ShEx (Shape Expressions) is a language for expressing constraints on RDF graphs. We consider the problem of SPARQL query containment in the presence of ShEx constraints. We first propose a sound and complete procedure for the problem of containment with ShEx, considering several SPARQL fragments. Particularly our procedure considers OPTIONAL query patterns, that turns out to be an important fragment to be studied with schemas. We then show the complexity bounds of our problem with respect to the fragments considered. To the best of our knowledge, this is the first work addressing SPARQL query containment in the presence of ShEx constraints.

1. SPARQL Query Containment with ShEx Constraints
SPARQL Query Containment with
ShEx Constraints
21st European Conference on Advances in Databases and
Information Systems (ADBIS 2017)
Abdullah Abbas
Pierre Genevès
Cécile Roisin
Nabil Layaïda
24 - 27 September 2017
1/32

2. SPARQL Query Containment with ShEx Constraints
RDF (Resource Description Framework)
RDF Triple
<subject> <predicate> <object>
{
:p1 :named "Alice".
:p1 :likes :tennis.
:p2 :named "Bob".
:p2 :likes :soccer.
}
2/32

3. SPARQL Query Containment with ShEx Constraints
RDF (Resource Description Framework)
RDF Triple
<subject> <predicate> <object>
{
:p1 :named "Alice".
:p1 :likes :tennis.
:p2 :named "Bob".
:p2 :likes :soccer.
}
p1
“Alice”named
2/32

4. SPARQL Query Containment with ShEx Constraints
RDF (Resource Description Framework)
RDF Graph
<subject> <predicate> <object>
{
:p1 :named "Alice".
:p1 :likes :tennis.
:p2 :named "Bob".
:p2 :likes :soccer.
}
p1
“Alice”
tennis
p2
“Bob”
soccer
named
likes
named
likes
2/32

5. SPARQL Query Containment with ShEx Constraints
SPARQL Query
RDF Graph
{
:p1 :named "Alice".
:p1 :likes :tennis.
:p2 :named "Bob".
:p2 :likes :soccer.
}
p1
“Alice”
tennis
p2
“Bob”
soccer
named
likes
named
likes
3/32

6. SPARQL Query Containment with ShEx Constraints
SPARQL Query
RDF Graph
{
:p1 :named "Alice".
:p1 :likes :tennis.
:p2 :named "Bob".
:p2 :likes :soccer.
}
SPARQL query
SELECT ?name
WHERE
{
?p :likes :tennis.
?p :named ?name.
}
p1
“Alice”
tennis
p2
“Bob”
soccer
named
likes
named
likes
3/32

7. SPARQL Query Containment with ShEx Constraints
SPARQL Query
RDF Graph
{
:p1 :named "Alice".
:p1 :likes :tennis.
:p2 :named "Bob".
:p2 :likes :soccer.
}
SPARQL query
SELECT ?name
WHERE
{
?p :likes :tennis.
?p :named ?name.
}
p1
“Alice”
tennis
p2
“Bob”
soccer
?p
?name
tennis
named
likes
named
likes
named
likes
3/32

8. SPARQL Query Containment with ShEx Constraints
SPARQL Query
RDF Graph
{
:p1 :named "Alice".
:p1 :likes :tennis.
:p2 :named "Bob".
:p2 :likes :soccer.
}
SPARQL query
SELECT ?name
WHERE
{
?p :likes :tennis.
?p :named ?name.
}
p1
“Alice”
tennis
p2
“Bob”
soccer
?p
?name
tennis
named
likes
named
likes
named
likes
3/32

