Semantic Recognition of Ontology Refactoring

Web Science & Technologies
University of Koblenz ▪ Landau, Germany

Semantic Recognition of Ontology
Refactoring
Gerd Gröner
Fernando Silva Parreiras
Steffen Staab

ISWC2010, Shanghai

Distributed Development of Ontologies

Ontology Ontology Ontology
Version V1 Change Version V2 Change Version V3 Change ...

Ontology
Change Version V4 Change ...
No change logs!

WeST Gerd Gröner ISWC 2010
groener@uni-koblenz.de 2

What has changed?
ontology version V ontology version V'

Compare

∆? Recognize,
analyze and explain!


Agenda

Problem Description and Ontology Refactoring
Analyze and describe Changes
Recognize Changes

Reasoning for Comparison of Ontology Versions

Refactoring Recognition

Discussion and Conclusion


Refactoring Scenario

ontology
version V'

ontology
version V
Change


Comparison: What has changed?
ontology version V ontology version V'

Employee ⊑ Person
Employee ⊑ Person Employee ⊑ ∃ department.Department
Employee ⊑ ∃ project.Project (d) Employee ⊑ ∃≥1 SSN.string (a)
Employee ⊑ ∃ department.Department Person ⊑ ∃ name.string
Employee ⊑ ∃=1 SSN.string (d) Person ⊑ ∃≤1 SSN.string (a)
Person ⊑ ∃ name.string Person ⊑ ∃ contact.ContactData (a)
Person ⊑ ∃ address.string (d) ContactData ⊑ ∃ telephone.string (a)
Person ⊑ ∃ telephone.string (d) ContactData ⊑ ∃ address.string (a)
Department ⊑ ∃ project.Project (a)

Analyze and Describe Changes

Observation:

Is the set of axioms (V and V') helpful to recognize changes?

How can we communicate about changes?
(domain knowledge, modeling details)

Idea:

➔ Categorize Changes by Refactorings


Refactoring Pattern
13 refactoring pattern

Example: Extract Class
Refactoring Pattern
Some properties p1, …, pn of class C should be extracted to a new class D

Refactoring
E.g., extract properties address and telephone


Refactoring: Extract Class
V V'

Employee ⊑ Person
Employee ⊑ ∃ department.Department
Employee ⊑ Person
Employee ⊑ ∃≥1 SSN.string (a)
Employee ⊑ ∃ project.Project (d)

Refactoring: Pull-Up Property
V V'

Employee ⊑ Person

Refactoring: Move Of Property
V V'

Employee ⊑ Person

Recognition: Difficulties

1. (syntactical) comparison
of axioms or triples in V
and V'

2. purely structural
comparison

➔ Semantic comparison

Agenda

Problem Motivation and Ontology Refactoring

Comparison Problem
Solution
➔ Combining Knowledge Bases
➔ Version Comparison




The Comparison Problem
V V'

Situation:
Conceptual relations in each ontology (version)
Same classes, e.g., Person

Person ⊑ ∃ address.string Person ⊑ ∃ address.string ?

Goal:
➔ Conceptual relation across versions


Comparison Methods
Matching: compare class and property names and types

Structural and semantic comparison: class subsumption
checking to compare their extensions
➔ Joint reasoning on two ontology versions to identify
conceptual relations

Problems:
How to connect them?
How to compare them?

Connecting two Versions
1. Matching between classes
2. Renaming of classes that appear in both versions

Person1 ⊑ ⊤
Person2 ⊑ ⊤

3. Introduce a common superclass
Person1 ⊑ Person
Person2 ⊑ Person

4. Relax range
ContactData ⊑ ∃ person . Person1
⇒ ContactData ⊑ ∃ person . Person

Comparison – affected axioms

Variety of modeling principles in OWL
➔ Only some need to be considered:

Property restrictions:

Corresponding axioms:
Person ⊑ ∃ contact.ContactData
Person ⊑ ∃ address.string ContactData ⊑ ∃ address.string

→ Analyzes: Class expressions of property restrictions

Comparison – affected axioms (2)
Sub- and superclasses:

Corresponding axioms:
Employee ⊑ Person
Employee ⊑ Person
Employee ⊑ ∃≥1 SSN.string
Employee ⊑ ∃=1 SSN.string
Person ⊑ ∃≤1 SSN.string

→ Analyzes: Subclass axioms and property restrictions

➔ Only certain kinds of axioms are relevant!
➔ Next Step: Normalization to ease version comparison


Normalization

Analyze axioms of class definitions of class C:

 Conjunctive normal form of C:
Ĉ ≡ C1 ⊓ … ⊓ Cn ∀ i = 1 … n: C ⊑ Ci


Reduced conjunctive normal form: Ċ
• Flattened nested conjunctions: A ⊓ (B ⊓ C) → A ⊓ B ⊓ C
• Normalized negation: ¬D → D is a named class
• B ⊑ A and A ⊔ B : A ⊔ B → A


Reduced Conjunctive Normal Form

 Uniqueness of the normal form Ċ

 Ċ is reduced conjunctive normal form of Ĉ ≡ C1 ⊓ … ⊓ Cn
for each Ci one of the following condition holds:
 Ci is a named class
 Ci is a data type or object property restriction
 Ci is a complex class definition that is neither a named
superclass of C nor a property restriction


Using the Normalization

Exploit two results
1. Only certain types of axioms are affected by the refactoring
➔ Other axioms can be neglected

2. Representation in the normal form
●
Axioms are covered by the normal form representation
● Uniqueness: class expressions C of C can be extracted
i
● Each Ci of C subsumes C

➔ Analyze changes by comparing class expressions Ci of C
and C' using subsumption checking


Diff and Common Algorithm
Diff: Compute class expressions (superclasses) from C and C'

1. Class expressions of C in version V' but not in V
E.g.,
For each class expression A of Ċ'
If the subsumption ( A ⊑ C ) does not hold then
Class expression A belongs to the difference

2. Likewise the expressions of C in version V but not in V'

➔ Difference is computed in two steps (invert V and V'):

Reduced conjunctive normal form applies to the class expressions of the result


Agenda

Problem Motivation and Ontology Refactoring






 Each pattern:
 specification of differences for comparing two versions
 description of conditions on these differences

 Comparison algorithms: determining the different and
common parts of a class in two versions
 Comparing class expressions of Ċ
 Using subsumption checking to test the conditions on the
differences


Extract Class
V V'

Difference (C = Person):

D2 = { ∃ address.string, D1 = { ∃ contact.ContactData }
∃ telephone.string }

Extracted Class: RC = ContactData
(range of ∃ contact.ContactData)

Condition:
ContactData ⊑ ∃ address.string
ContactData ⊑ ∃ telephone.string are inferred in V'

Conclusion
Described Solution:
Adopted 13 refactoring patterns and described the recognition

Realization:
Class comparison using subsumption checking
 Connect versions (V and V' are unaffected)
 Compare classes and class expressions of Ċ
 Only certain class expressions are relevant in the refactoring

Future Work:
Consider further refactoring patterns


Thank You!

Supported by: MOST-Project


Semantic Recognition of Ontology Refactoring

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