RuleML2015: Ontology-Based Multidimensional Contexts with Applications to Quality Data Specification and Extraction

Ontology-Based Multidimensional Contexts with
Applications to Quality Data Speciﬁcation and
Extraction
Mostafa Milani Leopoldo Bertossi
Carleton University
School of Computer Science
Ottawa, Canada
(Carleton University) Ontology-Based Multidimensional Contexts 1 / 23

Problem Statement Introduction
Multidimensional Contexts and Data Quality
Measurements table
contains the
temperatures of patients
at a hospital
Measurements
Time Patient Value
Sep/5-12:10 Tom Waits 38.2
Sep/6-11:05 Lou Reed 37.5

Measurements table
contains the
at a hospital
Measurements
Time Patient Value
A doctor suppose/expects the table to contain:

Measurements table
contains the
at a hospital
Measurements
Time Patient Value
”The body temperatures of Tom Waits for September 5
taken around noon with a thermometer of brand B1”

Measurements table
contains the
at a hospital
Measurements
Time Patient Value
”The body temperatures of Tom Waits for September 5
taken around noon with a thermometer of brand B1”
But Measurements does not contain the information to make this
assessment

An external context can provide that information, making it possible
to assess the given data

Contex is modeled as relational databases (Bertossi et al., BIRTE 2010)

The database under assessment is mapped into the contextual
database for further data quality analysis and cleaning

Context is commonly of a multi-dimensional nature

Context is commonly of a multi-dimensional nature
The dimensional aspects of context are not considered in
(Bertossi et al., BIRTE 2010)

Multidimensional Context Extended HM Data Model
Extending Context with Multidimensional Data
We can see the context as an ontology, containing:

A MD data model/instance:

PatientWard: A table containing the location of patients
Hospital dimension: Represents the hierarchy of locations

Information such as a hospital guideline:

”Temperature measurement for patients in standard care unit
have to be taken with thermometers of Brand B1”

Basis data model: HM model (Hurtado and Mendelzon, 2005)

Basis data model: HM model (Hurtado and Mendelzon, 2005)
We extend the HM model (Maleki et al., AMW 2012)

Informally, some of the new ingredients in MD contexts:

Dimensions as in the HM

Categorical relations: Generalize fact tables, not necessarily numerical
values, linked to diﬀerent levels of dimensions, possibly incomplete

Dimensional rules: Generate data where missing

Dimensional constraints: Constraints on (combinations of) categorical
relations, involve values from dimension categories)

Dimensional constraints: Constraints on (combinations of) categorical
relations, involve values from dimension categories)
Dimensional rules and constraints can support and restrict
upward/downard navigation

Example
Ward and Unit:
categories of Hospital
dimension

Example
Ward and Unit:
dimension
UnitWard(unit,ward): a
parent/child relation

Example
Ward and Unit:
dimension
PatientUnit
id Unit Day Patient
1 Standard Sep/5 Tom Waits
3 Intensive Sep/7 Tom Waits
4 Intensive Sep/6 Lou Reed
5 Standard Sep/5 Lou Reed
PatientWard
id Ward Day Patient
1 W1 Sep/5 Tom Waits
4 W3 Sep/6 Lou Reed
5 W2 Sep/5 Lou Reed
AllHospital
Institution
Unit
Ward
Standard Intensive Terminal
W1 W2 W3 W4
H1 H2
allHospital
AllTime
Year
Month
Day
Time

Example
Ward and Unit:
dimension
PatientUnit
id Unit Day Patient
3 Intensive Sep/7 Tom Waits
4 Intensive Sep/6 Lou Reed
5 Standard Sep/5 Lou Reed
PatientWard
id Ward Day Patient
4 W3 Sep/6 Lou Reed
5 W2 Sep/5 Lou Reed
AllHospital
Institution
Unit
Ward
W1 W2 W3 W4
H1 H2
allHospital
AllTime
Year
Month
Day
Time
PatientWard: categorical relation with Ward and Day categorical
attributes taking values from dimension categories

Dimensional Constraints
Example
Categorical relations are subject to dimensional constraints:

Example
A referential constraint restricting units in PatientUnit
to elements in the Unit category, as a negative constraint:

Example
⊥ ← PatientUnit(u, d; p), ¬Unit(u)

Example
“All thermometers used in a unit are of the same type”:

Example
t = t ← Thermometer(w, t; n), Thermometer(w , t ; n ),
UnitWard(u, w), UnitWard(u, w ) An EGD

Example
“No patient in intensive care unit on August /2005”:

Example
“No patient in intensive care unit on August /2005”:
⊥ ← PatientWard(w, d; p), UnitWard(Intensive, w),
MonthDay(August/2005, d)

Dimensional Rules
Example
Data in PatientWard generate data about patients for
higher-level categorical relation PatientUnit:

Dimensional Rules
Example
PatientUnit(u, d; p) ← PatientWard(w, d; p),
UnitWard(u, w)

Dimensional Rules
Example
UnitWard(u, w)
Since relation schemas ”match”, ∃-variable in the head is not needed

Dimensional Rules
Example
UnitWard(u, w)
Rule is used to navigate from PatientWard.Ward upwards to
PatientUnit.Unit via UnitWard

Dimensional Rules
Example
UnitWard(u, w)
Once at the level of Unit, it is possible to take advantage of a
guideline -in the form of a rule- stating that:

Dimensional Rules
Example
UnitWard(u, w)
Once at the level of Unit, it is possible to take advantage of a
guideline -in the form of a rule- stating that:
“Temperatures of patients in a standard care unit are taken with oral
thermometers”

Dimensional Rules
Example
WorkingSchedules
id Unit Day Nurse Type
1 Intensive Sep/5 Cathy cert.
2 Standard Sep/5 Helen cert.
4 Terminal Sep/5 Susan non-cert.
5 Standard Sep/9 Mark non-cert.
Shifts
id Ward Day Nurse Shift
1 W4 Sep/5 Cathy night
2 W1 Sep/6 Helen morning
3 W4 Sep/5 Susan evening
Unit
Institution
W1 W2 W3 W4
AllHospital
Ward
H1 H2
allHospital
AllTime
Year
Day
Time
Month

Dimensional Rules
Example
WorkingSchedules
id Unit Day Nurse Type
1 Intensive Sep/5 Cathy cert.
4 Terminal Sep/5 Susan non-cert.
5 Standard Sep/9 Mark non-cert.
Shifts
id Ward Day Nurse Shift
1 W4 Sep/5 Cathy night
2 W1 Sep/6 Helen morning
3 W4 Sep/5 Susan evening
Unit
Institution
W1 W2 W3 W4
AllHospital
Ward
H1 H2
allHospital
AllTime
Year
Day
Time
Month
Data in categorical relation WorkingSchedules generates data in
categorical relation Shifts

Dimensional Rules
Example
∃z Shifts(w, d; n, z) ← WorkingSchedules(u, d; n, t),
UnitWard(u, w)

Dimensional Rules
Example
UnitWard(u, w)
Captures a guideline stating that: “If a nurse works in a unit on a
speciﬁc day, he/she has shifts in every ward of that unit on the same day”

Dimensional Rules
Example
UnitWard(u, w)
Head has existential variable z for missing values for shift attribute

Dimensional Rules
Example
UnitWard(u, w)
Head has existential variable z for missing values for shift attribute
Rule can be used for downward navigation

Multidimensional Context Ontological Representation of the Extended MD Model
Datalog± as Representation Language
We use Datalog± as our representation language (Cali et al., 2009)

An extension of Datalog for ontology building with eﬃcient
access to underlying data sources

Our approach to representation of MD contexts is general and
systematic with the following general forms:

Negative constraints capturing referential constraints from categorical
attributes to categories:

⊥ ← Ri (¯ei ; ¯ai ), ¬K(e)

⊥ ← Ri (¯ei ; ¯ai ), ¬K(e)
e, ¯ei stand for categorical attributes,

⊥ ← Ri (¯ei ; ¯ai ), ¬K(e)
Ri a categorical predicate, and

⊥ ← Ri (¯ei ; ¯ai ), ¬K(e)
Ri a categorical predicate, and
K a category predicate

Dimensional constraints as EGDs or negative constraints:

x = x ← Ri (¯ei ; ¯ai ), ..., Rj (¯ej ; ¯aj ), Dn(en, en), ..., Dm(em, em)

⊥ ← Ri (¯ei ; ¯ai ), ..., Rj (¯ej ; ¯aj ), Dn(en, en), ..., Dm(em, em)
Di are parent-child predicates and Ri are categorical predicates

Dimensional rules as TGDs:

∃¯az Rk (¯ek ; ¯ak ) ← Ri (¯ei ; ¯ai ), ..., Rj (¯ej ; ¯aj ), Dn(en, en), ..., Dm(em, em)

Existential quantiﬁers (possibly not needed) over non-categorical
attributes, which may get labeled nulls as values

