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Ontology-Based Multidimensional Contexts with
Applications to Quality Data Specification and
Extraction
Mostafa Milani Leop...
Problem Statement Introduction
Multidimensional Contexts and Data Quality
Measurements table
contains the
temperatures of ...
Problem Statement Introduction
Multidimensional Contexts and Data Quality
Measurements table
contains the
temperatures of ...
Problem Statement Introduction
Multidimensional Contexts and Data Quality
Measurements table
contains the
temperatures of ...
Problem Statement Introduction
Multidimensional Contexts and Data Quality
Measurements table
contains the
temperatures of ...
Problem Statement Introduction
Multidimensional Contexts and Data Quality
An external context can provide that information...
Problem Statement Introduction
Multidimensional Contexts and Data Quality
An external context can provide that information...
Problem Statement Introduction
Multidimensional Contexts and Data Quality
An external context can provide that information...
Problem Statement Introduction
Multidimensional Contexts and Data Quality
An external context can provide that information...
Problem Statement Introduction
Multidimensional Contexts and Data Quality
An external context can provide that information...
Multidimensional Context Extended HM Data Model
Extending Context with Multidimensional Data
We can see the context as an ...
Multidimensional Context Extended HM Data Model
Extending Context with Multidimensional Data
We can see the context as an ...
Multidimensional Context Extended HM Data Model
Extending Context with Multidimensional Data
We can see the context as an ...
Multidimensional Context Extended HM Data Model
Extending Context with Multidimensional Data
We can see the context as an ...
Multidimensional Context Extended HM Data Model
Extending Context with Multidimensional Data
We can see the context as an ...
Multidimensional Context Extended HM Data Model
Extending Context with Multidimensional Data
We can see the context as an ...
Multidimensional Context Extended HM Data Model
Extending Context with Multidimensional Data
We can see the context as an ...
Multidimensional Context Extended HM Data Model
Extending Context with Multidimensional Data
Informally, some of the new i...
Multidimensional Context Extended HM Data Model
Extending Context with Multidimensional Data
Informally, some of the new i...
Multidimensional Context Extended HM Data Model
Extending Context with Multidimensional Data
Informally, some of the new i...
Multidimensional Context Extended HM Data Model
Extending Context with Multidimensional Data
Informally, some of the new i...
Multidimensional Context Extended HM Data Model
Extending Context with Multidimensional Data
Informally, some of the new i...
Multidimensional Context Extended HM Data Model
Extending Context with Multidimensional Data
Informally, some of the new i...
Multidimensional Context Extended HM Data Model
Extending Context with Multidimensional Data
Example
Ward and Unit:
catego...
Multidimensional Context Extended HM Data Model
Extending Context with Multidimensional Data
Example
Ward and Unit:
catego...
Multidimensional Context Extended HM Data Model
Extending Context with Multidimensional Data
Example
Ward and Unit:
catego...
Multidimensional Context Extended HM Data Model
Extending Context with Multidimensional Data
Example
Ward and Unit:
catego...
Multidimensional Context Extended HM Data Model
Dimensional Constraints
Example
Categorical relations are subject to dimen...
Multidimensional Context Extended HM Data Model
Dimensional Constraints
Example
Categorical relations are subject to dimen...
Multidimensional Context Extended HM Data Model
Dimensional Constraints
Example
Categorical relations are subject to dimen...
Multidimensional Context Extended HM Data Model
Dimensional Constraints
Example
Categorical relations are subject to dimen...
Multidimensional Context Extended HM Data Model
Dimensional Constraints
Example
Categorical relations are subject to dimen...
Multidimensional Context Extended HM Data Model
Dimensional Constraints
Example
Categorical relations are subject to dimen...
Multidimensional Context Extended HM Data Model
Dimensional Constraints
Example
Categorical relations are subject to dimen...
Multidimensional Context Extended HM Data Model
Dimensional Rules
Example
Data in PatientWard generate data about patients...
Multidimensional Context Extended HM Data Model
Dimensional Rules
Example
Data in PatientWard generate data about patients...
Multidimensional Context Extended HM Data Model
Dimensional Rules
Example
Data in PatientWard generate data about patients...
Multidimensional Context Extended HM Data Model
Dimensional Rules
Example
Data in PatientWard generate data about patients...
Multidimensional Context Extended HM Data Model
Dimensional Rules
Example
Data in PatientWard generate data about patients...
Multidimensional Context Extended HM Data Model
Dimensional Rules
Example
Data in PatientWard generate data about patients...
Multidimensional Context Extended HM Data Model
Dimensional Rules
Example
WorkingSchedules
id Unit Day Nurse Type
1 Intens...
Multidimensional Context Extended HM Data Model
Dimensional Rules
Example
WorkingSchedules
id Unit Day Nurse Type
1 Intens...
Multidimensional Context Extended HM Data Model
Dimensional Rules
Example
∃z Shifts(w, d; n, z) ← WorkingSchedules(u, d; n...
Multidimensional Context Extended HM Data Model
Dimensional Rules
Example
∃z Shifts(w, d; n, z) ← WorkingSchedules(u, d; n...
Multidimensional Context Extended HM Data Model
Dimensional Rules
Example
∃z Shifts(w, d; n, z) ← WorkingSchedules(u, d; n...
Multidimensional Context Extended HM Data Model
Dimensional Rules
Example
∃z Shifts(w, d; n, z) ← WorkingSchedules(u, d; n...
Multidimensional Context Ontological Representation of the Extended MD Model
Datalog± as Representation Language
We use Da...
Multidimensional Context Ontological Representation of the Extended MD Model
Datalog± as Representation Language
We use Da...
Multidimensional Context Ontological Representation of the Extended MD Model
Datalog± as Representation Language
We use Da...
Multidimensional Context Ontological Representation of the Extended MD Model
Datalog± as Representation Language
We use Da...
Multidimensional Context Ontological Representation of the Extended MD Model
Datalog± as Representation Language
We use Da...
Multidimensional Context Ontological Representation of the Extended MD Model
Datalog± as Representation Language
We use Da...
Multidimensional Context Ontological Representation of the Extended MD Model
Datalog± as Representation Language
We use Da...
Multidimensional Context Ontological Representation of the Extended MD Model
Datalog± as Representation Language
We use Da...
Multidimensional Context Ontological Representation of the Extended MD Model
Datalog± as Representation Language
(Carleton...
