knowledge representation Knowledge representation (KR) aims to model information in a structured manner to formally represent it as knowledge in knowledge-based systems whereas knowledge representation and reasoning (KRR, KR&R, or KR²) also aims to understand, reason, and ...

, particularly in the

Semantic Web The Semantic Web, sometimes known as Web 3.0, is an extension of the World Wide Web through standards set by the World Wide Web Consortium (W3C). The goal of the Semantic Web is to make Internet data machine-readable. To enable the encoding o ...

, a metaclass is a

class Class, Classes, or The Class may refer to: Common uses not otherwise categorized * Class (biology), a taxonomic rank * Class (knowledge representation), a collection of individuals or objects * Class (philosophy), an analytical concept used d ...

whose instances can themselves be classes. Similar to their role in programming languages, metaclasses in ontology languages can have properties otherwise applicable only to individuals, while retaining the same class's ability to be classified in a concept hierarchy. This enables knowledge about instances of those metaclasses to be inferred by semantic reasoners using statements made in the metaclass. Metaclasses thus enhance the expressivity of knowledge representations in a way that can be intuitive for users. While classes are suitable to represent a population of individuals, metaclasses can, as one of their feature, be used to represent the conceptual dimension of an

ontology Ontology is the philosophical study of existence, being. It is traditionally understood as the subdiscipline of metaphysics focused on the most general features of reality. As one of the most fundamental concepts, being encompasses all of realit ...

. Metaclasses are supported in the

Web Ontology Language The Web Ontology Language (OWL) is a family of Knowledge representation and reasoning, knowledge representation languages for authoring Ontology (information science), ontologies. Ontologies are a formal way to describe Taxonomy, taxonomies and ...

(OWL) and the data-modeling vocabulary RDFS. Metaclasses are often modeled by setting them as the

object Object may refer to: General meanings * Object (philosophy), a thing, being, or concept ** Object (abstract), an object which does not exist at any particular time or place ** Physical object, an identifiable collection of matter * Goal, an a ...

of claims involving rdf:type and rdfs:subClassOf—built-in properties commonly referred to as ''instance of'' and ''subclass of''. ''Instance of'' entails that the subject of the claim is an instance, i.e. an individual that is a member of a class. ''Subclass of'' entails that the subject is a class. In the context of ''instance of'' and ''subclass of'', the key difference between metaclasses and ordinary classes is that metaclasses are the object of ''instance of'' claims used on a class, while ordinary classes are not objects of such claims. (e.g. in a claim Bob ''instance of'' Human, Bob is the subject and an Instance, while the object, Human, is an ordinary class; but a further claim that Human ''instance of'' Animal species makes "Animal species" a metaclass because it has a member, "Human", that is also a Class). OWL 2 DL supports metaclasses by a feature called punning, in which one entity is interpreted as two different types of thing—a class and an individual—depending on its syntactic context. For example, through punning, an ontology could have a concept hierarchy such as

Harry the eagle ''instance of'' golden eagle 





The golden eagle (''Aquila chrysaetos'') is a bird of prey living in the Northern Hemisphere. It is the most widely distributed species of eagle. Like all eagles, it belongs to the family Accipitridae. They are one of the best-known bird of pr ...

golden eagle ''subclass of'' bird 









Birds are a group of warm-blooded vertebrates constituting the class (biology), class Aves (), characterised by feathers, toothless beaked jaws, the Oviparity, laying of Eggshell, hard-shelled eggs, a high Metabolism, metabolic rate, a fou ...

, and

golden eagle ''instance of'' species 





A species () is often defined as the largest group of organisms in which any two individuals of the appropriate sexes or mating types can produce fertile offspring, typically by sexual reproduction. It is the basic unit of Taxonomy (biology),  ...

. In this case, the punned entity would be golden eagle, because it is represented as a class (second claim) and an instance (third claim); whereas the metaclass would be species, as it has an instance that is a class. Punning also enables other properties that would otherwise be applicable only to ordinary instances to be used directly on classes, for example "golden eagle ''conservation status''

least concern A least-concern species is a species that has been evaluated and categorized by the International Union for Conservation of Nature (IUCN) as not being a focus of wildlife conservation because the specific species is still plentiful in the wil ...

