Submissions:NegativePropertyAssertions

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|Motivation=Prior to OWL 2 negative property assertions (NPA) are difficult to model and, if it they are contained in an ontology, difficult to understand by humans. On the other side, using OWL 2 one can transform these ''helping'' axioms modeling NPAs into OWL2 NPA axiom.
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|Motivation=The motivation of this pattern is to model ''negative property assertions'' (NPAs) in ontology languages such as OWL 1 [1] that do not provide a special constructor for expressing it. It is worth mentioning that not all knowledge base systems can be migrated to OWL 2 [2] for several reasons. On the other hand, NPAs modeled according to this pattern can be migrated to OWL 2 using the newly introduced constructor.
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A negative property assertion as defined in the upcoming OWL 2 states that a given individual ''i'' is never connected to a given individual ''j'' by a given property expression ''P''. In other words, asserting that ''i'' is connected to ''j'' by ''P'' results in an inconsistent ontology. In this sense this assertion can be considered as a constraint that should not be violated. In contrast, considering an ontology where it cannot be inferred that ''i'' is connected to ''j'' by ''P'' does not necessarily mean that there cannot be such a connection - in fact, it is merely not modeled.
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This pattern describe NPA for ontologies not containing explicit NPA axioms as syntactical sugars and allows for transforming axioms into OWL NPA axioms.
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[1] Patel-Schneider, P.F., Hayes, P., Horrocks, I.: OWL Web Ontology Language
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Semantics and Abstract Syntax, W3C Recommendation 10 February 2004.
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[2] Motik, B., Patel-Schneider, P.F., Parsia, B.: OWL 2 Structural Specification and Functional-Style Syntax. W3C Candidate Recommendation 11 June 2009, 2009.
|Aim=Expressing NPAs in ontologies prior to OWL 2 as well as given an transformation rule when using OWL 2.
|Aim=Expressing NPAs in ontologies prior to OWL 2 as well as given an transformation rule when using OWL 2.
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|Solution=NegativeObjectPropertyAssertion(i1 prop i2) is equivalent to:
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|Solution=NegativeObjectPropertyAssertion(prop i1 i2) is equivalent to (using OWL 2 Abstract Syntax):
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SubClassOf(ObjectOneOf(i1), ObjectComplementOf(ObjectSomeValuesFrom(prop, ObjectOneOf(i2)))))
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SubClassOf(ObjectOneOf(i1), ObjectComplementOf(ObjectSomeValuesFrom(prop, ObjectOneOf(i2))))
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Let ''C'' and ''D'' be concepts. Then ''C'' and ''D'' are disjoint if, and only if, ''C'' is subsumed by the complement of ''D'', i.e., '(
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SubClassOf( C ObjectComplementOf(D) ).
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The equivalence is correct because of the duality of disjointness, equivalence, and unsatisfiability: ''C'' is subsumed by ''D'' if, and only if,
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ObjectIntersectionOf( C ObjectComplementOf(D) ) is unsatisfiable, and the intersection of ''C'' and ''D'' is unsatisfiable if, and only if, ''C' and ''D'' are disjoint.
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One also reminds that the extension of the concept
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ObjectSomeValuesFrom(prop C) is the set of individuals ''i'' which are connected to an individual ''j'' that is in the extension of the concept ''C'', by the property ''prop''.
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Let ''NegativePropertyAssertion(p a b)'' be a negative property assertion axiom, i.e., the individual ''a'' is not related to ''b'' by the property ''p''. Then the extension of
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''ObjectSomeValuesFrom( p ObjectOneOf(b) )'' which contain all individuals that are connected to ''b'' by ''p'' must not contain ''a''. This is true, if, and only if ''ObjectOneOf(a)'' is disjoint to ObjectSomeValuesFrom( p ObjectOneOf(b) )''
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ObjectProperty prop
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|ProblemExample=Consider a social network containing facts about people and their relationships.
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Let ''Adam'' and ''Eve'' be two persons and like a property (''A likes B''). Furthermore we know that ''Adam'' does not like ''Eve'' but we have no dislike relationship. Moreover, our language (such as OWL 1) does not have any NPA axiom constructor.
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The sample ontology is interpreted with respect to the open-world semantics,
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i. e. , one can not infer the dislike merely from the lack of a property assertion axiom ''ObjectPropertyAssertion(like Adam Eve)''. Then this fact can be expressed with the following axiom (we will also use the OWL 2 Abstract Syntax here):
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''SubClassOf (Adam ComplementOf(ObjectSomeValuesFrom( likes ObjectOneOf(Eve))))''
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|Event=WOP2009:Main
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|Event=WOP:2009
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Current revision ID: 9705