Multidimensional Context Ontological Representation of the Extended MD Model
Datalog± as Representation Language
Dimension...
Multidimensional Context Ontological Representation of the Extended MD Model
Datalog± as Representation Language
Dimension...
Multidimensional Context Ontological Representation of the Extended MD Model
Datalog± as Representation Language
Dimension...
Multidimensional Context Ontological Representation of the Extended MD Model
Datalog± as Representation Language
Dimension...
Multidimensional Context Ontological Representation of the Extended MD Model
Datalog± as Representation Language
Dimension...
Multidimensional Context Ontological Representation of the Extended MD Model
Datalog± as Representation Language
Dimension...
Multidimensional Context Ontological Representation of the Extended MD Model
Datalog± as Representation Language
Dimension...
Multidimensional Context Ontological Representation of the Extended MD Model
Datalog± as Representation Language
Dimension...
Multidimensional Context Ontological Representation of the Extended MD Model
Properties of MD Ontologies
Datalog± is a fam...
Multidimensional Context Ontological Representation of the Extended MD Model
Properties of MD Ontologies
Datalog± is a fam...
Multidimensional Context Ontological Representation of the Extended MD Model
Properties of MD Ontologies
Datalog± is a fam...
Multidimensional Context Ontological Representation of the Extended MD Model
Properties of MD Ontologies
Datalog± is a fam...
Multidimensional Context Ontological Representation of the Extended MD Model
Properties of MD Ontologies
Datalog± is a fam...
Multidimensional Context Ontological Representation of the Extended MD Model
Properties of MD Ontologies
The separability ...
Multidimensional Context Ontological Representation of the Extended MD Model
Properties of MD Ontologies
The separability ...
Multidimensional Context Ontological Representation of the Extended MD Model
Properties of MD Ontologies
The separability ...
Multidimensional Context Ontological Representation of the Extended MD Model
Properties of MD Ontologies
The separability ...
Multidimensional Context Ontological Representation of the Extended MD Model
Properties of MD Ontologies
The separability ...
Multidimensional Context Ontological Representation of the Extended MD Model
Properties of MD Ontologies
The separability ...
Multidimensional Context Ontological Representation of the Extended MD Model
Query Answering on MD Ontology
A non-determin...
Multidimensional Context Ontological Representation of the Extended MD Model
Query Answering on MD Ontology
A non-determin...
Multidimensional Context Ontological Representation of the Extended MD Model
Query Answering on MD Ontology
A non-determin...
Multidimensional Context Ontological Representation of the Extended MD Model
Query Answering on MD Ontology
A non-determin...
Multidimensional Context Ontological Representation of the Extended MD Model
Query Answering on MD Ontology
A non-determin...
Multidimensional Context Ontological Representation of the Extended MD Model
Query Answering on MD Ontology
The new algori...
Multidimensional Context Ontological Representation of the Extended MD Model
Query Answering on MD Ontology
The new algori...
Multidimensional Context Ontological Representation of the Extended MD Model
Query Answering on MD Ontology
The new algori...
Multidimensional Context Ontological Representation of the Extended MD Model
Query Answering on MD Ontology
The new algori...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
The MD o...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
The MD o...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
The MD o...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
The MD o...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
The MD o...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
The MD o...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
The MD o...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Quality ...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Quality ...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Quality ...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Quality ...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Quality ...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Quality ...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Quality ...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Quality ...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Example
...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Example
...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Example
...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Example
...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Example
...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Example
...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Example
...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Example
...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Example
...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Example
...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Example
...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Example
...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Example
...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Example
...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Example
...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Example
...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Example
...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Example
...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Example
...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Example
...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Example
...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Example
...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Example
...
Multidimensional Context MD Context for Quality Data Assessment
MD Contexts and Quality Query Answering: The Gist
Example
...
Conclusions
Conclusions
Multidimensional contexts are represented as Datalog± ontologies
(Carleton University) Ontology-Ba...
Conclusions
Conclusions
Multidimensional contexts are represented as Datalog± ontologies
They allow us to specify data qua...
Conclusions
Conclusions
Multidimensional contexts are represented as Datalog± ontologies
They allow us to specify data qua...
Conclusions
Conclusions
Multidimensional contexts are represented as Datalog± ontologies
They allow us to specify data qua...
Conclusions
Conclusions
Multidimensional contexts are represented as Datalog± ontologies
They allow us to specify data qua...
Conclusions
Conclusions
Multidimensional contexts are represented as Datalog± ontologies
They allow us to specify data qua...
Conclusions
Conclusions
Multidimensional contexts are represented as Datalog± ontologies
They allow us to specify data qua...
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RuleML2015: Ontology-Based Multidimensional Contexts with Applications to Quality Data Specification and Extraction

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Published on

Data quality assessment and data cleaning are context
dependent activities. Starting from this observation, in previous work
a context model for the assessment of the quality of a database was
proposed. A context takes the form of a possibly virtual database or
a data integration system into which the database under assessment is
mapped, for additional analysis, processing, and quality data extraction.
In this work, we extend contexts with dimensions, and by doing so, multidimensional
data quality assessment becomes possible. At the core of
multidimensional contexts we find ontologies written as Datalog
±
programs
with provably good properties in terms of query answering. We
use this language to represent dimension hierarchies, dimensional constraints,
dimensional rules, and specifying quality data. Query answering
relies on and triggers dimensional navigation, and becomes an important
tool for the extraction of quality data.