." Having arisen from the fields of

description logic Description logics (DL) are a family of formal knowledge representation languages. Many DLs are more expressive than propositional logic but less expressive than first-order logic. In contrast to the latter, the core reasoning problems for DLs are ...

and

formal ontology In philosophy, the term formal ontology is used to refer to an ontology defined by axioms in a formal language with the goal to provide an unbiased (Problem domain, domain- and application-independent) view on Reality#Western philosophy, realit ...

, Semantic Web languages have a closer relationship to philosophical ontology than do conventional programming languages such as

Java Java is one of the Greater Sunda Islands in Indonesia. It is bordered by the Indian Ocean to the south and the Java Sea (a part of Pacific Ocean) to the north. With a population of 156.9 million people (including Madura) in mid 2024, proje ...

or Python. Accordingly, the nature of metaclasses is informed by philosophical notions such as

abstract objects In philosophy and the arts, a fundamental distinction exists between abstract and concrete entities. While there is no universally accepted definition, common examples illustrate the difference: numbers, sets, and ideas are typically classified ...

, the

abstract and concrete In philosophy and the arts, a fundamental distinction exists between abstract and concrete entities. While there is no universally accepted definition, common examples illustrate the difference: numbers, sets, and ideas are typically classified ...

, and type-token distinction. Metaclasses permit concepts to be construed as tokens of other concepts while retaining their ontological status as types. This enables types to be enumerated over, while preserving the ability to inherit from types. For example, metaclasses could allow a machine reasoner to infer from a human-friendly ontology how many elements are in the

periodic table The periodic table, also known as the periodic table of the elements, is an ordered arrangement of the chemical elements into rows (" periods") and columns (" groups"). It is an icon of chemistry and is widely used in physics and other s ...

, or, given that number of protons is a property of chemical element and isotopes are a subclass of elements, how many protons exist in the isotope

hydrogen-2 Deuterium (hydrogen-2, symbol H or D, also known as heavy hydrogen) is one of two stable isotopes of hydrogen; the other is protium, or hydrogen-1, H. The deuterium nucleus (deuteron) contains one proton and one neutron, whereas the far more c ...

. Metaclasses are sometime organized by levels, in a similar way to the simple Theory of types where classes that are not metaclasses are assigned the first level, classes of classes in the first level are in the second level, classes of classes in the second level on the next and so on.

Examples

Following the type-token distinction, real world objects such as

Abraham Lincoln Abraham Lincoln (February 12, 1809 – April 15, 1865) was the 16th president of the United States, serving from 1861 until Assassination of Abraham Lincoln, his assassination in 1865. He led the United States through the American Civil War ...

or the planet

Mars Mars is the fourth planet from the Sun. It is also known as the "Red Planet", because of its orange-red appearance. Mars is a desert-like rocky planet with a tenuous carbon dioxide () atmosphere. At the average surface level the atmosph ...

are regrouped into classes of similar objects. Abraham Lincoln is said to be an ''instance of'' human, and Mars is an ''instance of'' planet. This is a kind of

is-a In knowledge representation, ontology components and ontology engineering, including for object-oriented programming and design, is-a (also written as is_a or is a) is a subsumptive relationship between abstractions (e.g., types, classes), wh ...

relationship. Metaclasses are class of classes, such as for example the

nuclide Nuclides (or nucleides, from nucleus, also known as nuclear species) are a class of atoms characterized by their number of protons, ''Z'', their number of neutrons, ''N'', and their nuclear energy state. The word ''nuclide'' was coined by the A ...

concept. In chemistry,

atom Atoms are the basic particles of the chemical elements. An atom consists of a atomic nucleus, nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished fr ...

s are often classified as elements and, more specifically,

isotope Isotopes are distinct nuclear species (or ''nuclides'') of the same chemical element. They have the same atomic number (number of protons in their Atomic nucleus, nuclei) and position in the periodic table (and hence belong to the same chemica ...

s. The glass of water one last drank has many hydrogen atoms, each of which is an ''instance of''

hydrogen Hydrogen is a chemical element; it has chemical symbol, symbol H and atomic number 1. It is the lightest and abundance of the chemical elements, most abundant chemical element in the universe, constituting about 75% of all baryon, normal matter ...

Hydrogen Hydrogen is a chemical element; it has chemical symbol, symbol H and atomic number 1. It is the lightest and abundance of the chemical elements, most abundant chemical element in the universe, constituting about 75% of all baryon, normal matter ...

itself, a class of atoms, is an ''instance of''

. Nuclide is a class of classes, hence a metaclass.