9. SPARQL Query Containment with ShEx Constraints
Supported SPARQL Fragments
Basic SPARQL Query
SELECT ?name
WHERE
{
?p :likes :tennis.
?p :named ?name.
}
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10. SPARQL Query Containment with ShEx Constraints
Supported SPARQL Fragments
Basic SPARQL Query
SELECT ?name
WHERE
{
?p :likes :tennis.
?p :named ?name.
}
UNION
SELECT ?name
WHERE
{
?p :likes :tennis.
?p :named ?name.
}
UNION
{
?p :likes :tennis.
?p :named ?name.
}
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11. SPARQL Query Containment with ShEx Constraints
Supported SPARQL Fragments
OPTIONAL
SELECT ?name, ?other
WHERE
{
?p :likes :tennis.
?p :named ?name.
}
OPTIONAL
{
?p :likes ?other.
?p :named ?name.
}
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12. SPARQL Query Containment with ShEx Constraints
ShEx Constraints
ShEx Constraints
<Person> {
:named xsd:string ;
:likes @<Sport>
}
<Sport> {
:category xsd:string
}
RDF Graph 1 (Not valid)
{
:p1 :named "Bob".
:p1 :likes :soccer.
}
RDF Graph 2 (Valid)
{
:p2 :named "Bob".
:p2 :likes :soccer.
:soccer :category "team sports"
}
6/32

13. SPARQL Query Containment with ShEx Constraints
Motivation:
SPARQL query containment is well studied in the
literature.
Query containment is useful for query planning and
optimization.
7/32

14. SPARQL Query Containment with ShEx Constraints
Motivation:
SPARQL query containment is well studied in the
literature.
Query containment is useful for query planning and
optimization.
RDF documents in real life applications are constrained.
ShEx is an emerging schema language (FHIR, WebIndex).
Containment without constraints → False negatives
7/32

15. SPARQL Query Containment with ShEx Constraints
Motivation:
SPARQL query containment is well studied in the
literature.
Query containment is useful for query planning and
optimization.
RDF documents in real life applications are constrained.
ShEx is an emerging schema language (FHIR, WebIndex).
Containment without constraints → False negatives
Purpose:
SPARQL query containment in the presence of ShEx
constraints.
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16. SPARQL Query Containment with ShEx Constraints
Motivation:
SPARQL query containment is well studied in the
literature.
Query containment is useful for query planning and
optimization.
RDF documents in real life applications are constrained.
ShEx is an emerging schema language (FHIR, WebIndex).
Containment without constraints → False negatives
Purpose:
SPARQL query containment in the presence of ShEx
constraints.
How?
We benefit from existing containment solvers, and ShEx
validators. We apply novel query transformations that does
not increase the complexity of containment.
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17. SPARQL Query Containment with ShEx Constraints
Table of Contents
1 Introduction
Containment Overview
ShEx (Shape Expressions)
2 Containment Examples with ShEx Constraints
SPARQL (Conjunctive)
SPARQL (with OPTIONALs)
3 Containment Procedure Definition
Procedure Overview
Query Transformation
ShEx Schema Transformation
Containment Procedure Summary
Complexity
4 Alternative Method
5 Conclusion
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18. SPARQL Query Containment with ShEx Constraints
Introduction
Table of Contents
1 Introduction
Containment Overview
ShEx (Shape Expressions)
2 Containment Examples with ShEx Constraints
SPARQL (Conjunctive)
SPARQL (with OPTIONALs)
3 Containment Procedure Definition
Procedure Overview
Query Transformation
ShEx Schema Transformation
Containment Procedure Summary
Complexity
4 Alternative Method
5 Conclusion
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19. SPARQL Query Containment with ShEx Constraints
Introduction
Containment Overview
Containment Overview
Query 1 Query 2
For any dataset, the results of Query 1 are contained in the
results of Query 2.
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20. SPARQL Query Containment with ShEx Constraints
Introduction
Containment Overview
Containment Overview
Query 1 Query 2
For any dataset, the results of Query 1 are contained in the
results of Query 2.
Containment Solver:
Q1
Q2
Containment
Solver
(𝑸 𝟏 ⊑ 𝑸 𝟐)
(𝑸 𝟏 ⋢ 𝑸 𝟐)
No
Yes
Input queries Results
10/32