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

  1. 1. 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
  2. 2. 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/6-11:50 Tom Waits 37.1 Sep/7-12:15 Tom Waits 37.7 Sep/9-12:00 Tom Waits 37.0 Sep/6-11:05 Lou Reed 37.5 Sep/5-12:05 Lou Reed 38.0 (Carleton University) Ontology-Based Multidimensional Contexts 2 / 23
  3. 3. 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/6-11:50 Tom Waits 37.1 Sep/7-12:15 Tom Waits 37.7 Sep/9-12:00 Tom Waits 37.0 Sep/6-11:05 Lou Reed 37.5 Sep/5-12:05 Lou Reed 38.0 A doctor suppose/expects the table to contain: (Carleton University) Ontology-Based Multidimensional Contexts 2 / 23
  4. 4. 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/6-11:50 Tom Waits 37.1 Sep/7-12:15 Tom Waits 37.7 Sep/9-12:00 Tom Waits 37.0 Sep/6-11:05 Lou Reed 37.5 Sep/5-12:05 Lou Reed 38.0 A doctor suppose/expects the table to contain: ”The body temperatures of Tom Waits for September 5 taken around noon with a thermometer of brand B1” (Carleton University) Ontology-Based Multidimensional Contexts 2 / 23
  5. 5. 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/6-11:50 Tom Waits 37.1 Sep/7-12:15 Tom Waits 37.7 Sep/9-12:00 Tom Waits 37.0 Sep/6-11:05 Lou Reed 37.5 Sep/5-12:05 Lou Reed 38.0 A doctor suppose/expects the table to contain: ”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 (Carleton University) Ontology-Based Multidimensional Contexts 2 / 23
  6. 6. Problem Statement Introduction Multidimensional Contexts and Data Quality An external context can provide that information, making it possible to assess the given data (Carleton University) Ontology-Based Multidimensional Contexts 3 / 23
  7. 7. Problem Statement Introduction Multidimensional Contexts and Data Quality 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) (Carleton University) Ontology-Based Multidimensional Contexts 3 / 23
  8. 8. Problem Statement Introduction Multidimensional Contexts and Data Quality 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 (Carleton University) Ontology-Based Multidimensional Contexts 3 / 23
  9. 9. Problem Statement Introduction Multidimensional Contexts and Data Quality 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 (Carleton University) Ontology-Based Multidimensional Contexts 3 / 23
  10. 10. Problem Statement Introduction Multidimensional Contexts and Data Quality 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 The dimensional aspects of context are not considered in (Bertossi et al., BIRTE 2010) (Carleton University) Ontology-Based Multidimensional Contexts 3 / 23
  11. 11. Multidimensional Context Extended HM Data Model Extending Context with Multidimensional Data We can see the context as an ontology, containing: (Carleton University) Ontology-Based Multidimensional Contexts 4 / 23
  12. 12. 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: (Carleton University) Ontology-Based Multidimensional Contexts 4 / 23
  13. 13. 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 (Carleton University) Ontology-Based Multidimensional Contexts 4 / 23
  14. 14. 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: (Carleton University) Ontology-Based Multidimensional Contexts 4 / 23
  15. 15. 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” (Carleton University) Ontology-Based Multidimensional Contexts 4 / 23
  16. 16. 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) (Carleton University) Ontology-Based Multidimensional Contexts 4 / 23
  17. 17. 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) We extend the HM model (Maleki et al., AMW 2012) (Carleton University) Ontology-Based Multidimensional Contexts 4 / 23
  18. 18. Multidimensional Context Extended HM Data Model Extending Context with Multidimensional Data Informally, some of the new ingredients in MD contexts: (Carleton University) Ontology-Based Multidimensional Contexts 5 / 23
  19. 19. Multidimensional Context Extended HM Data Model Extending Context with Multidimensional Data Informally, some of the new ingredients in MD contexts: Dimensions as in the HM (Carleton University) Ontology-Based Multidimensional Contexts 5 / 23
  20. 20. Multidimensional Context Extended HM Data Model Extending Context with Multidimensional Data 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 (Carleton University) Ontology-Based Multidimensional Contexts 5 / 23
  21. 21. Multidimensional Context Extended HM Data Model Extending Context with Multidimensional Data 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 (Carleton University) Ontology-Based Multidimensional Contexts 5 / 23
  22. 22. Multidimensional Context Extended HM Data Model Extending Context with Multidimensional Data 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 (Carleton University) Ontology-Based Multidimensional Contexts 5 / 23
  23. 23. Multidimensional Context Extended HM Data Model Extending Context with Multidimensional Data 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 rules and constraints can support and restrict upward/downard navigation (Carleton University) Ontology-Based Multidimensional Contexts 5 / 23
  24. 24. Multidimensional Context Extended HM Data Model Extending Context with Multidimensional Data Example Ward and Unit: categories of Hospital dimension (Carleton University) Ontology-Based Multidimensional Contexts 6 / 23
  25. 25. Multidimensional Context Extended HM Data Model Extending Context with Multidimensional Data Example Ward and Unit: categories of Hospital dimension UnitWard(unit,ward): a parent/child relation (Carleton University) Ontology-Based Multidimensional Contexts 6 / 23
  26. 26. Multidimensional Context Extended HM Data Model Extending Context with Multidimensional Data Example Ward and Unit: categories of Hospital dimension UnitWard(unit,ward): a parent/child relation PatientUnit id Unit Day Patient 1 Standard Sep/5 Tom Waits 2 Standard Sep/6 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 2 W1 Sep/6 Tom Waits 3 W3 Sep/7 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 (Carleton University) Ontology-Based Multidimensional Contexts 6 / 23
  27. 27. Multidimensional Context Extended HM Data Model Extending Context with Multidimensional Data Example Ward and Unit: categories of Hospital dimension UnitWard(unit,ward): a parent/child relation PatientUnit id Unit Day Patient 1 Standard Sep/5 Tom Waits 2 Standard Sep/6 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 2 W1 Sep/6 Tom Waits 3 W3 Sep/7 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 PatientWard: categorical relation with Ward and Day categorical attributes taking values from dimension categories (Carleton University) Ontology-Based Multidimensional Contexts 6 / 23
  28. 28. Multidimensional Context Extended HM Data Model Dimensional Constraints Example Categorical relations are subject to dimensional constraints: (Carleton University) Ontology-Based Multidimensional Contexts 7 / 23
