1. Interactive repairing of inconsistent knowledge bases
DaQuaTa International Workshop Lyon - France
12/12/2017
Interactive repairing of inconsistent knowledge bases
Abdallah Arioua
Angela Bonifati
University of Lyon 1 / LIRIS
France.

2. 1 Motivation Interactive repairing of knowledge bases
Motivation
Interactive repairing of knowledge bases
Knowledge Bases are ubiquitous:
The Semantic Web, ontology-based reasoning and data access.
Big data integration and fusion.
Knowledge and concept graphs in industry
Errors can be introduced from mappings, typos, knowledge fusion, etc.
Automatic repairing is costly and lossy.
Bring human to the loop for a better quality.
The democratization of data cleaning.
A new paradigm that seeks to exploit knowledge, typically domain knowledge, when querying data.
More precisely, instead of a database, we consider a knowledge base which is composed of data and of an ontology, and we want to query the data while taking into account inferences enabled by the ontology.
More generally, adding an ontological layer on top of data has at least three kinds of well-acknowledged advantages:
Ontologies can be used to enrich the vocabulary of data sources, thereby allowing users to formulate their queries in a richer, more familiar vocabulary which abstracts from the specific way data is stored.
By allowing inference of new facts, ontologies allow for incomplete data.
Data incompleteness may come from a lack of information but it may also be deliberate because one does not want to explicitely store all details about objects in the database.
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3. 1 Preliminaries Logical language and knowledge bases
Preliminaries
Logical language and knowledge bases
A knowledge base K is a set of facts, TGDs (rules) and CDDs (constraints).
Formalism
Weakly-acyclic
Correspond to Denial Constraints with equality
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4. 1 Preliminaries Logical language and knowledge bases
Preliminaries
Logical language and knowledge bases
A knowledge base K is a set of facts, TGDs (rules) and CDDs (constraints).
Reasoning
Formalism
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5. 1 Preliminaries Logical language and knowledge bases
Preliminaries
Logical language and knowledge bases
A knowledge base K is a set of facts, TGDs (rules) and CDDs (constraints).
Reasoning
Formalism
Example:
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6. 1 Preliminaries Inconsistency handling
Preliminaries
Inconsistency handling
A knowledge base K is inconsistent iff:
K is inconsistent:
Conflicts discovery
Repairing K using Deletions:
Remove facts that are involved in conflicts.
Lossy approach.
Repairing K using Updates:
E.g. John has an allergy against Penicillin rather than Aspirin
Penicillin is prescribed to John rather than Aspirin …
User interaction
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7. O utline Update-based repairing User intervention
Given a KB equipped with a set of TGDs and CDDs, produce an error-free KB:
Accounting for the interplay of TGDs and CDDs.
Minimizing user interaction.
utline O
Update-based repairing
User intervention
Questioning strategies
Experimental study
Conclusion
A new paradigm that seeks to exploit knowledge, typically domain knowledge, when querying data.
More precisely, instead of a database, we consider a knowledge base which is composed of data and of an ontology, and we want to query the data while taking into account inferences enabled by the ontology.
More generally, adding an ontological layer on top of data has at least three kinds of well-acknowledged advantages:
Ontologies can be used to enrich the vocabulary of data sources, thereby allowing users to formulate their queries in a richer, more familiar vocabulary which abstracts from the specific way data is stored.
By allowing inference of new facts, ontologies allow for incomplete data.
Data incompleteness may come from a lack of information but it may also be deliberate because one does not want to explicitely store all details about objects in the database.

8. Update-based repairing2
Update-based repairing
Introduction
Repairing using updates in KBs and RDBs1
On Functional Dependencies (FDs), Conditional FDs, Denial Constraints (DCs).
Repairing using updates in KBs:
TGDs are natural in KB reasoning but they may introduce new conflicts.
1. Apply TGDs then 2. apply CDDs then go to 1. and repeat.
+ TGDs
CDDs …
Computationally expensive, overwhelming and some finiteness issues.
A new paradigm that seeks to exploit knowledge, typically domain knowledge, when querying data.
More precisely, instead of a database, we consider a knowledge base which is composed of data and of an ontology, and we want to query the data while taking into account inferences enabled by the ontology.
More generally, adding an ontological layer on top of data has at least three kinds of well-acknowledged advantages:
Ontologies can be used to enrich the vocabulary of data sources, thereby allowing users to formulate their queries in a richer, more familiar vocabulary which abstracts from the specific way data is stored.
By allowing inference of new facts, ontologies allow for incomplete data.
Data incompleteness may come from a lack of information but it may also be deliberate because one does not want to explicitely store all details about objects in the database.
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1 Philip Bohannon et al. 2005, Kolahi and Lakshmanan 2009, Yakout et al. 2011, Xu Chu et al. 2013, Farid et al. 2016

