Semantic relation

Contemporary ontologies share many structural similarities, regardless of the language in which they are expressed. Most ontologies describe individuals (instances), classes (concepts), attributes, and relations.

Common components of ontologies include:

Ontologies are commonly encoded using ontology languages.

Individuals (instances) are the basic, "ground level" components of an ontology. The individuals in an ontology may include concrete objects such as people, animals, tables, automobiles, molecules, and planets, as well as abstract individuals such as numbers and words (although there are differences of opinion as to whether numbers and words are classes or individuals). Strictly speaking, an ontology need not include any individuals, but one of the general purposes of an ontology is to provide a means of classifying individuals, even if those individuals are not explicitly part of the ontology.

In formal extensional ontologies, only the utterances of words and numbers are considered individuals – the numbers and names themselves are classes. In a 4D ontology, an individual is identified by its spatio-temporal extent. Examples of formal extensional ontologies are ISO 15926 and the model in development by the IDEAS Group.

Classes – concepts that are also called type, sort, category, and kind – can be defined as an extension or an intension. According to an extensional definition, they are abstract groups, sets, or collections of objects. According to an intensional definition, they are abstract objects that are defined by values of aspects that are constraints for being member of the class. The first definition of class results in ontologies in which a class is a subclass of collection. The second definition of class results in ontologies in which collections and classes are more fundamentally different. Classes may classify individuals, other classes, or a combination of both. Some examples of classes:

Ontologies vary on whether classes can contain other classes, whether a class can belong to itself, whether there is a universal class (that is, a class containing everything), etc. Sometimes restrictions along these lines are made in order to avoid certain well-known paradoxes.

The classes of an ontology may be extensional or intensional in nature. A class is extensional if and only if it is characterized solely by its membership. More precisely, a class C is extensional if and only if for any class C', if C' has exactly the same members as C, then C and C' are identical. If a class does not satisfy this condition, then it is intensional. While extensional classes are more well-behaved and well-understood mathematically, as well as less problematic philosophically, they do not permit the fine grained distinctions that ontologies often need to make. For example, an ontology may want to distinguish between the class of all creatures with a kidney and the class of all creatures with a heart, even if these classes happen to have exactly the same members. In most upper ontologies, the classes are defined intensionally. Intensionally defined classes usually have necessary conditions associated with membership in each class. Some classes may also have sufficient conditions, and in those cases the combination of necessary and sufficient conditions make that class a fully defined class.

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