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Two of the predominant types of relationships in knowledge-representation systems are predication and the universally quantified conditional. Predication relationships express the notion that an individual entity is an example of a certain type (for example, John is a bachelor), while universally quantified conditionals express the notion that a type is a subtype of another type (for example, "A dog is a mammal", which means the same as "All dogs are mammals"). The "has-a" relationship is quite different: an elephant has a trunk; a trunk is a part, not a subtype of elephant. The study of part-whole relationships is mereology. Taxonomies are often represented as is-a hierarchies where each level is more specific than the level above it (in mathematical language is "a subset of" the level above). For example, a basic biology taxonomy would have concepts such as mammal, which is a subset of animal, and dogs and cats, which are subsets of mammal. This kind of taxonomy is called an is-a model because the specific objects are considered as instances of a concept. For example, Fido is-an instance of the concept dog and Fluffy is-a cat. In linguistics, is-a relations are called hyponymy. When one word describes a category, but another describe some subset of that category, the larger term is called a hypernym with respect to the smaller, and the smaller is called a "hyponym" with respect to the larger. Such a hyponym, in turn, may have further subcategories for which it is a hypernym. In the simple biology example, dog is a hypernym with respect to its subcategory collie, which in turn is a hypernym with respect to Fido which is one of its hyponyms. Typically, however, hypernym is used to refer to subcategories rather than single individuals.

== Research ==

Researchers reported that large populations consistently develop highly similar category systems. This may be relevant to lexical aspects of large communication networks and cultures such as folksonomies and language or human communication, and sense-making in general.

== Theoretical approaches ==

=== Knowledge organization === Hull (1998) suggested "The fundamental elements of any classification are its theoretical commitments, basic units and the criteria for ordering these basic units into a classification". There is a widespread opinion in knowledge organization and related fields that such classes corresponds to concepts. We can, for example, classify "waterfowls" into the classes "ducks", "geese", and "swans"; we can also say, however, that the concept "waterfowl" is a generic broader term in relation to the concepts "ducks", "geese", and "swans". This example demonstrates the close relationship between classification theory and concept theory. A main opponent of concepts as units is Barry Smith. Arp, Smith and Spear (2015) discuss ontologies and criticize the conceptualist understanding. The book writes (7): “The code assigned to France, for example, is ISO 3166 2:FR and the code is assigned to France itself — to the country that is otherwise referred to as Frankreich or Ranska. It is not assigned to the concept of France (whatever that might be).” Smith's alternative to concepts as units is based on a realist orientation, when scientists make successful claims about the types of entities that exist in reality, they are referring to objectively existing entities which realist philosophers call universals or natural kinds. Smith's main argument - with which many followers of the concept theory agree - seems to be that classes cannot be determined by introspective methods, but must be based on scientific and scholarly research. Whether units are called concepts or universals, the problem is to decide when a thing (say a "blackbird") should be considered a natural class. In the case of blackbirds, for example, recent DNA analysis have reconsidered the concept (or universal) "blackbird" and found that what was formerly considered one species (with subspecies) are in reality many different species, which just have chosen similar characteristics to adopt to their ecological niches. An important argument for considering concepts the basis of classification is that concepts are subject to change and that they change when scientific revolutions occur. Our concepts of many birds, for example, have changed with recent development in DNA analysis and the influence of the cladistic paradigm - and have demanded new classifications. Smith's example of France demands an explanation. First, France is not a general concept, but an individual concept. Next, the legal definition of France is determined by the conventions that France has made with other countries. It is still a concept, however, as Leclercq (1978) demonstrates with the corresponding concept Europe. Hull (1998) continued: "Two fundamentally different sorts of classification are those that reflect structural organization and those that are systematically related to historical development." What is referred to is that in biological classification the anatomical traits of organisms is one kind of classification, the classification in relation to the evolution of species is another (in the section below, we expand these two fundamental sorts of classification to four). Hull adds that in biological classification, evolution supplies the theoretical orientation.

=== Ereshevsky === Ereshefsky (2000) presented and discussed three general philosophical schools of classification: "essentialism, cluster analysis, and historical classification. Essentialism sorts entities according to causal relations rather than their intrinsic qualitative features." These three categories may, however, be considered parts of broader philosophies. Four main approaches to classification may be distinguished: (1) logical and rationalist approaches including "essentialism"; (2) empiricist approaches including cluster analysis. (It is important to notice that empiricism is not the same as empirical study, but a certain ideal of doing empirical studies. With the exception of the logical approaches they all are based on empirical studies, but are basing their studies on different philosophical principles). (3) Historical and hermeneutical approaches including Ereshefsky's "historical classification" and (4) Pragmatic, functionalist and teleological approaches (not covered by Ereshefsky). In addition, there are combined approaches (e.g., the so-called evolutionary taxonomy", which mixes historical and empiricist principles).