”Web Ontology Language” (cutely named “OWL” for no reason) is a W3C standard which enables the Semantic Web. OWL is heavily related to SPARQL, which it was developed alongside of. It is aware of RDF, and maps to it. OWL is not a Syntax, but instead may use many syntaxes, such as RDF/XML (which appears to be the preferred syntax by the designers of the language), and Turtle. The source uses 5 syntaxes which can be toggled, nice. OWL is a mechanism to enable Modeling as a Knowledge Base, creating an Ontology. Ultimate nerd stuff.
Vocabulary Words
- Axioms are basic statements, asserted as truth by definition
- Entities are used to refer to real-world objects, a collective term i for:
- Individuals - sometimes referred to as ”objects” e.g.
Mary - Classes - sometimes referred to as ”categories” e.g.
woman- Disjoint - two classes that are disjoint cannot share a common individual
- Properties - subdivide into two types:
- Object Properties - relate individuals to other individuals
- See: Domain and Range
- Inverse - two properties that are the inverse of one another, e.g.
hasChildandhasParent - Symmetric - properties that always go both ways, e.g.
hasSpouse - Asymmetric - properties that CANNOT go both ways, e.g.
hasParent - Disjoint - properties can also be disjoint, saying no two individuals can be linked via both, e.g.
bestFriendsWithanddoesNotKnow - Reflexive - relating to yourself, e.g.
knows(because you know yourself) - Irrelflexive - CANNOT be used to relate to yourself, e.g
hasParent - Functional - an individual may only have one relation of that type, e.g.
hasBiologicalMother - Inverse Functional - same as functional, but inverse, e.g.
biologicalMotherOf - Transitive - when A is related to B, and B is related to C, then A is related to C too, e.g.
inSameRoomAs - Key - every individual has a unique value for the property, would be used for things like
hasSSN
- Datatype Properties - assign data values to objects
- Annotation Properties - are for metadata about the ontology itself
- Object Properties - relate individuals to other individuals
- Individuals - sometimes referred to as ”objects” e.g.
- Expressions - combine basic axioms and entities to form more complex ones
Tooling
OWL can be written by hand, obviously, but there exist a number of tools. The only one I’ve any experience with is Protege.
Reasoners
OWL tooling includes Reasoners, which use the rules of the language to infer new knowledge as a result of the logical consequences of their context. In Protege there are many reasoners that can be toggled on and off.
Reasoners say:
Assert
All humans are mortalMary is a humanReasoner infers:
Mary is mortal
Reasoners are powerful. They allow for compounding returns on your knowledge representation. They do come with “gotchas”, though. Example from the source - if you assert a domain and range for the Object Property :hasAge, and the domain is :Person, then later you use the :hasAge relation on a cat, then the reasoner would deduce that the cat is also a person.
Complex Classes
You can state complex conditions to empower your reasoners. An example that resonated with me - any Individual that is both of class Parent and class Woman is then of class Mother:
:Mother owl:equivalentClass [
rdf:type owl:Class ;
owl:intersectionOf ( :Woman :Parent )
] .These types of relationship implications are what’s missing from systems modeling tools, IMHO.
Restrictions
Restrictions can be implemented to assert rules about Cardinality, and to give reasoners the chance to infer new classes through situations like:
:JohnsChildren owl:equivalentClass [
rdf:type owl:Restriction ;
owl:onProperty :hasParent ;
owl:hasValue :John
] .Misc Facts
- OWL seems to use camelCase for their relations
- Negative Property Assertion - it’s possible to explicitly say a relation does not exist
- subPropertyOf - can be used for situations like
:hasWife rdfs:subPropertyOf :hasSpouse . - differentFrom - can be used to explicitly state two things are not the same
- sameAs - also exists, the opposite of different from. An aliasing mechanism.
- Property Chains - you can chain things together to form fancy class restrictions based on relations of relations, e.g.
:hasFriendWithBoat owl:propertyChainAxiom ( :hasFriend :hasBoat ) .
Reference Ontology
This is pulled directly from the source.
@prefix : <http://example.com/owl/families/> .
@prefix otherOnt: <http://example.org/otherOntologies/families/> .
@prefix owl: <http://www.w3.org/2002/07/owl#> .
@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@prefix rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
<http://example.com/owl/families>
rdf:type owl:Ontology ;
owl:imports <http://example.org/otherOntologies/families.owl> .
:hasSpouse rdf:type owl:SymmetricProperty .
:hasRelative rdf:type owl:ReflexiveProperty .
:parentOf rdf:type owl:IrreflexiveProperty .
:hasAncestor rdf:type owl:TransitiveProperty .
:hasHusband rdf:type owl:FunctionalProperty .
:hasHusband rdf:type owl:InverseFunctionalProperty .
:hasWife rdf:type owl:ObjectProperty .
:hasWife rdfs:domain :Man ;
rdfs:range :Woman .
:hasWife rdfs:subPropertyOf :hasSpouse .
:hasSon owl:propertyDisjointWith :hasDaughter.
:hasFather rdfs:subPropertyOf :hasParent.
