The Knowledge Presentation Language

Web Ontology Language (OWL)  Web Ontology Language (OWL) extends RDF and RDFS languages by adding several other constructs such as owl:class (in addition to the rdfs:class ), relationships between class and individuals, and property characteristics  These new constructs facilitate interoperability among distributed resources  OWL is encoded in RDF/XML  OWL is said to be ‘monotonic’, meaning that addition of new information to a knowledge base does not falsify previous conclusions

Owl dialects  OWL has three species (dialects): OWL-Lite, OWL DL, and OWL Full  The differences are on the limitations on restrictions on classes  OWL Lite: supports class and property hierarchies and simple restrictions, allowing us to develop thesauri and simple ontologies  OWL DL is the decidable version of OWL Full, with some limitation; it is a restricted version of RDF  OWL Full has no limitation, but may not be decidable

Features of OWL Is compatible with (serializable in) XML. Uses XSD datatypes Follows description logic in having class, property, and individuals Has constructs that are identified by the URIref Allow us to define complex classes with Boolean combinations (intersection, union, complement) Makes it possible to define properties and subproperties and assigning logical metadata (e.g., transitivity) Has features to set two classes, properties, and individuals as equivalent

… Allows setting the cardinality constraints Setting classes as instances Resources defined by it can have labels such that they can be displayed in different natural languages Allows developing Web-distributed ontologies Lets us import and reuse other owl code (ontologies) by extension Allows saving the same ontologies with different versions Allows defining metadata for ontologies (e.g., author, version)

OWL ontology header info Includes namespace declaration Information about the ontology is put within the owl:Ontology Qname, e.g., version, comments, and import The version includes: owl:versionInfo, owl:priorVersion, owl:backwardCompatibleWith, owl:incompatibleWith, owl.deprecatedClass, and owl:deprecatedProperty We can also use the rdfs:comment, rdfs:label, rdfs:seeAlso, and rdfs:isDefinedBy

Part of Structural Geology Structural Geology

Two Types of Property in OWL  Datatype Property has a typed literal (e.g., XSD or RDF literal) as its range  As a binary relation, the datatype property relates a set of instances of a [domain] class to a set of instances of a datatype (range; object)  A datatype property is declared using the owl:DatatypeProperty  Or:

Object Property  Object property has a URIref as its range  As a binary property, it relates a set of individuals of one class to the set of individuals of another class  That is, the subject and objects of a triple using an object property are both individuals  Object properties are declared in two different ways: or:

Example in N3 struc:foldDescription rdf:type owl:DatatypeProperty. struc:foldDescription rdfs:domain struc:Fold. struc:foldDescription rdfs:range xsd:string. struc: Fold struc: foldDescriptionxsd:tring struc:foldAxis rdf:type owl:ObjectProperty. struc:foldAxis rdfs:domainstruc:Fold. struc:foldAxis rdfs:rangestruc:Line. struc:Foldstruc:foldAxisstruc:Line

Domain and range of properties Can be assigned in a short form: Or the long way, as is shown in the following slide!

owl:inveseOf  Properties themselves have properties  owl:inverseOf property relates two properties to each other  Many properties in one direction have an inverse property in the opposite direction  For example, the first property in each of the following pairs reverses the direction of the second property  ‘ analyzes’ and ‘analyzedBy’  ‘investigates’ and ‘investigatedBy’  ‘hasSample’ and ‘sampleOf  ‘wrote’ and ‘writtenBy’  ‘locatedIn’ and ‘locationOf’  These follow the definition of the mathematical inverse function that state: if f(x) = y, then f -1 (y) = x.

Inference of the owl:inverseOf P owl:inverseOf Q. If x P y. Then y Q x.  Example: The partOf property is an inverse property struc : Fold hasPart struc : limb. partOf owl : inveseOf struc : hasPart.  This means that if fold has limb as part, then limb is part of fold FoldLimb xy hasPart partOf Q P

FoldLimb xy hasPart partOf

partOf owl:inverseOf hasPart

owl:symmetricProperty  If the property that relates two classes is the same (has the same name) in both directions, we declare the property as symmetric  For example: ‘equals’ or ‘siblingOf’ is a symmetric property  if x is siblingOf y, then y is siblingOf x  Symmetric properties must be declared as such P rdf : type owl:SymmetricProperty.  The inference for a symmetric property is as follows: P owl:inverseOf P.  That is, the symmetric property is an inverse property.

owl:transitiveProperty  In mathematics, a relation is said to be transitive if P(a,b) and P(b,c) implies P(a,c). This is represented by the owl:TransitiveProperty, which applies to a property. P rdf : type owl:TransitiveProperty. The inference for this property is as follows: IF x P y. y P z. THEN x P z. C part of B B part of A C part of A. A B C FaultBendFaultSegment xy P Fault z P

partOf  The partOf property (containment) may be transitive (not always). Finger is part of hand, and hand is part of body  However, someone’s hand is not part of the group to which the person is part of  Geologically, being fractal, faults have segments that have smaller fault segments, which have even smaller segments which are themselves fault struc:FaultSegment struc:partOf struc: FaultSegment. struc:partOf rdf :type owl:TransitiveProperty. struc:FaultSegment rdfs:subClassOf struc:Fault. FaultBendFaultSegment xy partOf Fault z partOf

Transitive partOf partOf owl:inverseOf hasPart

locatedIn is transitive C locatedIn B B locatedIn A C locatedIn A. geo:locatedInrdf:typeowl:TransitiveProperty. If tect:SanAndreasFault geo:locatedIn geo:California. geo:California geo:locatedIn geo:United States. Then geo:SanAndreasFault geo:locatedIn geo:United States. A B C