  29. 29. Multidimensional Context Extended HM Data Model Dimensional Constraints Example Categorical relations are subject to dimensional constraints: A referential constraint restricting units in PatientUnit to elements in the Unit category, as a negative constraint: (Carleton University) Ontology-Based Multidimensional Contexts 7 / 23
  30. 30. Multidimensional Context Extended HM Data Model Dimensional Constraints Example Categorical relations are subject to dimensional constraints: A referential constraint restricting units in PatientUnit to elements in the Unit category, as a negative constraint: ⊥ ← PatientUnit(u, d; p), ¬Unit(u) (Carleton University) Ontology-Based Multidimensional Contexts 7 / 23
  31. 31. Multidimensional Context Extended HM Data Model Dimensional Constraints Example Categorical relations are subject to dimensional constraints: A referential constraint restricting units in PatientUnit to elements in the Unit category, as a negative constraint: ⊥ ← PatientUnit(u, d; p), ¬Unit(u) “All thermometers used in a unit are of the same type”: (Carleton University) Ontology-Based Multidimensional Contexts 7 / 23
  32. 32. Multidimensional Context Extended HM Data Model Dimensional Constraints Example Categorical relations are subject to dimensional constraints: A referential constraint restricting units in PatientUnit to elements in the Unit category, as a negative constraint: ⊥ ← PatientUnit(u, d; p), ¬Unit(u) “All thermometers used in a unit are of the same type”: t = t ← Thermometer(w, t; n), Thermometer(w , t ; n ), UnitWard(u, w), UnitWard(u, w ) An EGD (Carleton University) Ontology-Based Multidimensional Contexts 7 / 23
  33. 33. Multidimensional Context Extended HM Data Model Dimensional Constraints Example Categorical relations are subject to dimensional constraints: A referential constraint restricting units in PatientUnit to elements in the Unit category, as a negative constraint: ⊥ ← PatientUnit(u, d; p), ¬Unit(u) “All thermometers used in a unit are of the same type”: t = t ← Thermometer(w, t; n), Thermometer(w , t ; n ), UnitWard(u, w), UnitWard(u, w ) An EGD “No patient in intensive care unit on August /2005”: (Carleton University) Ontology-Based Multidimensional Contexts 7 / 23
  34. 34. Multidimensional Context Extended HM Data Model Dimensional Constraints Example Categorical relations are subject to dimensional constraints: A referential constraint restricting units in PatientUnit to elements in the Unit category, as a negative constraint: ⊥ ← PatientUnit(u, d; p), ¬Unit(u) “All thermometers used in a unit are of the same type”: t = t ← Thermometer(w, t; n), Thermometer(w , t ; n ), UnitWard(u, w), UnitWard(u, w ) An EGD “No patient in intensive care unit on August /2005”: ⊥ ← PatientWard(w, d; p), UnitWard(Intensive, w), MonthDay(August/2005, d) (Carleton University) Ontology-Based Multidimensional Contexts 7 / 23
  35. 35. Multidimensional Context Extended HM Data Model Dimensional Rules Example Data in PatientWard generate data about patients for higher-level categorical relation PatientUnit: (Carleton University) Ontology-Based Multidimensional Contexts 8 / 23
  36. 36. Multidimensional Context Extended HM Data Model Dimensional Rules Example Data in PatientWard generate data about patients for higher-level categorical relation PatientUnit: PatientUnit(u, d; p) ← PatientWard(w, d; p), UnitWard(u, w) (Carleton University) Ontology-Based Multidimensional Contexts 8 / 23
  37. 37. Multidimensional Context Extended HM Data Model Dimensional Rules Example Data in PatientWard generate data about patients for higher-level categorical relation PatientUnit: PatientUnit(u, d; p) ← PatientWard(w, d; p), UnitWard(u, w) Since relation schemas ”match”, ∃-variable in the head is not needed (Carleton University) Ontology-Based Multidimensional Contexts 8 / 23
  38. 38. Multidimensional Context Extended HM Data Model Dimensional Rules Example Data in PatientWard generate data about patients for higher-level categorical relation PatientUnit: PatientUnit(u, d; p) ← PatientWard(w, d; p), UnitWard(u, w) Since relation schemas ”match”, ∃-variable in the head is not needed Rule is used to navigate from PatientWard.Ward upwards to PatientUnit.Unit via UnitWard (Carleton University) Ontology-Based Multidimensional Contexts 8 / 23
  39. 39. Multidimensional Context Extended HM Data Model Dimensional Rules Example Data in PatientWard generate data about patients for higher-level categorical relation PatientUnit: PatientUnit(u, d; p) ← PatientWard(w, d; p), UnitWard(u, w) Since relation schemas ”match”, ∃-variable in the head is not needed Rule is used to navigate from PatientWard.Ward upwards to PatientUnit.Unit via UnitWard Once at the level of Unit, it is possible to take advantage of a guideline -in the form of a rule- stating that: (Carleton University) Ontology-Based Multidimensional Contexts 8 / 23
  40. 40. Multidimensional Context Extended HM Data Model Dimensional Rules Example Data in PatientWard generate data about patients for higher-level categorical relation PatientUnit: PatientUnit(u, d; p) ← PatientWard(w, d; p), UnitWard(u, w) Since relation schemas ”match”, ∃-variable in the head is not needed Rule is used to navigate from PatientWard.Ward upwards to PatientUnit.Unit via UnitWard 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 thermometers of brand B1” (Carleton University) Ontology-Based Multidimensional Contexts 8 / 23
  41. 41. Multidimensional Context Extended HM Data Model Dimensional Rules Example WorkingSchedules id Unit Day Nurse Type 1 Intensive Sep/5 Cathy cert. 2 Standard Sep/5 Helen cert. 3 Standard Sep/6 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 Standard Intensive Terminal H1 H2 allHospital AllTime Year Day Time Month (Carleton University) Ontology-Based Multidimensional Contexts 9 / 23
  42. 42. Multidimensional Context Extended HM Data Model Dimensional Rules Example WorkingSchedules id Unit Day Nurse Type 1 Intensive Sep/5 Cathy cert. 2 Standard Sep/5 Helen cert. 3 Standard Sep/6 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 Standard Intensive Terminal H1 H2 allHospital AllTime Year Day Time Month Data in categorical relation WorkingSchedules generates data in categorical relation Shifts (Carleton University) Ontology-Based Multidimensional Contexts 9 / 23
  43. 43. Multidimensional Context Extended HM Data Model Dimensional Rules Example ∃z Shifts(w, d; n, z) ← WorkingSchedules(u, d; n, t), UnitWard(u, w) (Carleton University) Ontology-Based Multidimensional Contexts 10 / 23
  44. 44. Multidimensional Context Extended HM Data Model Dimensional Rules Example ∃z Shifts(w, d; n, z) ← WorkingSchedules(u, d; n, t), 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” (Carleton University) Ontology-Based Multidimensional Contexts 10 / 23
  45. 45. Multidimensional Context Extended HM Data Model Dimensional Rules Example ∃z Shifts(w, d; n, z) ← WorkingSchedules(u, d; n, t), 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” Head has existential variable z for missing values for shift attribute (Carleton University) Ontology-Based Multidimensional Contexts 10 / 23
