KR12 Semantic Index and TBox optimisation with respect to dependencies

Mariano Rodríguez-Muro and Diego Calvanese
KRDB Research Group
Free University of Bozen-Bolzano
KR’12
Realizing OBDA
with data dependencies
Thursday, June 14, 2012

OBDA and -Quest-
DL-Lite (OWL 2 QL) - promise
• Light-weight DL
• Allows for QA by query rewriting into FO-queries (i.e,. SQL)
• Mapping techniques that allow for OBDA
(sound, GAV mappings)
• Fast query rewriting techniques
• Implementations available
2

OBDA and -Quest-
• UCQ = 729 CQs,
UNION of 729 SPJ SQL
queries
• Datalog = 9 rules,
1 SPJ of UNIONS (3
nested UNIONS of 9
elements each)
An trivial example
3
A
B
E D F
C
G H I
q(x) ← A(x), R(x, y), A(y), R(y, z), A(z)

OBDA and -Quest-
• Focused on “size” of the
rewriting and dealing
with
ended up playing an
“encoding” game...
• The role of SQL engines,
their features and
limitations has been
neglected
DL-Lite (OWL 2 QL) - reality
• Query answering by query
rewriting still slow, but
not due to the rewriting
technique
• RDBMS cannot handle our
queries efﬁciently
4
A ∃R

OBDA and -Quest- 5
“Efﬁcient query answering in OBDA or QAO requires exploiting
and optimizing every element/resource in the query answering
system, not just query rewriting algorithms”

OBDA and -Quest-
ABOX DEPENDENCIES
Describing out data sources
6

OBDA and -Quest-
QAO revisited
Reasoner Application
TBox
ABox
Inputs

OBDA and -Quest-
QAO revisited
TBox
ABox
Inputs
Source

OBDA and -Quest-
QAO revisited
TBox
ABox
Inputs
SourceOBDA
Model

OBDA and -Quest-
OBDA
Reasoner
Source
Application
Direct
Communication
TBox
OBDA
Model
Inputs

CardiacArrest Condition
Clog Condition
Patient ∃name
Patient ∃age
Patient ∃ssn
Patient ∃affectedBy
OBDA and -Quest-
An ontology
9
∃name Patient
∃age Patient
∃ssn Patient
∃affectedBy Patient
∃affectedBy−
Condition

OBDA and -Quest-
An example
id [PKEY] name age ssn
12 John 37 xxx-999
Table: patient
patient_id [FKEY] c_code
12 33
Table: conditionOBDA Model

OBDA and -Quest-
An example
SELECT id,name,age,ssn FROM patient
:person/{$id} a Patient; name $name;
age $age^^xsd:int; ssn $ssn
12 John 37 xxx-999
Table: patient
12 33
Table: conditionOBDA Model

OBDA and -Quest-
An example
12 John 37 xxx-999
Table: patient
12 33
Table: condition
SELECT id, c_id FROM condition
:person/{$id} affectedBy :cond/{$id}.
:cond/{$id} a Condition
OBDA Model

OBDA and -Quest-
An example
12 John 37 xxx-999
Table: patient
12 33
Table: condition
SELECT id, c_id FROM condition
:person/{$id} affectedBy :cond/{$id}.
:cond/{$id} a Condition
SELECT id FROM condition WHERE c_code = 33
:cond/{$id} a CardiacArrest
SELECT id,c_id FROM condition WHERE c_code = 27
:cond/{$id} a Clog
OBDA Model

R := P | P−
∀x.B1(x) ∈ A → B2(x) ∈ A
∀x, y.R1(x, y) ∈ A → R2(x, y) ∈ A
B1 A B2
R1 A R2
OBDA and -Quest-
ABox dependencies for DL-Lite
11
Concept descriptions
Role descriptions
ABox constraints
• Semantics:
B := A | ∃R
• In addition to TBox and ABox (or OBDA model), we introduce
a set of ABox dependencies Sigma Σ

CardiacArrest A Condition
Clog A Condition
Patient A ∃name
Patient A ∃age
Patient A ∃ssn
Patient A ∃affectedBy
∃name A Patient
∃age A Patient
∃ssn A Patient
∃affectedBy A Patient
∃affectedBy−
A Condition
OBDA and -Quest-
ABox constraints,example
12

OBDA and -Quest-
ABOX CONSTRAINTS
13
Optimizing your TBox

Given a TBox T and a set of ABox dependencies Σ we want to compute T
s.t. each α ∈ T
is not redundant w.r.t. Σ
OBDA and -Quest-
Redundancy inT w.r.t.Sigma
14

Given a TBox T and a set of ABox dependencies Σ we want to compute T
s.t. each α ∈ T
is not redundant w.r.t. Σ
OBDA and -Quest-
Redundancy inT w.r.t.Sigma
14
A T -chain from B to C is a sequence of inclusion assertions (Bi B
i)n
i=0
for some n ≥ 0, such that:
1. B0 = B, B
n = C, and
2. for 1 ≤ i ≤ n, we have that B
i−1 and Bi are basic concepts s.t., either
(i) B
i−1 = Bi, or (ii) B
i−1 = ∃R
and Bi = ∃R−
, for some basic role R
.
Respectively for role chains.
Chains in T and Sigma

