Spring 2012 DISC 210 Notes on Protege

= General Notes on Ontologies and Protege =
 * Ontologies are used to capture knowledge about some domain of interest
 * An ontology describes the concepts in the domain and also the relationships that hold between those concepts.
 * Different ontology languages provide different facilities. The most recent development in standard ontology languages is OWL from the World Wide Web Consortium (W3C)
 * Complex concepts can therefore be built up in definitions out of simpler concepts
 * The logical model allows the use of a reasoner which can check whether or not all of the statements and definitions in the ontology are mutually consistent and can also recognise which concepts fit under which definitions. The reasoner can therefore help to maintain the hierarchy correctly

= Pieces of the puzzle =

Individuals
Individuals are objects of interest (e.g., "Paul Anderson")

Properties
Properties are binary relations on individuals (two individuals specifically). e.g., the property hasSibling may link Matthew to Paul
 * Two types of properties
 * 1) Object properties (individual to individual)
 * 2) Datatype properties (individual to XML Schema Datatype value or an rdf literal)
 * Properties can have inverses. e.g., the inverse of hasOwner is isOwnedBy, or hasChild and hasParent.
 * Properties can be limited to having single values (functional). e.g., the property hasBirthMother - something can only have one birth mother. If a property is inverse functional then that means that the inverse property is functional.
 * Properties can be transitive. e.g., the transitive property hasAncestor. If Matthew has an ancestor named Peter, and Peter has an ancestor that is William, then we can infer that Matthew has an ancestor that is William.
 * Properties can be symmetric. e.g., property hasSibling - Matthew hasSibling Gemma implies Gemma hasSibling Matthew.
 * Properties can be asymmetric. e.g., Robert is related to David via the isChildOf property, then David cannot be related to Robert via the isChildOf property.
 * Properties can be reflexive, when the property must relate individuals to themselves. e.g., the property knows for George. George must know himself.
 * Properties can be irreflexive, when individual a to individual b, but they are not the same. Alice cannot be mother of herself.

Domains and Ranges
Properties may have a domain and range. Properties link individuals from the domain to individuals from the range. e.g., hasTopping would link the domain Pizza to the range of PizzaTopping.
 * Domains and ranges are not constraints. They are used as Axioms for reasoning.

Classes
OWL classes are interpreted as sets that contain individuals. For example, the class Cat would contain all the individuals that are cats in our domain of interest.
 * Classes may be organized into a superclass-subclass hierarchy, which is also known as taxonomy.
 * OWL Classes are assumed to `overlap'. We therefore cannot assume that an individual is not a member of a particular class simply because it has not been asserted to be a member of that class. In order to `separate' a group of classes we must make them disjoint from one another. This ensures that an individual which has been asserted to be a member of one of the classes in the group cannot be a member of any other classes in that group.

Restrictions
OWL restrictions fall into three main categories
 * 1) Quantifier restrictions
 * 2) Existential restrictions - individuals participate in at lease one relationship (e.g., hasTopping some MozzarellaTopping)
 * 3) Universal restrictions - they constrain relationships along a given property to individuals that are members of a specific class. e.g., VegetarianPizza hasTopping only (CheeseTopping or VegetableTopping)
 * 4) Cardinality restrictions - minimum, maximum, exact
 * 5) hasValue restrictions. e.g., MozzarellaTopping has its countryOfOrigin hasValue Italy

Reasoners
Reasoners can be used to check the logical consistency of the ontology.

Necessary and Sufficient Conditions
The conditions are not only necessary for membership of A but also sufficient to determine that something satisfying these conditions is a member of A.

Enumerated Classes
Classes that contain specific individuals and only those individuals. e.g., DaysOfTheWeek are Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, and Saturday.