  46. 46. Multidimensional Context Extended HM Data Model Dimensional Rules Example ∃z Shifts(w, d; n, z) ← WorkingSchedules(u, d; n, t), 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” Head has existential variable z for missing values for shift attribute Rule can be used for downward navigation (Carleton University) Ontology-Based Multidimensional Contexts 10 / 23
  47. 47. Multidimensional Context Ontological Representation of the Extended MD Model Datalog± as Representation Language We use Datalog± as our representation language (Cali et al., 2009) (Carleton University) Ontology-Based Multidimensional Contexts 11 / 23
  48. 48. 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 (Carleton University) Ontology-Based Multidimensional Contexts 11 / 23
  49. 49. 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: (Carleton University) Ontology-Based Multidimensional Contexts 11 / 23
  50. 50. 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: (Carleton University) Ontology-Based Multidimensional Contexts 11 / 23
  51. 51. 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: ⊥ ← R(¯e; ¯a), ¬K(e) (Carleton University) Ontology-Based Multidimensional Contexts 11 / 23
  52. 52. 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: ⊥ ← R(¯e; ¯a), ¬K(e) ¯e, e ∈ ¯e stand for categorical attributes, (Carleton University) Ontology-Based Multidimensional Contexts 11 / 23
  53. 53. 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: ⊥ ← R(¯e; ¯a), ¬K(e) ¯e, e ∈ ¯e stand for categorical attributes, R a categorical predicate, and (Carleton University) Ontology-Based Multidimensional Contexts 11 / 23
  54. 54. 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: ⊥ ← R(¯e; ¯a), ¬K(e) ¯e, e ∈ ¯e stand for categorical attributes, R a categorical predicate, and K a category predicate (Carleton University) Ontology-Based Multidimensional Contexts 11 / 23
  55. 55. Multidimensional Context Ontological Representation of the Extended MD Model Datalog± as Representation Language (Carleton University) Ontology-Based Multidimensional Contexts 12 / 23
  56. 56. Multidimensional Context Ontological Representation of the Extended MD Model Datalog± as Representation Language Dimensional constraints as EGDs or negative constraints: (Carleton University) Ontology-Based Multidimensional Contexts 12 / 23
  57. 57. Multidimensional Context Ontological Representation of the Extended MD Model Datalog± as Representation Language Dimensional constraints as EGDs or negative constraints: x = x ← R1(¯e1; ¯a1), ..., Rn(¯en; ¯an), D1(e1, e1), ..., Dm(em, em) (Carleton University) Ontology-Based Multidimensional Contexts 12 / 23
  58. 58. Multidimensional Context Ontological Representation of the Extended MD Model Datalog± as Representation Language Dimensional constraints as EGDs or negative constraints: x = x ← R1(¯e1; ¯a1), ..., Rn(¯en; ¯an), D1(e1, e1), ..., Dm(em, em) ⊥ ← R1(¯e1; ¯a1), ..., Rn(¯en; ¯an), D1(e1, e1), ..., Dm(em, em) Di are parent-child predicates and Ri are categorical predicates (Carleton University) Ontology-Based Multidimensional Contexts 12 / 23
  59. 59. Multidimensional Context Ontological Representation of the Extended MD Model Datalog± as Representation Language Dimensional constraints as EGDs or negative constraints: x = x ← R1(¯e1; ¯a1), ..., Rn(¯en; ¯an), D1(e1, e1), ..., Dm(em, em) ⊥ ← R1(¯e1; ¯a1), ..., Rn(¯en; ¯an), D1(e1, e1), ..., Dm(em, em) Di are parent-child predicates and Ri are categorical predicates Dimensional rules as TGDs: (Carleton University) Ontology-Based Multidimensional Contexts 12 / 23
  60. 60. Multidimensional Context Ontological Representation of the Extended MD Model Datalog± as Representation Language Dimensional constraints as EGDs or negative constraints: x = x ← R1(¯e1; ¯a1), ..., Rn(¯en; ¯an), D1(e1, e1), ..., Dm(em, em) ⊥ ← R1(¯e1; ¯a1), ..., Rn(¯en; ¯an), D1(e1, e1), ..., Dm(em, em) Di are parent-child predicates and Ri are categorical predicates Dimensional rules as TGDs: ∃¯az Rk (¯ek ; ¯ak ) ← R1(¯e1; ¯a1), ..., Rn(¯en; ¯an), D1(e1, e1), ..., Dm(em, em) (Carleton University) Ontology-Based Multidimensional Contexts 12 / 23
  61. 61. Multidimensional Context Ontological Representation of the Extended MD Model Datalog± as Representation Language Dimensional constraints as EGDs or negative constraints: x = x ← R1(¯e1; ¯a1), ..., Rn(¯en; ¯an), D1(e1, e1), ..., Dm(em, em) ⊥ ← R1(¯e1; ¯a1), ..., Rn(¯en; ¯an), D1(e1, e1), ..., Dm(em, em) Di are parent-child predicates and Ri are categorical predicates Dimensional rules as TGDs: ∃¯az Rk (¯ek ; ¯ak ) ← R1(¯e1; ¯a1), ..., Rn(¯en; ¯an), D1(e1, e1), ..., Dm(em, em) Existential quantifiers (possibly not needed) over non-categorical attributes, which may get labeled nulls as values (Carleton University) Ontology-Based Multidimensional Contexts 12 / 23
  62. 62. Multidimensional Context Ontological Representation of the Extended MD Model Datalog± as Representation Language Dimensional constraints as EGDs or negative constraints: x = x ← R1(¯e1; ¯a1), ..., Rn(¯en; ¯an), D1(e1, e1), ..., Dm(em, em) ⊥ ← R1(¯e1; ¯a1), ..., Rn(¯en; ¯an), D1(e1, e1), ..., Dm(em, em) Di are parent-child predicates and Ri are categorical predicates Dimensional rules as TGDs: ∃¯az Rk (¯ek ; ¯ak ) ← R1(¯e1; ¯a1), ..., Rn(¯en; ¯an), D1(e1, e1), ..., 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 (Carleton University) Ontology-Based Multidimensional Contexts 12 / 23
  63. 63. Multidimensional Context Ontological Representation of the Extended MD Model Datalog± as Representation Language Dimensional constraints as EGDs or negative constraints: x = x ← R1(¯e1; ¯a1), ..., Rn(¯en; ¯an), D1(e1, e1), ..., Dm(em, em) ⊥ ← R1(¯e1; ¯a1), ..., Rn(¯en; ¯an), D1(e1, e1), ..., Dm(em, em) Di are parent-child predicates and Ri are categorical predicates Dimensional rules as TGDs: ∃¯az Rk (¯ek ; ¯ak ) ← R1(¯e1; ¯a1), ..., Rn(¯en; ¯an), D1(e1, e1), ..., 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 ”Upward or downward navigation captured by joins between categorical predicates and parent-child predicates in bodies” (Carleton University) Ontology-Based Multidimensional Contexts 12 / 23
  64. 64. Multidimensional Context Ontological Representation of the Extended MD Model Properties of MD Ontologies Datalog± is a family of languages with different syntactic restrictions on rules and their interaction to guarantee tractability (Carleton University) Ontology-Based Multidimensional Contexts 13 / 23
  65. 65. Multidimensional Context Ontological Representation of the Extended MD Model 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) (Carleton University) Ontology-Based Multidimensional Contexts 13 / 23
  66. 66. Multidimensional Context Ontological Representation of the Extended MD Model 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) (Carleton University) Ontology-Based Multidimensional Contexts 13 / 23