21. SPARQL Query Containment with ShEx Constraints
Introduction
Containment Overview
Containment Overview
Query 1 Query 2
For any dataset, the results of Query 1 are contained in the
results of Query 2.
Example:
RDF Data (Big)
SELECT* {
?x name ?name.
?x role manager. }
Query 1
SELECT * {
?x name ?name.
?x role ?role. }
Query 2 Query 2 Results
Query 1 Results
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22. SPARQL Query Containment with ShEx Constraints
Introduction
Containment Overview
Containment Overview
Query 1 Query 2
For any dataset, the results of Query 1 are contained in the
results of Query 2.
Example:
RDF Data (Big)
SELECT* {
?x name ?name.
?x role manager. }
Query 1
SELECT * {
?x name ?name.
?x role ?role. }
Query 2 Query 2 Results
Query 1 Results
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23. SPARQL Query Containment with ShEx Constraints
Introduction
ShEx (Shape Expressions)
ShEx (Shape Expressions)
What is ShEx?
ShEx is an RDF constraint language.
Validate RDF documents
ShEx uses logical operators to define constraints inductively:
e ::= | Σ × Γ | e∗ | e[m;n] | (e|e ) | (e e )
11/32

24. SPARQL Query Containment with ShEx Constraints
Introduction
ShEx (Shape Expressions)
ShEx (Shape Expressions)
ShEx is an RDF constraint language.
Validate RDF documents
Definition (ShEx Expression)
Given a set of edge labels (Σ), and a set of types (Γ), then
Σ × Γ is a shape expression. ShEx uses logical operators to
define constraints inductively:
e ::= | Σ × Γ | e∗ | e[m;n] | (e|e ) | (e e )
Definition (ShEx Schema)
A ShEx schema is a tuple S = (Σ, Γ, δ), where δ is a type
definition function that maps elements of Γ to shape
expressions e over Σ × Γ.
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25. SPARQL Query Containment with ShEx Constraints
Introduction
ShEx (Shape Expressions)
Containment with ShEx Definition
Containment with ShEx: Query 1 S Query 2
For any dataset valid with respect to the ShEx schema S, the
results of Query 1 are contained in the results of Query 2.
Containment Solver:
Q1
Q2
Containment
Solver
(𝑸 𝟏 ⊑ 𝑺 𝑸 𝟐)
(𝑸 𝟏 ⋢ 𝑺 𝑸 𝟐)
No
Yes
Input queries & schema Results
Schema (S)
13/32

26. SPARQL Query Containment with ShEx Constraints
Introduction
ShEx (Shape Expressions)
Containment with ShEx Definition
Containment with ShEx: Query 1 S Query 2
For any dataset valid with respect to the ShEx schema S, the
results of Query 1 are contained in the results of Query 2.
Containment Solver:
Q1
Q2
Containment
Solver
(𝑸 𝟏 ⊑ 𝑺 𝑸 𝟐)
(𝑸 𝟏 ⋢ 𝑺 𝑸 𝟐)
No
Yes
Input queries & schema Results
Schema (S)
Why query containment with ShEx?
More containment cases can be inferred.
13/32

27. SPARQL Query Containment with ShEx Constraints
Containment Examples with ShEx Constraints
Table of Contents
1 Introduction
Containment Overview
ShEx (Shape Expressions)
2 Containment Examples with ShEx Constraints
SPARQL (Conjunctive)
SPARQL (with OPTIONALs)
3 Containment Procedure Definition
Procedure Overview
Query Transformation
ShEx Schema Transformation
Containment Procedure Summary
Complexity
4 Alternative Method
5 Conclusion
14/32

