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GraphicallyRepresentedBy Npa-diagram.png +
LogicalODPAim Expressing NPAs in ontologies prior to OWL 2 as well as given an transformation rule when using OWL 2.
LogicalODPDescription NegativeObjectPropertyAssertion(prop i1 i2 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) )'' ObjectSomeValuesFrom( p ObjectOneOf(b) )''
LogicalODPElements Individiual i1 Individual i2 ObjectProperty prop
LogicalODPMotivation The motivation of this pattern is to model 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 Speciļ¬cation and Functional-Style Syntax. W3C Candidate Recommendation 11 June 2009, 2009. ndidate Recommendation 11 June 2009, 2009.
LogicalODPName NegativePropertyAssertions  +
LogicalODPScenario Consider a social network containing facts 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))))'' omeValuesFrom( likes ObjectOneOf(Eve))))''
Modification dateThis property is a special property in this wiki. 31 May 2010 08:29:25  +
SubmittedBy OlafNoppens +
SubmittedToEvent 2009 +
Categories LogicalOP +, ProposedLogicalOP +, Review assigned +, Submitted to event +
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