Outline
Ontology Debugging
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—— Debugging Semantic Defects
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Background
Explanations for the Semantic Defects
Unsatisfiable Concepts & Incoherent Ontologies
Inconsistent Ontologies
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Zlatan Dragisic and Qiang Liu
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Linköpings universitet, Sweden
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Ontologies based on DL
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Repairing the Unsatisfiable Concepts
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Diagnosis
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Pinpointing
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Hitting sets with axiom ranking
Summary
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Concepts: C ⊑ D, C ≡ D
Roles: hasMember
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OWL ontology maps to DL knowledge base
OWL DL – based on SHOIN(D)
(ALC + transitive roles,
ABox – assertion component
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Glass-box approach
Black-box approach
OWL DL
TBox – terminological axioms
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Find the Explanations for the Unsatisfiable Concepts
Ontologies and Ontology Engineering, VT 2011
Individuals: C(a), D(b), R(a, b)
→S
role hierarchies,
→H
nominals,
→O
inverse roles,
→I
number restrictions) →N
Knowledge base:
data type properties, data values or data types →(D)
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Semantic defects
Ontology defects
Three main categories of defects:
l Syntactic defects
l Semantic defects
l Modeling defects
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Contradictions in TBox
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Contradictions in ABox
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Unsatisfiable concepts & incoherent ontologies
Inconsistent ontologies
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Unsatisfiable concepts
Inconsistent Ontologies
A concept is
unsatisfiable iff AI= ∅
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for all models I of the
ontology
Unsatisfiable concepts
can not have any
individuals
Ontology is incoherent
if has an unsatisfiable
concept
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An ontology is
inconsistent if it has no
models
Contradiction in the
ABox
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Animal
⊓
CanFly
¬
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Bird
Eagle
Animal
⊓
¬
Bird
Eagle
⊓
CanFly
⊓
Penguin
Penguin
Pingu
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Outline
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Example : an Incoherent Ontology
Background
Explanations for the Semantic Defects
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Unsatisfiable Concepts & Incoherent Ontologies
Inconsistent Ontologies
Find the Explanations for the Unsatisfiable Concepts
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Glass-box approach
Black-box approach
Repairing the Unsatisfiable Concepts
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DL Reasoner
Diagnosis
Pinpointing
Hitting sets with axiom ranking
Summary
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What are the root causes of these defects? 10
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Minimal Unsatisfiability Preserving
Sub-TBoxes (MUPS)
Explain the Semantic Defects
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We need to identify the sets of axioms which are necessary
for causing the logic contradictions.
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For example, for the unsatisfiable concept “A1”, there are two (and
only two) sets of axioms rendering A1 = ⊥
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The MUPS of an unsatisfiable concept implies the solutions for
repairing.
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Remove at least one axiom from each axiom set in the MUPS
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Minimal Incoherence Preserving
Sub-TBox (MIPS)
Example
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For all the unsatisfiable concepts in the ontology, we have
Possible ways of repairing all the unsatisfiable concepts in
the ontology:
How to represent all these possibilities?
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Minimal Inconsistent Preserving
Sub-Ontologies (MISO)
Example : an Inconsistent Ontology
DL Reasoner
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Outline
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Unsatisfiable Concepts & Incoherent Ontologies
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Inconsistent Ontologies
Find the Explanations for the Unsatisfiable Concepts
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The Example Seen Before
Background
Explanations for the Semantic Defects
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DL Reasoner
Glass-box approach
Black-box approach
Repairing the Unsatisfiable Concepts
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Diagnosis
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Pinpointing
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Hitting sets with axiom ranking
Summary
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How to make the program to find MUPS?18
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Glass-box Approach
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Glass-box Approach
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By modifying the internals of a DL reasoner for
extract and reveal the cause for unsatisfiability.
Phase 1 : Clash detection procedure
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DL Reasoner
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It gives explanation to why the error occurs.
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Use tableaux algorithm by applying transformation rules
to individuals in the ontology until no more rules are
applicable or an individual has a clash.
e.g. find out the axioms in the ontology responsible for the
logic contradictions.
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For example, an individual belongs to a concept and its
complement.
Phase 2 : Tableaux trace procedure
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Trace back to find the source axioms supporting the
clash and determine the minimal sets of support (i.e.
MUPS).
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Glass-box Approach
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Black-box Approach
Advantage
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By tightly integrating the debugging with the reasoning
procedure, precise results can be obtained.
By using DL reasoner as an oracle for a certain set of
questions (standard inferences such as satisfiability,
subsumption, etc.)
Disadvantage
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The reasoner needs to maintain extra data structures to track
the source and its dependencies, which introduces
additional memory and computation consumption.
DL Reasoner
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Give explanation to the dependencies between
unsatisfiable concepts.
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i.e. distinguish root from derived unsatisfiable concepts.