28. SPARQL Query Containment with ShEx Constraints
Containment Examples with ShEx Constraints
SPARQL (Conjunctive)
SPARQL (Conjunctive)
Query 1
SELECT * WHERE {
?p :named ?name .
?p :likes "tennis". }
Query 2
SELECT * WHERE {
?p :named ?name .
?p :plays "soccer" }
Query 1 Query 2
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29. SPARQL Query Containment with ShEx Constraints
Containment Examples with ShEx Constraints
SPARQL (Conjunctive)
SPARQL (Conjunctive)
Query 1 (No results)
SELECT * WHERE {
?p :named ?name .
?p :likes "tennis". }
Query 2
SELECT * WHERE {
?p :named ?name .
?p :plays "soccer" }
Query 1 Query 2
More Containment with ShEx?
ShEx Schema (S)
<Person> {
:named xsd:string ;
:plays xsd:string }
Query 1 S Query 2
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30. SPARQL Query Containment with ShEx Constraints
Containment Examples with ShEx Constraints
SPARQL (with OPTIONALs)
SPARQL (with OPTIONALs)
OPTIONAL patterns in queries are more interesting for
query static analysis with constraints:
Semantics: Only get extended results if available.
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31. SPARQL Query Containment with ShEx Constraints
Containment Examples with ShEx Constraints
SPARQL (with OPTIONALs)
SPARQL (with OPTIONALs)
ShEx Schema (S)
<Product> {
:name xsd:string ;
:expiryDate xsd:date ;
:producer @<Company> + ;
:feature xsd:string }
Query 1
{ ?x :producer :p1 . ?x :feature "feature 1" }
OPTIONAL
{ ?x :feature "feature 2" . ?x :expiryDate ?d }
Query 2
{ ?x :producer ?y . ?x :feature "feature 1"}
17/32

32. SPARQL Query Containment with ShEx Constraints
Containment Examples with ShEx Constraints
SPARQL (with OPTIONALs)
SPARQL (with OPTIONALs)
ShEx Schema (S)
<Product> {
:name xsd:string ;
:expiryDate xsd:date ;
:producer @<Company> + ;
:feature xsd:string }
Query 1
{ ?x :producer :p1 . ?x :feature "feature 1" }
OPTIONAL
{ ?x :feature "feature 2" . ?x :expiryDate ?d }
Query 2
{ ?x :producer ?y . ?x :feature "feature 1"}
Results: Query 1 S Query 2
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33. SPARQL Query Containment with ShEx Constraints
Containment Examples with ShEx Constraints
SPARQL (with OPTIONALs)
SPARQL (with OPTIONALs)
Complex OPTIONAL Query
{ :product1 :label ?productLabel . }
OPTIONAL {
?offer :product :product1 .
?offer :price ?price .
?offer :vendor ?vendor } .
OPTIONAL {
?review :reviewFor :product1 .
?review :rating ?rating .
}
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34. SPARQL Query Containment with ShEx Constraints
Containment Examples with ShEx Constraints
SPARQL (with OPTIONALs)
SPARQL (with OPTIONALs)
Complex OPTIONAL Query
{ :product1 :label ?productLabel . }
OPTIONAL {
?offer :product :product1 .
?offer :price ?price .
?offer :vendor ?vendor } .
OPTIONAL {
?review :reviewFor :product1 .
OPTIONAL {
?review :reviewer ?reviewer .
OPTIONAL { ?reviewer :name ?revName }} .
?review :rating ?rating .
OPTIONAL {
?rating :nbOfRaters ?n }
}
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35. SPARQL Query Containment with ShEx Constraints
Containment Examples with ShEx Constraints
SPARQL (with OPTIONALs)
Well-designed OPTIONAL Fragment
Definition:
For every subpattern q = (q1 OPT q2) of q and every variable
x occurring in q, it holds that: if x occurs inside q2 and outside
q , then x also occurs inside q1.
Containment of the w.d. OPT fragment is studied. A sound and
complete procedure is available [Leterlier et al., 2012].
+ UNION at top level.
Representation as pattern trees:
((P1 OPT (P11 OPT P111 OPT P112)) OPT P12) OPT P13
P1
P11 P12 P13
P111 P112 19/32

