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Internet Technologies An Introduction to Ontologies in OWL Bibliography The OWL Guide The OWL Overview Description Logic slides from Enrico Franconi Artificial Intelligence A Modern Approach by Russel and Nordig

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Internet Technologies What is an Ontology? A representation of terms and their interrelationships (OWL Overview) A formal conceptualization of the world Smart data

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Internet Technologies Ontology Languages Typically introduce concepts, properties, relationships between concepts and constraints May be expressed with diagrams ER Diagrams and UML Class Diagrams are ontology languages OWL (The Web Ontology Language) is expressed in XML OWL is a distributed ontology language

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Internet Technologies The OWL Language February 10, 2004 OWL and RDF become W3C Recommendations See Jena from Hewlett-Packard Research for an existing Java API See Protégé-2000 at Stanford University for an existing OWL editor Big names in this space include Jim Hendler, and Debra McGuiness A large example can be found at http://www.mindswap.org/2003/CancerOntology/ nciOncology.owl

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Internet Technologies From the W3C

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Internet Technologies The three sublanguages of OWL OWL Lite (decidable) OWL DL (Description Logic) (Decidable) OWL Full (Allows classes as instances) As we move from OWL Lite to OWL full we increase expressiveness and logical complexity.

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Internet Technologies Decidability A proof procedure r is incomplete if there are true statements that the procedure cannot infer. Godel (1930’s) showed that, for first order logic, any statement entailed by a set of statements can be proved from the set. In other words, a proof procedure exists. In 1965, Robinson found the resolution method.

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Internet Technologies Decidability But, entailment is semi-decidable. If a statement does not follow from the premises it may go on and on. Resolution is complete Premises Statment S If S follows the proof of S will emerge after some time. If S does not follow the procedure may loop forever.

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Internet Technologies OWL Lite is a Decidable Language A Class is a set of individuals The class Thing is the superclass of all OWL classes The class Nothing is a subclass of all OWL classes and has no individuals members Classes may be defined as subClasses of other classes

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Internet Technologies Three classes that subclass Thing These terms may be referred to from within this Document by ‘#Winery’,’ #Region’ and ‘#ConsumableThing’. Other ontologies may refer to these terms with ‘SomeURI#Winery’, ‘SomeURI#Region’ and so on.

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Internet Technologies Class Hierarchies built with subClassOf … … Deduction: If x is a PotableLiquid then x is a ConsumableThing

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Internet Technologies Wine and Pasta …

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Internet Technologies SweetFruit and NonSweetFruit

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Internet Technologies Defining Individuals Is identical to

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Internet Technologies Another individual Deduction: CabernetSauvignon is a SweetFruit

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So far we have… Thing WineryRegion ConsumableThing PotableLiquid EdibleThing SweetFruitNonSweetFruitPasta Grape WineGrape CabernetSauvignonGrape CentralCoastalRegion Wine

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Internet Technologies So far we have … Classes Individuals We now need properties to state facts about classes and facts about individuals

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Internet Technologies Properties Properties are binary relations A binary relation R from a set X to a set Y is a subset of the Cartesian product X x Y. If (x,y) ε R, we write xRy and say x is related to y.

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Internet Technologies Binary Relations Suppose the set X has members {a,b} and the set Y has members {c,d,e}. XxY = {(a,c),(a,d),(a,e),(b,c),(b,d),(b,e)} Let R = {(a,c),(b,e)} Since (a,c) ε R and (b,e) ε R we write aRc and bRe. Notice that a binary relation is a set of ordered pairs.

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Internet Technologies The set {x ε X | (x,y) ε R for some y ε Y} is called the domain of R. The domain of R = {(a,c),(b,e)} is {a,b}. The set {y ε Y | (x,y) ε R for some x ε X} is called the range of R. The range of R = {(a,c),(b,e)} is {c,e}. Domain and Range

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Internet Technologies Properties R is Transitive if and only if xRy and yRz imply xRz locateIn is transitive in the wine ontology R is Symmetric if and only if xRy iff yRx adjacentTo is symmetric in the wine ontology

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Internet Technologies Properties R is Functional if and only if xRy and xRz implies y = z hasVintageYear is functional in the wine ontology R 1 and R 2 are Inverse Properties if and only if xR 1 y iff yR 2 x hasMaker and producesWine are inverse relations in the wine ontology

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Internet Technologies OWL’s Property Hierarchy Thing is a superset of Property Property is a superset of ObjectProperty Property is a superset of DataProperty An ObjectProperty associates a class instance with another class instance. A DataProperty associates a class instance with a datatype value

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Internet Technologies OWL’s Property Hierarchy Example Thing Mammal Person Mike Sue ObjectProperty DataProperty Property hasRelative hasSibling (Mike,Sue) hasAge (Mike,23) Indentation shows subset relationships. Set elements are marked with dots.

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Internet Technologies OWL Property Syntax

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Internet Technologies Adding pairs to locatedIn

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Internet Technologies locatedIn locatedIn is defined as a set of ordered pairs. Each pair must contain an owl:Thing (maybe a Region) followed by value from the set Region. For example: locatedIn = {(SantaCruzMountainsRegion, CaliforniaRegion), (SantaCruzMountainVinyardCabernetSauvignon, SantaCruzMountainsRegion)…} A deduction like the following is not yet possible… The Thing SantaCruzMountainVinyardCabernetSauvignon is locatedIn CaliforniaRegion

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Internet Technologies locatedIn is Transitive

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Internet Technologies Given the madeFromGrape property madeFromGrape (#Wine,#WineGrape)

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Internet Technologies And… We can deduce that LindemansBin65Chardonnay is a Wine.

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Internet Technologies Given a Property… …

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Internet Technologies We can define a subproperty … hasWineDescriptor (#Wine,#WineDescriptor) (#Wine,#WineColor)

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Internet Technologies And make it functional. … hasWineDescriptor (#Wine,#WineDescriptor) (#Wine,#WineColor) Now, for each Wine, there can be at most one WineColor.

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Internet Technologies

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Internet Technologies A Wine Individual

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Internet Technologies What does this mean?

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Internet Technologies And this?

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Internet Technologies How about this one?

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Chapter 9. 9 RDFS (RDF Schema) RDFS Part of the Ontological Primitive layer Adds features to RDF Provides standard vocabulary for describing concepts.

Chapter 9. 9 RDFS (RDF Schema) RDFS Part of the Ontological Primitive layer Adds features to RDF Provides standard vocabulary for describing concepts.

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