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Black-box Approach
Black-box Approach
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Dependency detection algorithm
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For each unsatisfiable concept in the ontology, the
algorithm returns all its parent dependency unsatisfiable
concepts along with the corresponding axioms that link
this concept to the parent.
Advantage
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Disadvantage
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Reasoner independence, i.e., you do not need a specialized,
explanation generating reasoner.
Avoid the performance penalty (memory consumption) of
glass box techniques.
Since it does not follow the standard reasoning procedure,
the results are sound but not complete.
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Diagnosis
Outline
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Background
Explanations for the Semantic Defects
Unsatisfiable Concepts & Incoherent Ontologies
Inconsistent Ontologies
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Glass-box approach
Black-box approach
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System represented as the set (SD, COMP)
l SD – system description
l COMP – set of system components
Example
Repairing the Unsatisfiable Concepts
Diagnosis
Pinpointing
Hitting sets with axiom ranking
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Generic method – applicable to a number of domains
Find the Explanations for the Unsatisfiable Concepts
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Summary
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SD
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COMP – ax1, ax2, ax3, ax4, ax5, ax6 , ax7
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Diagnosis
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Diagnosis
Observations made about the system – set OBS
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Naïve approach:
Example: A1, A3, A6, A7 – are unsatisfiable
Generate subsets ∆ of COMP and check for
consistency of
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Problem: complexity
Diagnoses for our example:
{ax1, ax4}, {ax1, ax5, ax7}, {ax2, ax4},…
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Conflict sets and hitting sets
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Hitting set example
Conflict sets for our example:
{ax1, ax2}, {ax3, ax4, ax5}, {ax4, ax7}
Conflict sets for our example:
{ax1, ax2}, {ax3, ax4, ax5}, {ax4, ax7}
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Pinpointing
Diagnosis with hitting sets still computationaly too
expensive – NP complete
Compute set of axioms which need to be removed/fixed
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Algorithm:
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Find unsatisfiable concepts
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Search for MUPS for unsatisfiable concepts
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Calculate MIPS from MUPS
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Calculate the pinpoint from MIPS
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Remove axioms in the pinpoint from the ontology
How to find conflict sets?
Compute all refutations of
Record the AB instances entering the refutation
is set of of AB instances used in the refutation then
If
does not have to be minimal
is a conflict set.
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Pinpointing
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Pinpointing
Find unsatisfiable concepts
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Search for MUPS for unsatisfiable concepts
Calculate MIPS from MUPS
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Pinpointing
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Hitting set with axiom ranking
Calculate the pinpoint from MIPSs
Remove axioms in pinpoint from the ontology
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To do this we need to calculate cores.
Cores are sets of axioms occuring in several incoherent TBoxes.
Core arity – number of incoherent TBoxes an axiom appears in
Core size – number of axioms in the core
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Hitting sets generated from MUPS
Ranking criteria introduced into the algorithm
Optimality based on minimal path rank
We are interested in cores of maximal arity (and size)
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Axiom Ranking strategies
Hitting set with axiom ranking
Ranking based on:
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User test cases
Provenance information regarding change
Syntactic relevance
Further improvements
Focus on root unsatisfiable concepts
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Summary
Outline
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Background
Explanations for the Semantic Defects
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In this presentation, we introduced the existing research work
on ontology debugging, focusing on one kind of ontological
defects —— semantic defects.
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We reviewed different kinds of semantic defects and
explanations for these semantic defects.
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We reviewed the ontology debugging techniques for
Glass-box approach
Black-box approach
Repairing the Unsatisfiable Concepts
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Unsatisfiable Concepts & Incoherent Ontologies
Inconsistent Ontologies
Find the Explanations for the Unsatisfiable Concepts
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Diagnosis
Pinpointing
Hitting sets with axiom ranking
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Finding explanations for the unsatisfiable concepts
Repairing the unsatisfiable concepts
Summary
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References
[1] Schlobach S, Debugging and semantic clarification by pinpointing,
Proceedings of the 2nd European Semantic Web Conference - ESWC05,
LNCS 3532, 226-240, 2005.
[2] Kalyanpur A, Parsia B, Sirin E, Cuenca-Grau B, Repairing unsatisfiable
concepts in OWL ontologies, Proceedings of the 3rd European Semantic
Web Conference - ESWC06, LNCS 4011, 170-184, 2006.
[3] Kalyanpur A, Parsia B, Sirin E, Hendler J, Debugging unsatisfiable
classes in OWL ontologies, Journal of Web semantics, 3(4):268-293,
2005.
[4] Schlobach S and Huang Z, Inconsistent Ontology Diagnosis and Repair,
SEKT Deliverable D3.6.3, 2007.
Thank you!
[5] R. Reiter. A theory of diagnosis from first principles. 1987. Artificial
Intelligence 32:57-95.
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