Repeated variables in bodies of TGDs only for categorical attributes

Repeated variables in bodies of TGDs only for categorical attributes
”Upward or downward navigation captured by joins between
categorical predicates and parent-child predicates in bodies”

Properties of MD Ontologies
Datalog± is a family of languages with diﬀerent syntactic restrictions
on rules and their interaction to guarantee tractability

Our Datalog± MD ontologies become weakly-sticky Datalog±
programs (Cali et al., 2012)

It is crucial that repeated variables in TGDs are for categorical
attributes (a ﬁnite number of values can be taken by them, the
category members)

category members)
The chase (that forwards propagates data through rules) may not
terminate

category members)
The chase (that forwards propagates data through rules) may not
terminate
Weak-stickiness guarantees tractability of conjunctive query
answering (QA): only an initial portion of the chase has to be
inspected

The separability condition on the (good) interaction between TGDs
and EGDs becomes application dependent (Cali et al., 2011)

However, if EGDs have categorical head variables, separability holds

Separability implies decidability of conjunctive query answering

Boolean conjunctive QA is tractable for weakly-sticky Datalog±
ontologies (the same applies to open conjunctive QA)

As opposed to sticky Datalog±, for weakly-sticky Datalog± there is
no general ﬁrst-order query rewriting methodology

As opposed to sticky Datalog±, for weakly-sticky Datalog± there is
no general ﬁrst-order query rewriting methodology
That is, rewriting of conjunctive queries into FO queries in terms of
underlying DB predicates

Query Answering on MD Ontology
A non-deterministic algorithm WeaklySticky-QAns for weakly-sticky
Datalog± (Cali et al., 2012)

WeaklyStickyQAns builds an accepting resolution proof schema, a
tree-like structure

tree-like structure
It shows how query atoms are entailed from extensional data

tree-like structure
The algorithm runs in polynomial time in the size of the extensional
database

tree-like structure
The algorithm runs in polynomial time in the size of the extensional
database
We proposed a deterministic version of the algorithm for
weakly-sticky programs (Milani and Bertossi, AMW 2015)

The new algorithm uses a modiﬁed parsimonious chase procedure
(parsimonious chase for shy programs) (Leone et al., KR 2012)

It takes advantage of information about the positions with ﬁnite ranks
(Fagin et al., 2005)

The algorithm explores only a suﬃciently large initial portion of the
chase with respect to the query

The algorithm explores only a suﬃciently large initial portion of the
chase with respect to the query
We also studied the magic-sets rewriting technique in combination
with this QA algorithm (Milani and Bertossi, AMW 2015)

Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
The MD ontology M becomes part of the context for data quality
assessment

assessment
The original instance D of schema S is to be assessed or cleaned
through the context

assessment
through the context
By mapping D into the contextual schema/instance C

assessment
through the context
In the context:
I
C
Di
q
schema C
quality predicates
P
categorical
relations
dimensions
M
Di
S’
nicknames
Ri
’
Sq
quality version
R1
q
Rn
q
Dq
S
under asessment
R1
D
Rn
…

assessment
through the context
In the context:
• Nickname predicates Ri ∈ S
I
C
Di
q
schema C
quality predicates
P
categorical
relations
dimensions
M
Di
S’
nicknames
Ri
’
Sq
quality version
R1
q
Rn
q
Dq
S
under asessment
R1
D
Rn
…

assessment
through the context
In the context:
• The core MD ontology M I
C
Di
q
schema C
quality predicates
P
categorical
relations
dimensions
M
Di
S’
nicknames
Ri
’
Sq
quality version
R1
q
Rn
q
Dq
S
under asessment
R1
D
Rn
…

assessment
through the context
In the context:
• The core MD ontology M
• A set of quality predicates P
I
C
Di
q
schema C
quality predicates
P
categorical
relations
dimensions
M
Di
S’
nicknames
Ri
’
Sq
quality version
R1
q
Rn
q
Dq
S
under asessment
R1
D
Rn
…

Quality predicates are deﬁned with non-recursive Datalog rules in
terms of categorical predicates and built-ins

Outside context there are Rq
1 , ..., Rq
n as quality versions

1 , ..., Rq
They are deﬁned by quality data extraction rules written in
non-recursive Datalog in terms of S , P, and built-ins

1 , ..., Rq
Quality query answering for Q imposed on S:

1 , ..., Rq
1 Replace predicates in Q with their quality versions obtaining Qq

1 , ..., Rq
2 Rewrite Qq
into QC
by applying the quality data extraction rules

1 , ..., Rq
2 Rewrite Qq
into QC
3 Unfold the deﬁnition of quality predicates P, that results into QM
in
terms of categorical relations and nicknames