9. Update-based repairing2
Update-based repairing
Basic concepts
A set of fixes P is called consistent fix if it produces a consistent KB.
P is a repair fix if KB is consistent and minimally changed (w.r.t set inclusion).
Example:
A new paradigm that seeks to exploit knowledge, typically domain knowledge, when querying data.
More precisely, instead of a database, we consider a knowledge base which is composed of data and of an ontology, and we want to query the data while taking into account inferences enabled by the ontology.
More generally, adding an ontological layer on top of data has at least three kinds of well-acknowledged advantages:
Ontologies can be used to enrich the vocabulary of data sources, thereby allowing users to formulate their queries in a richer, more familiar vocabulary which abstracts from the specific way data is stored.
By allowing inference of new facts, ontologies allow for incomplete data.
Data incompleteness may come from a lack of information but it may also be deliberate because one does not want to explicitely store all details about objects in the database.
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10. Update-based repairing2
Update-based repairing
∏-Repairability
Repairing with immutable set of positions ¦.
Trusted positions or previously fixed positions.
Some KBs cannot be fixed when some positions are immutable.
Example:
Consider:
Not p-repairable
Checking ¦-repairability:
Change all non-immutable positions to unique labelled nulls.
Check consistency.
The procedure is sound, complete and computed in linear time (data complexity).
Inconsistent
A new paradigm that seeks to exploit knowledge, typically domain knowledge, when querying data.
More precisely, instead of a database, we consider a knowledge base which is composed of data and of an ontology, and we want to query the data while taking into account inferences enabled by the ontology.
More generally, adding an ontological layer on top of data has at least three kinds of well-acknowledged advantages:
Ontologies can be used to enrich the vocabulary of data sources, thereby allowing users to formulate their queries in a richer, more familiar vocabulary which abstracts from the specific way data is stored.
By allowing inference of new facts, ontologies allow for incomplete data.
Data incompleteness may come from a lack of information but it may also be deliberate because one does not want to explicitely store all details about objects in the database.
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11. 3 User intervention Basic definitions Example:
User intervention
Basic definitions
A question © is a finite set of fixes.
If all the fixes in © yield a ¦-repairable KB then © is sound.
The user choses a fix from © as an answer.
A sequence of sound questions and answers is called an inquiry over K.
©: which fix is true from the following set?
Example:
A new paradigm that seeks to exploit knowledge, typically domain knowledge, when querying data.
More precisely, instead of a database, we consider a knowledge base which is composed of data and of an ontology, and we want to query the data while taking into account inferences enabled by the ontology.
More generally, adding an ontological layer on top of data has at least three kinds of well-acknowledged advantages:
Ontologies can be used to enrich the vocabulary of data sources, thereby allowing users to formulate their queries in a richer, more familiar vocabulary which abstracts from the specific way data is stored.
By allowing inference of new facts, ontologies allow for incomplete data.
Data incompleteness may come from a lack of information but it may also be deliberate because one does not want to explicitely store all details about objects in the database.
7/20

12. 3 User intervention Generating sound questions and inquiries
User intervention
Generating sound questions and inquiries
Procedure:
Generate a sound question by filtering values.
Ask the user and update, continue until no conflict is left.
A new paradigm that seeks to exploit knowledge, typically domain knowledge, when querying data.
More precisely, instead of a database, we consider a knowledge base which is composed of data and of an ontology, and we want to query the data while taking into account inferences enabled by the ontology.
More generally, adding an ontological layer on top of data has at least three kinds of well-acknowledged advantages:
Ontologies can be used to enrich the vocabulary of data sources, thereby allowing users to formulate their queries in a richer, more familiar vocabulary which abstracts from the specific way data is stored.
By allowing inference of new facts, ontologies allow for incomplete data.
Data incompleteness may come from a lack of information but it may also be deliberate because one does not want to explicitely store all details about objects in the database.
8/20

13. 3 User intervention Generating sound questions and inquiries
User intervention
Generating sound questions and inquiries
Procedure:
Generate a sound question by filtering values.
Ask the user and update, continue until no conflict is left.
A new paradigm that seeks to exploit knowledge, typically domain knowledge, when querying data.
More precisely, instead of a database, we consider a knowledge base which is composed of data and of an ontology, and we want to query the data while taking into account inferences enabled by the ontology.
More generally, adding an ontological layer on top of data has at least three kinds of well-acknowledged advantages:
Ontologies can be used to enrich the vocabulary of data sources, thereby allowing users to formulate their queries in a richer, more familiar vocabulary which abstracts from the specific way data is stored.
By allowing inference of new facts, ontologies allow for incomplete data.
Data incompleteness may come from a lack of information but it may also be deliberate because one does not want to explicitely store all details about objects in the database.
8/20