:hasParent owl:inverseOf :hasChild .
:hasParent owl:propertyDisjointWith :hasSpouse .
:hasGrandparent owl:propertyChainAxiom ( :hasParent :hasParent ) .
:hasUncle owl:propertyChainAxiom ( :hasFather :hasBrother ) .
:hasAge owl:equivalentProperty otherOnt:age .
:hasAge rdf:type owl:DatatypeProperty .
:hasAge rdf:type owl:FunctionalProperty .
:hasAge rdfs:domain :Person ;
rdfs:range xsd:nonNegativeInteger .
:hasChild owl:equivalentProperty otherOnt:child .
:hasChild rdf:type owl:AsymmetricProperty .
:Woman rdfs:subClassOf :Person .
:Mother rdfs:subClassOf :Woman .
:Mother owl:equivalentClass [
rdf:type owl:Class ;
owl:intersectionOf ( :Woman :Parent )
] .
:Person rdf:type owl:Class .
:Person owl:equivalentClass :Human .
:Person rdfs:comment "Represents the set of all people."^^xsd:string .
:Person owl:hasKey ( :hasSSN ) .
:hasSSN rdf:type owl:DataProperty .
:Parent owl:equivalentClass [
rdf:type owl:Class ;
owl:unionOf ( :Mother :Father )
] .
:Parent owl:equivalentClass [
rdf:type owl:Restriction ;
owl:onProperty :hasChild ;
owl:someValuesFrom :Person
] .
:Grandfather rdfs:subClassOf [
rdf:type owl:Class ;
owl:intersectionOf ( :Man :Parent )
] .
:HappyPerson
owl:equivalentClass [
rdf:type owl:Class ;
owl:intersectionOf ( [ rdf:type owl:Restriction ;
owl:onProperty :hasChild ;
owl:allValuesFrom :HappyPerson ]
[ rdf:type owl:Restriction ;
owl:onProperty :hasChild ;
owl:someValuesFrom :HappyPerson ]
)
] .
:JohnsChildren owl:equivalentClass [
rdf:type owl:Restriction ;
owl:onProperty :hasParent ;
owl:hasValue :John
] .
:NarcisticPerson owl:equivalentClass [
rdf:type owl:Restriction ;
owl:onProperty :loves ;
owl:hasSelf "true"^^xsd:boolean .
] .
:MyBirthdayGuests owl:equivalentClass [
rdf:type owl:Class ;
owl:oneOf ( :Bill :John :Mary )
] .
:Orphan owl:equivalentClass [
rdf:type owl:Restriction ;
owl:onProperty [ owl:inverseOf :hasChild ] ;
owl:allValuesFrom :Dead
] .
:Teenager rdfs:subClassOf
[ rdf:type owl:Restriction ;
owl:onProperty :hasAge ;
owl:someValuesFrom
[ rdf:type rdfs:Datatype ;
owl:onDatatype xsd:integer ;
owl:withRestrictions ( [ xsd:minExclusive "12"^^xsd:integer ]
[ xsd:maxInclusive "19"^^xsd:integer ]
)
]
] .
:Man rdfs:subClassOf :Person .
[] rdf:type owl:Axiom ;
owl:annotatedSource :Man ;
owl:annotatedProperty rdfs:subClassOf ;
owl:annotatedTarget :Person ;
rdfs:comment "States that every man is a person."^^xsd:string .
:Adult owl:equivalentClass otherOnt:Grownup .
:Father rdfs:subClassOf [
rdf:type owl:Class ;
owl:intersectionOf ( :Man :Parent )
] .
:ChildlessPerson owl:equivalentClass [
rdf:type owl:Class ;
owl:intersectionOf ( :Person [ owl:complementOf :Parent ] )
] .
:ChildlessPerson owl:subClassOf [
rdf:type owl:Class ;
owl:intersectionOf ( :Person
[ owl:complementOf [
rdf:type owl:Restriction ;
owl:onProperty [ owl:inverseOf :hasParent ] ;
owl:someValuesFrom owl:Thing
]
]
)
] .
[] rdf:type owl:Class ;
owl:intersectionOf ( [ rdf:type owl:Class ;
owl:oneOf ( :Mary :Bill :Meg ) ]
:Female
) ;
rdfs:subClassOf [
rdf:type owl:Class ;
owl:intersectionOf ( :Parent
[ rdf:type owl:Restriction ;
owl:maxCardinality "1"^^xsd:nonNegativeInteger ;
owl:onProperty :hasChild ]
[ rdf:type owl:Restriction ;
owl:onProperty :hasChild ;
owl:allValuesFrom :Female ]
)
] .
[] rdf:type owl:AllDisjointClasses ;
owl:members ( :Mother :Father :YoungChild ) .
[] rdf:type owl:AllDisjointClasses ;
owl:members ( :Woman :Man ) .
:personAge owl:equivalentClass
[ rdf:type rdfs:Datatype;
owl:onDatatype xsd:integer;
owl:withRestrictions (
[ xsd:minInclusive "0"^^xsd:integer ]
[ xsd:maxInclusive "150"^^xsd:integer ]
)
] .