1 , ..., Rq
2 Rewrite Qq
into QC
3 Unfold the deﬁnition of quality predicates P, that results into QM
in
terms of categorical relations and nicknames
4 Answer QM
by QA on M

Example
Dimensional rules in M:

Example
WorkingTimes(u, t; n, y) ← WorkingSchedules(u, d; n, y), DayTime(d, t)

Example
PatientUnit(u, t; p) ← PatientWard(w, d; p), DayTime(d, t),
UnitWard(u, w)

Example
UnitWard(u, w)
Quality predicates in P:

Example
UnitWard(u, w)
TakenByNurse(t, p, n, y) ← WorkingTimes(u, t; n, y), PatientUnit(u, t; p)

Example
UnitWard(u, w)
TakenByNurse(t, p, n, y) ← WorkingTimes(u, t; n, y), PatientUnit(u, t; p)
TakenWithTherm(t, p, b) ← PatientUnit(u, t; p), u = Standard, b = B1

Example
Quality version Measurementsq
:

Example
:
Measurementsq
(t, p, v) ← Measurements (t, p, v), TakenByNurse(t, p, n, y),
TakenWithTherm(t, p, b), b = B1, y = certified

Example
:
Measurementsq
A doctor asks the body temperatures of Tom Waits for September 5
taken around noon:

Example
:
Measurementsq
taken around noon:
Q(t, v) : Measurements(t, Tom Waits, v) ∧ Sep5-11:45 ≤ t ≤ Sep5-12:15

Example
:
Measurementsq
taken around noon:
Q(t, v) : Measurements(t, Tom Waits, v) ∧ Sep5-11:45 ≤ t ≤ Sep5-12:15
He expects that the measurements are taken by a certiﬁed nurse and
with a thermometer of brand B1

Example
Replacing predicates of S in Q with their quality versions in Sq:

Example
Qq
(t, v):Measurementsq
(t, Tom Waits, v)∧Sep5-11:45 ≤ t ≤ Sep5-12:15

Example
Qq
Applying the deﬁnition of quality versions:

Example
Qq
QC
(t, v): Measurements (t, p, v) ∧ TakenByNurse(t, p, n, certified) ∧
TakenWithTherm(t, p, B1) ∧ p = Tom Waits ∧
Sep/5-11:45 ≤ t ≤ Sep/5-12:15

Example
Qq
QC
Sep/5-11:45 ≤ t ≤ Sep/5-12:15
Unfolding the deﬁnition of quality predicates in P:

Example
Qq
QC
Sep/5-11:45 ≤ t ≤ Sep/5-12:15
Unfolding the deﬁnition of quality predicates in P:
QM
(t, v):Measurements (t, p, v) ∧ WorkingTimes(u, t; n, y) ∧
PatientUnit(u, t; p) ∧ u =Standard ∧ y =certified ∧
p = Tom Waits ∧ Sep/5-11:45 ≤ t ≤ Sep/5-12:15

Example
Measurements has the same extension of Measurements

Example
WorkingTimes and PatientUnit are computed by QA on M

Example
Measurements
Time Patient Value

Example
The ﬁrst second and last
measurements have the
expected quality
Measurements
Time Patient Value

Example
The ﬁrst second and last
measurements have the
expected quality
The ﬁrst measurement is a
clean answer to Q:
t = Sep/5-12:10 and v=38.2
Measurements
Time Patient Value

Conclusions
Conclusions
Multidimensional contexts are represented as Datalog± ontologies

Conclusions
Conclusions
They allow us to specify data quality conditions, and to retrieve
quality data

Conclusions
Conclusions
quality data
Development, implementation of the query answering algorithms is
ongoing work

Conclusions
Conclusions
quality data
ongoing work
Several extensions:

Conclusions
Conclusions
quality data
ongoing work
Several extensions:
Uncertain downward-navigation in dimensional rules

Conclusions
Conclusions
quality data
ongoing work
Several extensions:
Checking dimensional constraints not only on the result of the chase
but while data generation

Conclusions
Conclusions
quality data
ongoing work
Several extensions:
Checking dimensional constraints not only on the result of the chase
but while data generation
Relaxing the assumption of complete categorical data, and studying its
eﬀect on dimensions

RuleML2015: Ontology-Based Multidimensional Contexts with Applications to Quality Data Specification and Extraction

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RuleML2015: Ontology-Based Multidimensional Contexts with Applications to Quality Data Specification and Extraction