  67. 67. Multidimensional Context Ontological Representation of the Extended MD Model 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) The chase (that propagates data forward through rules) may not terminate (Carleton University) Ontology-Based Multidimensional Contexts 13 / 23
  68. 68. Multidimensional Context Ontological Representation of the Extended MD Model 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) The chase (that propagates data forward 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 (Carleton University) Ontology-Based Multidimensional Contexts 13 / 23
  69. 69. Multidimensional Context Ontological Representation of the Extended MD Model Properties of MD Ontologies The separability condition on the (good) interaction between TGDs and EGDs becomes application dependent (Cali et al., 2011) (Carleton University) Ontology-Based Multidimensional Contexts 14 / 23
  70. 70. Multidimensional Context Ontological Representation of the Extended MD Model Properties of MD Ontologies 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 (Carleton University) Ontology-Based Multidimensional Contexts 14 / 23
  71. 71. Multidimensional Context Ontological Representation of the Extended MD Model Properties of MD Ontologies 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 (Carleton University) Ontology-Based Multidimensional Contexts 14 / 23
  72. 72. Multidimensional Context Ontological Representation of the Extended MD Model Properties of MD Ontologies 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) (Carleton University) Ontology-Based Multidimensional Contexts 14 / 23
  73. 73. Multidimensional Context Ontological Representation of the Extended MD Model Properties of MD Ontologies 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 (Carleton University) Ontology-Based Multidimensional Contexts 14 / 23
  74. 74. Multidimensional Context Ontological Representation of the Extended MD Model Properties of MD Ontologies 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 That is, rewriting of conjunctive queries into FO queries in terms of underlying DB predicates (Carleton University) Ontology-Based Multidimensional Contexts 14 / 23
  75. 75. Multidimensional Context Ontological Representation of the Extended MD Model Query Answering on MD Ontology A non-deterministic algorithm WeaklySticky-QAns for weakly-sticky Datalog± (Cali et al., 2012) (Carleton University) Ontology-Based Multidimensional Contexts 15 / 23
  76. 76. Multidimensional Context Ontological Representation of the Extended MD Model 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 (Carleton University) Ontology-Based Multidimensional Contexts 15 / 23
  77. 77. Multidimensional Context Ontological Representation of the Extended MD Model 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 It shows how query atoms are entailed from extensional data (Carleton University) Ontology-Based Multidimensional Contexts 15 / 23
  78. 78. Multidimensional Context Ontological Representation of the Extended MD Model 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 It shows how query atoms are entailed from extensional data The algorithm runs in polynomial time in the size of the extensional database (Carleton University) Ontology-Based Multidimensional Contexts 15 / 23
  79. 79. Multidimensional Context Ontological Representation of the Extended MD Model 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 It shows how query atoms are entailed from extensional data 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) (Carleton University) Ontology-Based Multidimensional Contexts 15 / 23
  80. 80. Multidimensional Context Ontological Representation of the Extended MD Model Query Answering on MD Ontology The new algorithm uses a modified parsimonious chase procedure (parsimonious chase for shy programs) (Leone et al., KR 2012) (Carleton University) Ontology-Based Multidimensional Contexts 16 / 23
  81. 81. Multidimensional Context Ontological Representation of the Extended MD Model Query Answering on MD Ontology 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) (Carleton University) Ontology-Based Multidimensional Contexts 16 / 23
  82. 82. Multidimensional Context Ontological Representation of the Extended MD Model Query Answering on MD Ontology 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 (Carleton University) Ontology-Based Multidimensional Contexts 16 / 23
  83. 83. Multidimensional Context Ontological Representation of the Extended MD Model Query Answering on MD Ontology 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 We also studied the magic-sets rewriting technique in combination with this QA algorithm (Milani and Bertossi, AMW 2015) (Carleton University) Ontology-Based Multidimensional Contexts 16 / 23
  84. 84. 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 (Carleton University) Ontology-Based Multidimensional Contexts 17 / 23
  85. 85. 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 The original instance D of schema S is to be assessed or cleaned through the context (Carleton University) Ontology-Based Multidimensional Contexts 17 / 23
  86. 86. 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 The original instance D of schema S is to be assessed or cleaned through the context By mapping D into the contextual schema/instance C (Carleton University) Ontology-Based Multidimensional Contexts 17 / 23
  87. 87. 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 The original instance D of schema S is to be assessed or cleaned through the context By mapping D into the contextual schema/instance C 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 … (Carleton University) Ontology-Based Multidimensional Contexts 17 / 23
  88. 88. 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 The original instance D of schema S is to be assessed or cleaned through the context By mapping D into the contextual schema/instance C 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 … (Carleton University) Ontology-Based Multidimensional Contexts 17 / 23
  89. 89. 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 The original instance D of schema S is to be assessed or cleaned through the context By mapping D into the contextual schema/instance C In the context: • Nickname predicates Ri ∈ S • 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 … (Carleton University) Ontology-Based Multidimensional Contexts 17 / 23
  90. 90. 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 The original instance D of schema S is to be assessed or cleaned through the context By mapping D into the contextual schema/instance C In the context: • Nickname predicates Ri ∈ S • 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 … (Carleton University) Ontology-Based Multidimensional Contexts 17 / 23
  91. 91. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist Quality predicates are defined with non-recursive Datalog rules in terms of categorical predicates and built-ins (Carleton University) Ontology-Based Multidimensional Contexts 18 / 23