Implementations

RDF and RDFS

In RDF, the property is used to state that a resource is an instance of a class. This enables metaclasses to be easily created by using in a chain-like fashion. For example, in the two triples

Harry the eagle rdf:type golden eagle
golden eagle rdf:type species

the resource is a metaclass, because is used as a class in the first statement and the class is said to be an instance of the class in the second statement. RDF also provides as a way to create properties beyond those defined in the built-in vocabulary. Properties can be used directly on metaclasses, for example "", where is a property defined via and is a metaclass per the preceding example above. RDFS, an extension of RDF, introduced and and enriched how vocabularies can classify concepts. Whereas enables vocabularies to represent instantiation, the property enables vocabularies to represent

subsumption Subsumption may refer to: * A minor premise in symbolic logic (see syllogism) * The Liskov substitution principle in object-oriented programming * Subtyping in programming language theory * Subsumption architecture in robotics * A subsumption ...

. RDFS thus makes it possible for vocabularies to represent

taxonomies image:Hierarchical clustering diagram.png, 280px, Generalized scheme of taxonomy Taxonomy is a practice and science concerned with classification or categorization. Typically, there are two parts to it: the development of an underlying scheme o ...

, also known as subsumption hierarchies or concept hierarchies, which is an important addition to the

type–token distinction The type–token distinction is the difference between a ''type'' of objects (analogous to a ''class'') and the individual ''tokens'' of that type (analogous to ''instances''). Since each type may be instantiated by multiple tokens, there are g ...

made possible by RDF. Notably, the resource is an instance of itself, demonstrating both the use of metaclasses in the language's internal implementation and a reflexive usage of . RDFS is its own

metamodel A metamodel is a model of a model, and metamodeling is the process of generating such metamodels. Thus metamodeling or meta-modeling is the analysis, construction, and development of the frames, rules, constraints, models, and theories applica ...

OWL

In some OWL flavors like OWL1-DL, entities can be either classes or instances, but cannot be both. This limitations forbids metaclasses and metamodeling. This is not the case in the OWL1 full flavor, but this allows the model to be computationally undecidable. In OWL2, metaclasses can implemented with ''punning'', that is a way to treat classes as if they were individuals. Other approaches have also been proposed and used to check the properties of

ontologies In information science, an ontology encompasses a representation, formal naming, and definitions of the categories, properties, and relations between the concepts, data, or entities that pertain to one, many, or all domains of discourse. More ...

at a meta level.

Punning

OWL 2 supports metaclasses through a feature called ''punning''. In metaclasses implemented by punning, the same subject is interpreted as two fundamentally different types of thing—a class and an individual—depending on its syntactic context. This is similar to a

pun A pun, also known as a paronomasia in the context of linguistics, is a form of word play that exploits multiple meanings of a term, or of similar-sounding words, for an intended humorous or rhetorical effect. These ambiguities can arise from t ...

in natural language, where different senses of the same word are emphasized to illustrate a point. Unlike in natural language, where puns are typically used for comedic or rhetorical effect, the main goal of punning in Semantic Web technologies is to make concepts easier to represent, closer to how they are discussed in everyday speech or academic literature. Although OWL 2 permits the same symbol to assume different roles, its standard semantics (known as Direct Semantics) still interprets the symbol differently depending on whether it is used as an individual, a class, or a property.

Protégé

In the ontology editor

Protégé Mentorship is the patronage, influence, guidance, or direction given by a mentor. A mentor is someone who teaches or gives help and advice to a less experienced and often younger person. In an organizational setting, a mentor influences the perso ...

, metaclasses are templates for other classes who are their instances. §6.1 summary of the RDFS model

Classification

an example of ontology with a first metaclass order: the classification of some chemical atoms Some ontologies like the Cyc AI project's classifies classes and metaclasses. Classes are divided into ''fixed-order classes'' and ''variable-order classes''. In the case of fixed-order classes, an order is attributed for metaclasses by measuring the distance to individuals with respect to the number of "instance of" triples that are necessary to find an individual. Classes that are metaclasses are classes of individuals, so their order is "1" (''first-order classes''). Metaclasses that are classes of first-order classes' order is "2" (''second-order classes''), and so on. Variable-order metaclasses, on the other hand, can have instances; one example of variable-order metaclass is the class of all fixed-order classes.

References

{{reflist Ontology languages Web Ontology Language Resource Description Framework Knowledge representation