OBDA and -Quest-
Redundancy w.r.t.Sigma
15

B C is directly redundant in T w.r.t. Σ if (i) Σ |= B A C and (ii) for
every T -chain (Bi B
i)n
i=0 with B
n = B in T , there is a Σ-chain (Bi A B
i)n
i=0.
Similarly for roles.
OBDA and -Quest-
16
Direct redundancy
T-chain Sigma-chain

B C is redundant in T w.r.t. Σ if
(a) it is directly redundant, or
(b) there exists B
= B s.t. (i) T |= B
C, (ii) B
C is not directly
redundant in T w.r.t. Σ, and (iii) B B
is directly redundant.
OBDA and -Quest-
17
Redundancy
T-chain Sigma-chain

OBDA and -Quest-
18
• We can compute T’ by reducing redundancy checks to
reachability in DAGs
• Computable in polynomial time
• Optimal (no redundant axioms in T’)
T
is the set of inclusion assertions {α ∈ sat(T ) | α is not redundant in
sat(T ) w.r.t. sat(Σ)}.

OBDA and -Quest-
ABOX CONSTRAINTS
19
Enforcing dependencies

OBDA and -Quest-
OBDA with OWL 2 QL
OBDA
Model Manipulate mappings
Manipulate the data
Inference shifting. Separate
ground reasoning from existential
reasoning (efﬁciently)

OBDA and -Quest-
OBDA with OWL 2 QL
TBox
ABox
Inputs

OBDA and -Quest-
OBDA with OWL 2 QL
TBox
ABox
Inputs
OBDA
Model

OBDA and -Quest-
Creating semanticABox storage
24
ABox
1. Encode the hierarchies of T in indexes and intervals

OBDA and -Quest-
25
ABox
A
B
E D F
C
G H I

OBDA and -Quest-
26
ABox
A
B
E D F
C
G H I
1
2
3 4 5
6
7 8 9

OBDA and -Quest-
26
ABox
A
B
E D F
C
G H I
1
2
3 4 5
6
7 8 9
Insert into your DB using those indexes
C IDX
d 4
h 8
A = D(d), H(h)

A
B
E D F
C
G H I
1 [1,8]
2 [2,5]
3
[3,3]
4
[4,4]
5
[5,5]
6 [6,9]
7
[7,7]
8
[8,8]
9
[9,9]
OBDA and -Quest-
27
ABox
3. Define intervals to retrieve your data

A
B
E D F
C
G H I
1 [1,8]
2 [2,5]
3
[3,3]
4
[4,4]
5
[5,5]
6 [6,9]
7
[7,7]
8
[8,8]
9
[9,9]
OBDA and -Quest-
27
ABox
?x a A
SELECT c FROM t WHERE
IDX = 1 AND IDX = 8
OBDA
Model
4. Create mappings using those intervals

A
B
E D F
C
G H I
1 [1,8]
2 [2,5]
3
[3,3]
4
[4,4]
5
[5,5]
6 [6,9]
7
[7,7]
8
[8,8]
9
[9,9]
OBDA and -Quest-
27
ABox
?x a A
SELECT c FROM t WHERE
IDX = 1 AND IDX = 8
OBDA
Model
4. Create mappings using those intervals
5. Complement with mappings to cover
domain, range and inverse inferences

Experiments
28
• Experimentation using Stanford’s “Resource Index”
• Semantic search over
annotated documents
• 200 ontologies from Bio-portal
(only hierarchies 200k concepts,
millions of subClassOf)

Experiments
29
• Current system uses chase
• Naive chase: 7 days
• Optimized chase: 40 mins
• Cost 16 GB + 70 GB chase data
• Split second responses
• Pure query rewriting approaches
• not-feasible (UCQs or Datalog)
• Semantic index-based rewriting
• DAG computation and indexing 5 mins
• Cost: 16 GB
• Single queries, split second responses

OBDA and -Quest-
CONCLUSIONS

OBDA and -Quest-
Conclusions
• Introduced ABox dependencies to describe the structure
of data
• Showed how to optimize TBoxes w.r.t. dependencies,
• Introduced the idea of “shifting” inferences from TBox
reasoning to Mapping reasoning.
• Introduced “Semantic Index” repositories
• Not mentioned - “Equivalence optimization”
31

OBDA and -Quest-
Conclusions
• Inference shifting is also possible in strict OBDA (see
T-mappings [AMW’09])
• All (including T-mappings) is implemented in Quest and
-ontop-, now available as a P4 plugin.
• Combined with a fast rewriting technique (see [Kontchakov
et. al 12] and [Rosati, 12]) T-mappings and Semantic indexes
allow for OBDA and QAO in practice
• Practical and Theoretical evidence that we have covered
relevant cases
• Time to put things to practice!
(and look at the future, hybrid
approaches, EL, Datalog+-, OWL 2 RL)
32

OBDA and -Quest-
THANKYOU

KR12 Semantic Index and TBox optimisation with respect to dependencies

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