Graphical representation

Diagram

Image:Npa-diagram.png

General information

Name NegativePropertyAssertions
Also known as
Author(s)
SubmittedBy OlafNoppens


Description

Motivation The motivation of this pattern is to model negative property assertions (NPAs) in ontology languages such as OWL 1 [1] that do not provide a special constructor for expressing it. It is worth mentioning that not all knowledge base systems can be migrated to OWL 2 [2] for several reasons. On the other hand, NPAs modeled according to this pattern can be migrated to OWL 2 using the newly introduced constructor.

A negative property assertion as defined in the upcoming OWL 2 states that a given individual i is never connected to a given individual j by a given property expression P. In other words, asserting that i is connected to j by P results in an inconsistent ontology. In this sense this assertion can be considered as a constraint that should not be violated. In contrast, considering an ontology where it cannot be inferred that i is connected to j by P does not necessarily mean that there cannot be such a connection - in fact, it is merely not modeled.


[1] Patel-Schneider, P.F., Hayes, P., Horrocks, I.: OWL Web Ontology Language Semantics and Abstract Syntax, W3C Recommendation 10 February 2004.

[2] Motik, B., Patel-Schneider, P.F., Parsia, B.: OWL 2 Structural Specification and Functional-Style Syntax. W3C Candidate Recommendation 11 June 2009, 2009.

Aim Expressing NPAs in ontologies prior to OWL 2 as well as given an transformation rule when using OWL 2.
Solution description NegativeObjectPropertyAssertion(prop i1 i2) is equivalent to (using OWL 2 Abstract Syntax):

SubClassOf(ObjectOneOf(i1), ObjectComplementOf(ObjectSomeValuesFrom(prop, ObjectOneOf(i2))))


Let C and D be concepts. Then C and D are disjoint if, and only if, C is subsumed by the complement of D, i.e., '( SubClassOf( C ObjectComplementOf(D) ).

The equivalence is correct because of the duality of disjointness, equivalence, and unsatisfiability: C is subsumed by D if, and only if, ObjectIntersectionOf( C ObjectComplementOf(D) ) is unsatisfiable, and the intersection of C and D is unsatisfiable if, and only if, C' and D are disjoint.

One also reminds that the extension of the concept ObjectSomeValuesFrom(prop C) is the set of individuals i which are connected to an individual j that is in the extension of the concept C, by the property prop.


Let NegativePropertyAssertion(p a b) be a negative property assertion axiom, i.e., the individual a is not related to b by the property p. Then the extension of ObjectSomeValuesFrom( p ObjectOneOf(b) ) which contain all individuals that are connected to b by p must not contain a. This is true, if, and only if ObjectOneOf(a) is disjoint to ObjectSomeValuesFrom( p ObjectOneOf(b) )

Elements Individiual i1

Individual i2

ObjectProperty prop

Implementation
Reusable component
Component type


Example

Problem example Consider a social network containing facts about people and their relationships.

Let Adam and Eve be two persons and like a property (A likes B). Furthermore we know that Adam does not like Eve but we have no dislike relationship. Moreover, our language (such as OWL 1) does not have any NPA axiom constructor. The sample ontology is interpreted with respect to the open-world semantics, i. e. , one can not infer the dislike merely from the lack of a property assertion axiom ObjectPropertyAssertion(like Adam Eve). Then this fact can be expressed with the following axiom (we will also use the OWL 2 Abstract Syntax here):

SubClassOf (Adam ComplementOf(ObjectSomeValuesFrom( likes ObjectOneOf(Eve))))

Pattern solution example
Consequences


Pattern reference

Origin
Known use
Reference
Related ODP
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Test

Additional information

Scenarios

Scenarios about NegativePropertyAssertions

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Reviews

Reviews about NegativePropertyAssertions
Review article Posted on About revision (current is 9705)
ValentinaPresutti about NegativePropertyAssertions 24550849 September 2009 57695,769
StefanoDavid about NegativePropertyAssertions 245508510 September 2009 57785,778
RinkeHoekstra about NegativePropertyAssertions 245512924 October 2009 59035,903

This revision (revision ID 9705) takes in account the reviews: none

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Modeling issues

Modeling issues about NegativePropertyAssertions

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References

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Submission to event

WOP:2009

Retrieved from "http://ontologydesignpatterns.org/wiki/Submissions:NegativePropertyAssertions"
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