36. SPARQL Query Containment with ShEx Constraints
Containment Procedure Definition
Table of Contents
1 Introduction
Containment Overview
ShEx (Shape Expressions)
2 Containment Examples with ShEx Constraints
SPARQL (Conjunctive)
SPARQL (with OPTIONALs)
3 Containment Procedure Definition
Procedure Overview
Query Transformation
ShEx Schema Transformation
Containment Procedure Summary
Complexity
4 Alternative Method
5 Conclusion
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37. SPARQL Query Containment with ShEx Constraints
Containment Procedure Definition
Procedure Overview
Procedure Overview
Components:
ShEx validator
Containment Solver
Q1
S'
Q'1
SPARQL
Containment Solver
Query
SPARQL Containment
(𝑸′ 𝟏⊑ 𝑸′
𝟐)?
(𝑸 𝟏⊑ 𝑺 𝑸 𝟐)?
SPARQL Containment
with ShEx
≡
P1
𝓡𝓓𝓕
(P1 )
𝓡𝓓𝓕(𝑷n)
(variables  IRIs)
Validate parts of the
transformed pattern
tree and eliminate
the non-valid nodes.
P'1
Q2 Q'2P2
𝓡𝓓𝓕
(P2 )
Validate parts of the
transformed pattern
tree and eliminate
the non-valid nodes.
P'2
Pattern Tree
Pattern Tree
(new)
Results:
Query
Query Transformation
Schema
S 𝓜𝓘𝓝0(𝑺)
Minimals discarding
schema transformation
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38. SPARQL Query Containment with ShEx Constraints
Containment Procedure Definition
Query Transformation
Query Transformation
1- Original Query Pattern (P)
{
?x :producer :p1 .
?x :feature "feature 1"
}
OPTIONAL
{
?x :feature "feature 2" .
?x :expiryDate ?d
}
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39. SPARQL Query Containment with ShEx Constraints
Containment Procedure Definition
Query Transformation
Query Transformation
2- RDF(P)
{
:x :producer :p1 .
:x :feature "feature 1"
}
OPTIONAL
{
:x :feature "feature 2" .
:x :expiryDate :d
}
22/32

40. SPARQL Query Containment with ShEx Constraints
Containment Procedure Definition
Query Transformation
Query Transformation
3- Validate Against Schema S (Part 1)
{
:x :producer :p1 .
:x :feature "feature 1"
}
OPTIONAL
{
:x :feature "feature 2" .
:x :expiryDate :d
}
Not Valid? → Query is equivalent to the empty query!
Valid? → Validate Against Schema S (Part 1 and 2)
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41. SPARQL Query Containment with ShEx Constraints
Containment Procedure Definition
Query Transformation
Query Transformation
3- Validate Against Schema S (Part 1 and 2)
{
:x :producer :p1 .
:x :feature "feature 1" .
}
OPTIONAL
{
:x :feature "feature 2" .
:x :expiryDate :d
}
Not Valid? → Eliminate (Part 2) only!
Valid? → Keep the query as it is!
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42. SPARQL Query Containment with ShEx Constraints
Containment Procedure Definition
ShEx Schema Transformation
ShEx Schema Transformation
Minimal cardinality constraints should be ignored since the
query is not a complete representation of the data.
Example
Assume a ShEx constraint: At least three skills for each person.
Assume a query pattern: {:p1 :skill ?x}
The presence of only one triple is not a violation, the RDF data may
still have three skills for :p1.
Thus minimal cardinality constraints must be ignored.
MIN0(.) is a transformation function that takes a ShEx
document and returns another ShEx document ignoring all
minimal cardinalities.
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43. SPARQL Query Containment with ShEx Constraints
Containment Procedure Definition
Containment Procedure Summary
Containment Procedure Summary
Step 1: (Transformation)
Eliminate pattern tree nodes that are not valid.
Minimal cardinalities are not considered.
Query 1 Query 2
Step 2: (Containment)
Check the new modified queries for containment.
24/32

