μ1 ~ μ2 might hold, while π?y,?z (μ1) ~ π ?y,?z (μ2)
Tokens don’t suffice, keep pairs token-schema Ω
π?y,?z (Ω) ?x ?y ?z a b c d - ?x ?y ?z
Prov. a b c
(c1, {?x, ?y, ?z}) d -
(c2, {?x, ?y, ?z}) ?y ?z
Prov. b c
(c1, {?y, ?z}) -
(c2, {?y, ?z}) μ1 μ2 22

23. Towards a SPARQL Provenance Model
Define an algebra on token-schema pairs
3 operations
2 for SPARQL operators
1 for compatibility
What if there is no projection (or projection is not allowed to be pushed down) ?
annotations suffice (no need for schema information),
still in need of the compatibility operator
What if there is no Optional ?
previous models suffice, e.g. How 23

24. Future Work SPARQL Provenance Model
Extent model expressiveness to capture other computations on Linked Data
Logic explanations
Implementation 24

25. Questions ?