  92. 92. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist 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 (Carleton University) Ontology-Based Multidimensional Contexts 18 / 23
  93. 93. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist 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 They are defined by quality data extraction rules written in non-recursive Datalog in terms of S , P, and built-ins (Carleton University) Ontology-Based Multidimensional Contexts 18 / 23
  94. 94. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist 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 They are defined by quality data extraction rules written in non-recursive Datalog in terms of S , P, and built-ins Quality query answering for Q imposed on S: (Carleton University) Ontology-Based Multidimensional Contexts 18 / 23
  95. 95. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist 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 They are defined by quality data extraction rules written in non-recursive Datalog in terms of S , P, and built-ins Quality query answering for Q imposed on S: 1 Replace predicates in Q with their quality versions obtaining Qq (Carleton University) Ontology-Based Multidimensional Contexts 18 / 23
  96. 96. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist 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 They are defined by quality data extraction rules written in non-recursive Datalog in terms of S , P, and built-ins Quality query answering for Q imposed on S: 1 Replace predicates in Q with their quality versions obtaining Qq 2 Rewrite Qq into QC by applying the quality data extraction rules (Carleton University) Ontology-Based Multidimensional Contexts 18 / 23
  97. 97. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist 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 They are defined by quality data extraction rules written in non-recursive Datalog in terms of S , P, and built-ins Quality query answering for Q imposed on S: 1 Replace predicates in Q with their quality versions obtaining Qq 2 Rewrite Qq into QC by applying the quality data extraction rules 3 Unfold the definition of quality predicates P, that results into QM in terms of categorical relations and nicknames (Carleton University) Ontology-Based Multidimensional Contexts 18 / 23
  98. 98. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist 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 They are defined by quality data extraction rules written in non-recursive Datalog in terms of S , P, and built-ins Quality query answering for Q imposed on S: 1 Replace predicates in Q with their quality versions obtaining Qq 2 Rewrite Qq into QC by applying the quality data extraction rules 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 (Carleton University) Ontology-Based Multidimensional Contexts 18 / 23
  99. 99. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist Example Dimensional rules in M: (Carleton University) Ontology-Based Multidimensional Contexts 19 / 23
  100. 100. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist Example Dimensional rules in M: WorkingTimes(u, t; n, y) ← WorkingSchedules(u, d; n, y), DayTime(d, t) (Carleton University) Ontology-Based Multidimensional Contexts 19 / 23
  101. 101. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist Example Dimensional rules in M: WorkingTimes(u, t; n, y) ← WorkingSchedules(u, d; n, y), DayTime(d, t) PatientUnit(u, t; p) ← PatientWard(w, d; p), DayTime(d, t), UnitWard(u, w) (Carleton University) Ontology-Based Multidimensional Contexts 19 / 23
  102. 102. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist Example Dimensional rules in M: WorkingTimes(u, t; n, y) ← WorkingSchedules(u, d; n, y), DayTime(d, t) PatientUnit(u, t; p) ← PatientWard(w, d; p), DayTime(d, t), UnitWard(u, w) Quality predicates in P: (Carleton University) Ontology-Based Multidimensional Contexts 19 / 23
  103. 103. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist Example Dimensional rules in M: WorkingTimes(u, t; n, y) ← WorkingSchedules(u, d; n, y), DayTime(d, t) PatientUnit(u, t; p) ← PatientWard(w, d; p), DayTime(d, t), UnitWard(u, w) Quality predicates in P: TakenByNurse(t, p, n, y) ← WorkingTimes(u, t; n, y), PatientUnit(u, t; p) (Carleton University) Ontology-Based Multidimensional Contexts 19 / 23
  104. 104. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist Example Dimensional rules in M: WorkingTimes(u, t; n, y) ← WorkingSchedules(u, d; n, y), DayTime(d, t) PatientUnit(u, t; p) ← PatientWard(w, d; p), DayTime(d, t), UnitWard(u, w) Quality predicates in P: 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 (Carleton University) Ontology-Based Multidimensional Contexts 19 / 23
  105. 105. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist Example Quality version Measurementsq : (Carleton University) Ontology-Based Multidimensional Contexts 20 / 23
  106. 106. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist Example Quality version Measurementsq : Measurementsq (t, p, v) ← Measurements (t, p, v), TakenByNurse(t, p, n, y), TakenWithTherm(t, p, b), b = B1, y = certified (Carleton University) Ontology-Based Multidimensional Contexts 20 / 23
  107. 107. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist Example Quality version Measurementsq : Measurementsq (t, p, v) ← Measurements (t, p, v), TakenByNurse(t, p, n, y), TakenWithTherm(t, p, b), b = B1, y = certified A doctor asks the body temperatures of Tom Waits for September 5 taken around noon: (Carleton University) Ontology-Based Multidimensional Contexts 20 / 23
  108. 108. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist Example Quality version Measurementsq : Measurementsq (t, p, v) ← Measurements (t, p, v), TakenByNurse(t, p, n, y), TakenWithTherm(t, p, b), b = B1, y = certified A doctor asks the body temperatures of Tom Waits for September 5 taken around noon: Q(t, v) : Measurements(t, Tom Waits, v) ∧ Sep5-11:45 ≤ t ≤ Sep5-12:15 (Carleton University) Ontology-Based Multidimensional Contexts 20 / 23
  109. 109. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist Example Quality version Measurementsq : Measurementsq (t, p, v) ← Measurements (t, p, v), TakenByNurse(t, p, n, y), TakenWithTherm(t, p, b), b = B1, y = certified A doctor asks the body temperatures of Tom Waits for September 5 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 (Carleton University) Ontology-Based Multidimensional Contexts 20 / 23
  110. 110. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist Example Replacing predicates of S in Q with their quality versions in Sq: (Carleton University) Ontology-Based Multidimensional Contexts 21 / 23
  111. 111. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist Example Replacing predicates of S in Q with their quality versions in Sq: Qq (t, v):Measurementsq (t, Tom Waits, v)∧Sep5-11:45 ≤ t ≤ Sep5-12:15 (Carleton University) Ontology-Based Multidimensional Contexts 21 / 23