14. 3 User intervention Results
User intervention
Results
Proposition 1: questions are sound and polynomial.
Proposition 2: the procedure runs in finite time and produces a consistent knowledge base K.
When the procedure produces a repair of K?
If the user is an oracle then K is minimally repaired.
An oracle is a user who knows everything about K (a domain and knowledge expert).
Proposition 3: delay time between questions is polynomial.
A new paradigm that seeks to exploit knowledge, typically domain knowledge, when querying data.
More precisely, instead of a database, we consider a knowledge base which is composed of data and of an ontology, and we want to query the data while taking into account inferences enabled by the ontology.
More generally, adding an ontological layer on top of data has at least three kinds of well-acknowledged advantages:
Ontologies can be used to enrich the vocabulary of data sources, thereby allowing users to formulate their queries in a richer, more familiar vocabulary which abstracts from the specific way data is stored.
By allowing inference of new facts, ontologies allow for incomplete data.
Data incompleteness may come from a lack of information but it may also be deliberate because one does not want to explicitely store all details about objects in the database.
9/20

15. Questioning strategies4
Questioning strategies
Intuition by examples
Consider the following knowledge base:
Conflicts
Random strategy
Pick a conflict and generate all possible fixes.
No resolution if the user chooses:
We ask more questions.
Join positions!
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16. Questioning strategies4
Questioning strategies
Intuition by examples
Consider the following knowledge base:
Conflicts
Join strategy
Pick a conflict and generate all possible fixes over join positions.
We ask less questions
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17. Questioning strategies4
Questioning strategies
Intuition by examples
Consider the following knowledge base:
Conflicts
Join strategy
Pick a conflict and generate all possible fixes over join positions.
Reduce the size of the next questions.
Prune some questions.
We ask less questions
Improvement: propagate fixes.
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18. Questioning strategies4
Questioning strategies
Intuition by examples
Consider the following knowledge base:
Conflicts
MCD strategy
Rank join positions w.r.t inclusion in conflicts and choose the top ranked.
2 conflicts by one question in the example.
Observation: more overlapping less questions
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19. 5 Experimental study Experimental environment Variables:
Experimental study
Experimental environment
Variables:
Effectiveness: avg number of questions per strategy and average number of conflicts per question.
Delay time: average delay time between asked question.
Environment:
Java 8, 2.40GHz 4core, 16G RAM (windows 7).
Multi trial experiments with a cold start.
For each experimental variable we test our approach on synthetic and real-world datasets.
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20. 5 Experimental study Effectiveness KBs:
Experimental study
Effectiveness
KBs:
Durum Wheat Kb v1: manually constructed. TGDs and CDDs have been validated by experts.
Summary v1: 567 atoms, TGDs=269 , CDD=27, 185 conflicts.
Summary v2: 567 atoms, TGDs=269, CDD=100, 212 conflicts.
Results:
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21. 5 Experimental study Effectiveness: synthetic KBs no TGDs Results:5
Experimental study
Effectiveness: synthetic KBs no TGDs
Results:
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22. 5 Experimental study Effectiveness: synthetic KBs (convergence)5
Experimental study
Effectiveness: synthetic KBs (convergence)
Results:
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23. Experimental study
Effectiveness: synthetic KBs (convergence)
Results:

24. 5 Experimental study Delay time: synthetic KBs only CDDs
Experimental study
Delay time: synthetic KBs only CDDs
Reasonable delay time: less than 1 to 2 seconds1.
MCD strategy is used.
Drum wheat v1&2 less than 1 sec.
Results:
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1 Robert B Miller, Response time in man-computer conversational transactions,

25. 5 Experimental study Delay time: synthetic KBs CDDs and TGDs5
Experimental study
Delay time: synthetic KBs CDDs and TGDs
Reasonable delay time: less than 1 to 2 seconds1.
MCD strategy is used.
Drum wheat v1&2 less than 1 sec.
Results:
TGDs
CDDs D1 50
150 D2
100 D3 D4
200
Size
400 atoms
Inc ratio
100%
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1 Robert B Miller, Response time in man-computer conversational transactions,

26. 6 Conclusion Update-based repairing of inconsistent knowledge bases.
Conclusion
Summary:
Update-based repairing of inconsistent knowledge bases.
Interactive repairing in presence of interacting dependencies.
Strategies for interaction minimization.
Approach can be applied on portions of large knowledge bases.
Delay time is reasonable.
Perspectives:
Full Denial Constraints (but undecidability!).
Other Data Cleaning constraints (CFDs, Metric FDs etc.).
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27. End!
Thank you!
Questions
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