44. SPARQL Query Containment with ShEx Constraints
Containment Procedure Definition
Containment Procedure Summary
Containment Procedure Summary
Step 1: (Transformation)
Eliminate pattern tree nodes that are not valid.
Minimal cardinalities are not considered.
Query 1 Query 2
Step 2: (Containment)
Check the new modified queries for containment.
Results:
T(Query 1) T(Query 2) ≡ Query 1 S Query 2
24/32

45. SPARQL Query Containment with ShEx Constraints
Containment Procedure Definition
Complexity
Implementation and Theoretical Complexity
Implementation
Queries and ShEx documents transformation implemented using java.
ShEx validator, available from [Boneva et al., 2014] (NP-c)
Containment Solver, available from [Pichler and Skritek, 2014]. (ΠP
2-c)
Complexity of SPARQL containment with ShEx
SPARQL Fragment Without(ShEx) With(ShEx)
BGP [Chandra, 1977] NP-c NP-c
AND-OPT [Pichler, 2014] NP-c NP-c
AND-OPT-(UNION) [Pichler, 2014] ΠP
2-c ΠP
2-c
25/32

46. SPARQL Query Containment with ShEx Constraints
Alternative Method
Table of Contents
1 Introduction
Containment Overview
ShEx (Shape Expressions)
2 Containment Examples with ShEx Constraints
SPARQL (Conjunctive)
SPARQL (with OPTIONALs)
3 Containment Procedure Definition
Procedure Overview
Query Transformation
ShEx Schema Transformation
Containment Procedure Summary
Complexity
4 Alternative Method
5 Conclusion
26/32

47. SPARQL Query Containment with ShEx Constraints
Alternative Method
Alternative Method
We reduce query containment with ShEx into:
FOL (First Order Logic) formula satisfiability.
FOL with only two variable is a decidable FOL fragment
with NEXP-c satisfiability complexity.
It supports SPARQL fragment extensions.
Q1
Q2
Queries encoding
function
Schema encoding
function
Schema (S)
FOLAutomated
Theorem Prover
(𝜻)
𝓐(𝑸 𝟏)⋀¬𝓐(𝑸 𝟐)
axioms
conjecture
FOL
(𝑸 𝟏 ⊑ 𝑺 𝑸 𝟐)
(𝑸 𝟏 ⋢ 𝑺 𝑸 𝟐)
Result
FOL Problem
satisfiable
FOL Problem
unsatisfiable
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48. SPARQL Query Containment with ShEx Constraints
Alternative Method
Alternative Method
We reduce query containment with ShEx into:
FOL (First Order Logic) formula satisfiability.
FOL with only two variable is a decidable FOL fragment
with NEXP-c satisfiability complexity.
It supports SPARQL fragment extensions.
Method 1 Method 2 (FOL)
SPARQL Fragment Without/With(ShEx) Without/With(ShEx)
BGP NP-Complete NEXP
AND-OPT NP-Complete NEXP
AND-OPT-(UNION) ΠP
2-Complete NEXP
AND-OPT-(UNION)-Minus [not supported] NEXP
AND-OPT-(UNION)-FILTER [not supported] NEXP
AND-OPT-(UNION)-PP [not supported] NEXP
AND-OPT-(UNION)-MINUS-FILTER-PP [not supported] NEXP
27/32

49. SPARQL Query Containment with ShEx Constraints
Alternative Method
Alternative Method
We reduce query containment with ShEx into:
FOL (First Order Logic) formula satisfiability.
FOL with only two variable is a decidable FOL fragment
with NEXP-c satisfiability complexity.
It supports SPARQL fragment extensions.
Method 1 Method 2 (FOL)
SPARQL Fragment Without/With(ShEx) Without/With(ShEx)
BGP NP-Complete NEXP
AND-OPT NP-Complete NEXP
AND-OPT-(UNION) ΠP
2-Complete NEXP
AND-OPT-(UNION)-Minus [not supported] NEXP
AND-OPT-(UNION)-FILTER [not supported] NEXP
AND-OPT-(UNION)-PP [not supported] NEXP
AND-OPT-(UNION)-MINUS-FILTER-PP [not supported] NEXP
Method 2 is more complex but supports more fragments
27/32