  112. 112. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist Example Replacing predicates of S in Q with their quality versions in Sq: Qq (t, v):Measurementsq (t, Tom Waits, v)∧Sep5-11:45 ≤ t ≤ Sep5-12:15 Applying the definition of quality versions: (Carleton University) Ontology-Based Multidimensional Contexts 21 / 23
  113. 113. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist Example Replacing predicates of S in Q with their quality versions in Sq: Qq (t, v):Measurementsq (t, Tom Waits, v)∧Sep5-11:45 ≤ t ≤ Sep5-12:15 Applying the definition of quality versions: 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 (Carleton University) Ontology-Based Multidimensional Contexts 21 / 23
  114. 114. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist Example Replacing predicates of S in Q with their quality versions in Sq: Qq (t, v):Measurementsq (t, Tom Waits, v)∧Sep5-11:45 ≤ t ≤ Sep5-12:15 Applying the definition of quality versions: 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 Unfolding the definition of quality predicates in P: (Carleton University) Ontology-Based Multidimensional Contexts 21 / 23
  115. 115. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist Example Replacing predicates of S in Q with their quality versions in Sq: Qq (t, v):Measurementsq (t, Tom Waits, v)∧Sep5-11:45 ≤ t ≤ Sep5-12:15 Applying the definition of quality versions: 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 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 (Carleton University) Ontology-Based Multidimensional Contexts 21 / 23
  116. 116. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist Example Measurements has the same extension of Measurements (Carleton University) Ontology-Based Multidimensional Contexts 22 / 23
  117. 117. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist Example Measurements has the same extension of Measurements WorkingTimes and PatientUnit are computed by QA on M (Carleton University) Ontology-Based Multidimensional Contexts 22 / 23
  118. 118. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist Example Measurements has the same extension of Measurements WorkingTimes and PatientUnit are computed by QA on M Measurements Time Patient Value Sep/5-12:10 Tom Waits 38.2 Sep/6-11:50 Tom Waits 37.1 Sep/7-12:15 Tom Waits 37.7 Sep/9-12:00 Tom Waits 37.0 Sep/6-11:05 Lou Reed 37.5 Sep/5-12:05 Lou Reed 38.0 (Carleton University) Ontology-Based Multidimensional Contexts 22 / 23
  119. 119. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist Example Measurements has the same extension of Measurements WorkingTimes and PatientUnit are computed by QA on M The first second and last measurements have the expected quality Measurements Time Patient Value Sep/5-12:10 Tom Waits 38.2 Sep/6-11:50 Tom Waits 37.1 Sep/7-12:15 Tom Waits 37.7 Sep/9-12:00 Tom Waits 37.0 Sep/6-11:05 Lou Reed 37.5 Sep/5-12:05 Lou Reed 38.0 (Carleton University) Ontology-Based Multidimensional Contexts 22 / 23
  120. 120. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist Example Measurements has the same extension of Measurements WorkingTimes and PatientUnit are computed by QA on M The first second and last measurements have the expected quality Measurements Time Patient Value Sep/5-12:10 Tom Waits 38.2 Sep/6-11:50 Tom Waits 37.1 Sep/7-12:15 Tom Waits 37.7 Sep/9-12:00 Tom Waits 37.0 Sep/6-11:05 Lou Reed 37.5 Sep/5-12:05 Lou Reed 38.0 (Carleton University) Ontology-Based Multidimensional Contexts 22 / 23
  121. 121. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist Example Measurements has the same extension of Measurements WorkingTimes and PatientUnit are computed by QA on M 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 Sep/5-12:10 Tom Waits 38.2 Sep/6-11:50 Tom Waits 37.1 Sep/7-12:15 Tom Waits 37.7 Sep/9-12:00 Tom Waits 37.0 Sep/6-11:05 Lou Reed 37.5 Sep/5-12:05 Lou Reed 38.0 (Carleton University) Ontology-Based Multidimensional Contexts 22 / 23
  122. 122. Multidimensional Context MD Context for Quality Data Assessment MD Contexts and Quality Query Answering: The Gist Example Measurements has the same extension of Measurements WorkingTimes and PatientUnit are computed by QA on M 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 Sep/5-12:10 Tom Waits 38.2 Sep/6-11:50 Tom Waits 37.1 Sep/7-12:15 Tom Waits 37.7 Sep/9-12:00 Tom Waits 37.0 Sep/6-11:05 Lou Reed 37.5 Sep/5-12:05 Lou Reed 38.0 (Carleton University) Ontology-Based Multidimensional Contexts 22 / 23
  123. 123. Conclusions Conclusions Multidimensional contexts are represented as Datalog± ontologies (Carleton University) Ontology-Based Multidimensional Contexts 23 / 23
  124. 124. Conclusions Conclusions Multidimensional contexts are represented as Datalog± ontologies They allow us to specify data quality conditions, and to retrieve quality data (Carleton University) Ontology-Based Multidimensional Contexts 23 / 23
  125. 125. Conclusions Conclusions Multidimensional contexts are represented as Datalog± ontologies They allow us to specify data quality conditions, and to retrieve quality data Development, implementation of the query answering algorithms is ongoing work (Carleton University) Ontology-Based Multidimensional Contexts 23 / 23
  126. 126. Conclusions Conclusions Multidimensional contexts are represented as Datalog± ontologies They allow us to specify data quality conditions, and to retrieve quality data Development, implementation of the query answering algorithms is ongoing work Several extensions: (Carleton University) Ontology-Based Multidimensional Contexts 23 / 23
  127. 127. Conclusions Conclusions Multidimensional contexts are represented as Datalog± ontologies They allow us to specify data quality conditions, and to retrieve quality data Development, implementation of the query answering algorithms is ongoing work Several extensions: Uncertain downward-navigation in dimensional rules (Carleton University) Ontology-Based Multidimensional Contexts 23 / 23
  128. 128. Conclusions Conclusions Multidimensional contexts are represented as Datalog± ontologies They allow us to specify data quality conditions, and to retrieve quality data Development, implementation of the query answering algorithms is ongoing work Several extensions: Uncertain downward-navigation in dimensional rules Checking dimensional constraints not only on the result of the chase but while data generation (Carleton University) Ontology-Based Multidimensional Contexts 23 / 23
  129. 129. Conclusions Conclusions Multidimensional contexts are represented as Datalog± ontologies They allow us to specify data quality conditions, and to retrieve quality data Development, implementation of the query answering algorithms is ongoing work Several extensions: Uncertain downward-navigation in dimensional rules 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 (Carleton University) Ontology-Based Multidimensional Contexts 23 / 23

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