Functional Property … A functional property is a property that can have only one unique value y (object) for each instance x (subject) e.g., hasBirthMother is functional This means that there cannot be two distinct values y 1 and y 2 if (x, y 1 ) and (x, y 2 ) are instances of the functional property If x p y 1 and x p y 2, then y 1 =y 2 Ashley hasBirthMother Jane Ashley hasBirthMother Maria then jane=Maria Given x (subject individual) we can find y (object individual)! Both object and datatype properties can be declared functional! There could be many x ’s, but all relate to one y Example: husband property may be functional in some cultures: Woman husband Man(not in polygamy or same sex marriages) If x husband y 1 and x husband y 2, then y 1 =y 2 If Jane husband Jack and Jane husband Jeff, then Jack = Jeff y2 x y1 p p x x y x x x

Inference  The owl:FunctionalProperty can only take one value for any [object] individual, allowing sameness to be inferred  The inference rule for this construct is as follows  Note: x is a subject individual and A and B are object individuals If P rdf:type owl:FunctionalProperty. X P A X P B Then A owl:sameAs B. x A p B p x

A property p is functional if x p y 1 and x p y 2 imply that y 1 = y 2 We infer that the two object individuals are the same (y 1 owl:sameAs y 2 ) Note that the subjects are not asserted to be the same; only the objects are the same DaughterProduct daughterProductOf ParentIsotope Sample sampleLocation Location daughterProductOf and sampleLocation are functional properties, because there is one unique value y for x in the following triples: x sampleLocation y or x daughterProductOf y There is a unique location for each sample There is a unique ParentIsotope for each daughterProduct Parent Isotope Daughter Product daughterProductOf Location Sample sampleLocation

Sample Location sampleLocation

Inverse Functional Property This is the inverse property of the functional property. e.g., isBirthMotherOf which is the inverse of hasBirthMoterh The object y of an inverse functional property p uniquely determines the subject x (some individual) y can only be the value for p for a single instance x There cannot be two distinct x 1 and x 2 such that ( x 1, y ) and ( x 2, y ) are instances of p. If there are, then x 1 = x 2 Liz isBirthMotherOf Steven Myra isBirthMotherOf Steven then, Liz = Myra (same individual) Note: People’s name is not inverse functional (different people can have the same name) x1x1 y p p x2x2 Steven Liz Myra isBirthMotherOf

Inverse Functional Property  This property is the inverse of the owl:FunctionalProperty  It is very useful for merging data from different sources  The owl:FunctionalProperty and owl:InverseFunctionalProperty allow merging data for a same individual from different sources  The owl:InverseFunctionalProperty is equivalent to the key in relational databases, such as SSN and driving license number  These are unique  The inference rule of this construct is as follows: P rdf:type owl:InverseFunctionalProperty. A P X. B P X. Then A owl:sameAs B. A x p p B

owl:InverseFunctionalProperty If x p y, and p is inverse functional, then there can be only a single value of x for a given y, that is: The object individual y of an owl:InverseFunctionalProperty p uniquely determines a single subject individual x Given the object individual ( y ), we can find a unique subject individual ( x ) (i.e., x  y -1 ) In this case, if x 1 p y and x 2 p y, then x 1 and x 2 are the same! If x1 ssn and x2 ssn , then x1=x2 e.g., hasSingleAuthorArticle: a person (subject) may have many published papers (objects), but all are authored by one author (subject). PersonhasSingleAuthorArticleSingleAuthorArticle Given a singleAuthorArticle object individual ( y ) we can find a unique subject individual ( x ) y y y x

… A single value of the property (object y, e.g., doi of an Article) cannot be shared by two x subject entities (e.g., Authors). Example: Let’s assume that an isotope is produced by the decay of some unique isotope (may not be true in all cases!) Isotope parentOf DaughterIsotope An object individual y (some daughterIsotope) uniquely determines a single subject individual x (parent isotope) AuthorArticle hasSingleAuthorPaper y x

Example  Let’s assume location of any measurement is uniquely identified by the longitude and latitude (defined by the Location class), i.e., assume no two samples of a rock can be taken at the same exact spot :Station134 : locatedAt : LocationA. :Station346 : locatedAt : LocationA.  We infer that :Station134 owl:sameAs :Station346 StationLocation locatedAt

One-to-one Property  For a one-to-one relationship, we use a combination of the owl:FunctionalProperty and owl:inverseFunctionalProperty.  Note: Sample sampleId XSD:Integer is not a good example, because it is a datatype property, and not every number gives you the sample :hasimage rdfs:domain :ThinSection. :hasImage rdfs:range Image. :hasImage rdf:type owl:FunctionalProperty. :hasImage rdf:type owl:InverseFunctionalProperty.  So, any two thin sections with the same image must be the same thin section! SampleXSD:Integer sampleId x y X ThinSectionImage hasImage

One-to-one hasImage Property

rdf:Description rdf:about=" ThinSectionImage hasImage

 Note that not every functional property can also be an inverse functional property  For example, mineral composition can be functional only, because every mineral has a unique composition, but many individual minerals can share that same composition (if they belong to the same class) (compare with hasFather ) Every individual child has one biological father, but the father can have more than one child  Some properties can only be inverse functional, but not functional  For example, a single-author publication of an author (or description of an outcrop or a thin section by one person) may be inverse functional, because it only belongs to one person ◦ The person can have several such publications or descriptions MineralComposition hasComposition x1x1 x2x2