KR12 Semantic Index and TBox optimisation with respect to dependencies

Mariano Rodríguez-Muro and Diego CalvaneseKRDB Research Group

Free University of Bozen-Bolzano

KR’12

Realizing OBDAwith 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

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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

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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

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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 DEPENDENCIESDescribing out data sources

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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 � ∃agePatient � ∃ssnPatient � ∃affectedBy

OBDA and -Quest-

An ontology

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∃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


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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

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Concept descriptions

Role descriptions

ABox constraints

• Semantics:

B := A | ∃R

• In addition to TBox and ABox (or OBDA model), we introducea set of ABox dependencies Sigma Σ


CardiacArrest �A Condition

Clog �A Condition

Patient �A ∃name

Patient �A ∃agePatient �A ∃ssnPatient �A ∃affectedBy

∃name �A Patient

∃age �A Patient

∃ssn �A Patient

∃affectedBy �A Patient

∃affectedBy− �A Condition

OBDA and -Quest-

ABox constraints, example

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OBDA and -Quest-

ABOX CONSTRAINTS

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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 in T w.r.t. Sigma

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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 in T w.r.t. Sigma

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A T -chain from B to C is a sequence of inclusion assertions (Bi � B�i)

ni=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

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B � C is directly redundant in T w.r.t. Σ if (i) Σ |= B �A C and (ii) forevery T -chain (Bi � B�

i)ni=0 withB�

n = B in T , there is a Σ-chain (Bi �A B�i)

ni=0.

Similarly for roles.

OBDA and -Quest-


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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 directlyredundant in T w.r.t. Σ, and (iii) B � B� is directly redundant.

OBDA and -Quest-


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Redundancy

T-chain Sigma-chain


OBDA and -Quest-


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• 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 insat(T ) w.r.t. sat(Σ)}.


OBDA and -Quest-

ABOX CONSTRAINTS

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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 semantic ABox storage

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ABox

1. Encode the hierarchies of T in indexes and intervals


OBDA and -Quest-


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ABox


A

B

E D F

C

G H I


OBDA and -Quest-


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ABox


A

B

E D F

C

G H I

1

2

3 4 5

6

7 8 9


OBDA and -Quest-


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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-


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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-


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ABox


?x a ASELECT c FROM t WHEREIDX >= 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-


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ABox


?x a ASELECT c FROM t WHEREIDX >= 1 AND IDX <= 8

OBDA Model

4. Create mappings using those intervals

5. Complement with mappings to cover domain, range and inverse inferences


Experiments

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• Experimentation using Stanford’s “Resource Index”• Semantic search over

annotated documents• 200 ontologies from Bio-portal

(only hierarchies 200k concepts, millions of subClassOf)


Experiments

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• 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”

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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)

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OBDA and -Quest-

THANK YOU


KR12 Semantic Index and TBox optimisation with respect to dependencies

Technology

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