50. SPARQL Query Containment with ShEx Constraints
Alternative Method
Implementations Tests
2 implementations:
Method 1 (Validation+Containment)
Method 2 (FOL)
Test Queries from the Berlin SPARQL Benchmark
Hand-crafted ShEx schemas
Execution Time (with Method 1) ≈ 800 ms
Execution Time (with Method 2) ≈ 400 ms
Available implementations of FOL automated theorem provers
are highly optimized and efficient!
28/32

51. SPARQL Query Containment with ShEx Constraints
Conclusion
Table of Contents
1 Introduction
Containment Overview
ShEx (Shape Expressions)
2 Containment Examples with ShEx Constraints
SPARQL (Conjunctive)
SPARQL (with OPTIONALs)
3 Containment Procedure Definition
Procedure Overview
Query Transformation
ShEx Schema Transformation
Containment Procedure Summary
Complexity
4 Alternative Method
5 Conclusion
29/32

52. SPARQL Query Containment with ShEx Constraints
Conclusion
Conclusion
Motivation: SPARQL query containment with ShEx
constraints is important (due to constrained databases).
With ShEx more containment cases can be inferred.
30/32

53. SPARQL Query Containment with ShEx Constraints
Conclusion
Conclusion
Motivation: SPARQL query containment with ShEx
constraints is important (due to constrained databases).
With ShEx more containment cases can be inferred.
Contribution 1: We defined a sound and complete
procedure for SPARQL query containment with ShEx
constraints.
30/32

54. SPARQL Query Containment with ShEx Constraints
Conclusion
Conclusion
Motivation: SPARQL query containment with ShEx
constraints is important (due to constrained databases).
With ShEx more containment cases can be inferred.
Contribution 1: We defined a sound and complete
procedure for SPARQL query containment with ShEx
constraints.
Contribution 2: We provided the complexity bounds of
the problem considered. (ΠP
2-c for AND-OPT-(UNION))
30/32

55. SPARQL Query Containment with ShEx Constraints
Conclusion
Conclusion
Motivation: SPARQL query containment with ShEx
constraints is important (due to constrained databases).
With ShEx more containment cases can be inferred.
Contribution 1: We defined a sound and complete
procedure for SPARQL query containment with ShEx
constraints.
Contribution 2: We provided the complexity bounds of
the problem considered. (ΠP
2-c for AND-OPT-(UNION))
Contribution 3: We implemented the procedure in a
java framework using an existing ShEx validator and an
existing containment solver.
30/32

56. SPARQL Query Containment with ShEx Constraints
Conclusion
Conclusion
Motivation: SPARQL query containment with ShEx
constraints is important (due to constrained databases).
With ShEx more containment cases can be inferred.
Contribution 1: We defined a sound and complete
procedure for SPARQL query containment with ShEx
constraints.
Contribution 2: We provided the complexity bounds of
the problem considered. (ΠP
2-c for AND-OPT-(UNION))
Contribution 3: We implemented the procedure in a
java framework using an existing ShEx validator and an
existing containment solver.
Contribution 4: Alternative method for extending the
SPARQL fragment (reducing to FOL satisfiability).
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57. SPARQL Query Containment with ShEx Constraints
Conclusion
Further Perspectives
In Application:
There exist many FOL automated theorem provers that
participate annually in competitions.
Only 1 containment solver for the AND-OPT-(UNION)
fragment is available. [Pichler and Skritek, 2014]
Using available FOL automated theorem provers allowed
for more efficient problem solving implementations (even
for small fragments).
Perspective:
It is clear that there exists a space to make better
implementations of the containment solver and/or of
the ShEx validator.
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58. SPARQL Query Containment with ShEx Constraints
Conclusion
Thank You
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