generalization

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A generalization is a form of
abstraction Abstraction in its main sense is a conceptual process where general rules and concept Concepts are defined as abstract ideas or general notions that occur in the mind, in speech, or in thought. They are understood to be the fundamental buildin ...

whereby common properties of specific instances are formulated as general concepts or claims. Generalizations posit the existence of a domain or set of elements, as well as one or more common characteristics shared by those elements (thus creating a
conceptual model A conceptual model is a depiction, representation of a system. It consists of concepts used to help people knowledge, know, understanding, understand, or simulation, simulate a subject the model represents. It is also a set of concepts. In contrast ...
). As such, they are the essential basis of all valid
deductive Deductive reasoning, also deductive logic, is the process of reasoning from one or more statements (premises) to reach a logical conclusion. Deductive reasoning goes in the same direction as that of the conditionals, and links premises with con ...
inferences (particularly in
logic Logic is an interdisciplinary field which studies truth and reasoning Reason is the capacity of consciously making sense of things, applying logic Logic (from Ancient Greek, Greek: grc, wikt:λογική, λογική, label=none, lit ...

, mathematics and science), where the process of verification is necessary to determine whether a generalization holds true for any given situation. Generalization can also be used to refer to the process of identifying the parts of a whole, as belonging to the whole. The parts, which might be unrelated when left on their own, may be brought together as a group, hence belonging to the whole by establishing a common relation between them. However, the parts cannot be generalized into a whole—until a common relation is established among ''all'' parts. This does not mean that the parts are unrelated, only that no common relation has been established yet for the generalization. The concept of generalization has broad application in many connected disciplines, and might sometimes have a more specific meaning in a specialized context (e.g. generalization in psychology, generalization in learning). In general, given two related concepts ''A'' and ''B,'' ''A'' is a "generalization" of ''B'' (equiv., ''B'' is a
special case In logic Logic (from Ancient Greek, Greek: grc, wikt:λογική, λογική, label=none, lit=possessed of reason, intellectual, dialectical, argumentative, translit=logikḗ)Also related to (''logos''), "word, thought, idea, argument, a ...
of ''A'') if and only if both of the following hold: * Every instance of concept ''B'' is also an instance of concept ''A.'' * There are instances of concept ''A'' which are not instances of concept ''B''. For example, the concept ''animal'' is a generalization of the concept ''bird'', since every bird is an animal, but not all animals are birds (dogs, for instance). For more, see
Specialisation (biology)A generalist species is able to thrive in a wide variety of environmental conditions and can make use of a variety of different resources A resource is a source or supply from which a benefit is produced and that has some utility. Resources can bro ...
.

# Hypernym and hyponym

The connection of ''generalization'' to ''specialization'' (or ''particularization'') is reflected in the contrasting words
hypernym In linguistics Linguistics is the science, scientific study of language. It encompasses the analysis of every aspect of language, as well as the methods for studying and modeling them. The traditional areas of linguistic analysis include ...
and
hyponym In linguistics, hyponymy (from Greek language, Greek ὑπό, ''hupó'', "under", and ὄνυμα, ''ónuma'', "name") is a semantics, semantic relation between a hyponym denoting a subtype and a hypernym or hyperonym denoting a supertype. In oth ...
. A hypernym as a
generic Generic or generics may refer to: In business * Generic term, a common name used for a range or class of similar things not protected by trademark * Generic brand, a brand for a product that does not have an associated brand or trademark, other t ...
stands for a class or group of equally ranked items, such as the term ''tree'' which stands for equally ranked items such as ''peach'' and ''oak'', and the term ''ship'' which stands for equally ranked items such as ''cruiser'' and ''steamer''. In contrast, a hyponym is one of the items included in the generic, such as ''peach'' and ''oak'' which are included in ''tree'', and ''cruiser'' and ''steamer'' which are included in ''ship''. A hypernym is superordinate to a hyponym, and a hyponym is subordinate to a hypernym.

# Examples

## Biological generalization

An animal is a generalization of a
mammal Mammals (from Latin language, Latin , 'breast') are a group of vertebrate animals constituting the class (biology), class Mammalia (), and characterized by the presence of mammary glands which in Female#Mammalian female, females produce milk ...
, a bird, a fish, an
amphibian Amphibians are ectothermic, tetrapod vertebrates of the Class (biology), class Amphibia. All living amphibians belong to the group Lissamphibia. They inhabit a wide variety of habitats, with most species living within terrestrial animal, terr ...
and a reptile.

## Cartographic generalization of geo-spatial data

Generalization has a long history in
cartography Cartography (; from Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approximately 10 ...
as an art of creating maps for different scale and purpose.
Cartographic generalizationCartographic generalization, or map generalization, includes all changes in a map that are made when one derives a smaller-scale map from a larger-scale map or map data, or vice versa. It is a core part of cartographic design. Whether done manuall ...
is the process of selecting and representing information of a map in a way that adapts to the scale of the display medium of the map. In this way, every map has, to some extent, been generalized to match the criteria of display. This includes small cartographic scale maps, which cannot convey every detail of the real world. As a result, cartographers must decide and then adjust the content within their maps, to create a suitable and useful map that conveys the
geospatial Geographic data and information is defined in the ISO/TC 211 series of standards as data and information having an implicit or explicit association with a location relative to Earth (a geographic location or geographic position). It is also calle ...
information within their representation of the world. Generalization is meant to be context-specific. That is to say, correctly generalized maps are those that emphasize the most important map elements, while still representing the world in the most faithful and recognizable way. The level of detail and importance in what is remaining on the map must outweigh the insignificance of items that were generalized—so as to preserve the distinguishing characteristics of what makes the map useful and important.

## Mathematical generalizations

* A
polygon In geometry, a polygon () is a plane (mathematics), plane Shape, figure that is described by a finite number of straight line segments connected to form a closed ''polygonal chain'' (or ''polygonal circuit''). The bounded plane region (mathematic ...

is a generalization of a 3-sided
triangle A triangle is a polygon with three Edge (geometry), edges and three Vertex (geometry), vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC. In Euclidean geometry, any ...

, a 4-sided
quadrilateral A quadrilateral is a polygon in Euclidean geometry, Euclidean plane geometry with four Edge (geometry), edges (sides) and four Vertex (geometry), vertices (corners). Other names for quadrilateral include quadrangle (in analogy to triangle) and t ...

, and so on to ''n'' sides. * A
hypercube In geometry Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space th ...

is a generalization of a 2-dimensional square, a 3-dimensional
cube In geometry Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space ...
, and so on to ''n''
dimension thumb , 236px , The first four spatial dimensions, represented in a two-dimensional picture. In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), m ...
s. * A
quadric In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipse In mathematics, an ellipse is a plane curve surrounding two focus (geometry), focal points, such that ...
, such as a
hypersphere In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). I ...

,
ellipsoid An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional Scaling (geometry), scalings, or more generally, of an affine transformation. An ellipsoid is a quadric surface;  that is, a Surface (mathemati ...
,
paraboloid In geometry Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space tha ...

, or
hyperboloid In geometry Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space th ...
, is a generalization of a
conic section In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). ...
to higher dimensions. * A
Taylor series In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). ...
is a generalization of a
MacLaurin seriesMaclaurin or MacLaurin is a surname. Notable people with the surname include: * Colin Maclaurin (1698–1746), Scottish mathematician * Normand MacLaurin (1835–1914), Australian politician and university administrator * Henry Normand MacLaurin (1 ...
. * The
binomial formula In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of exponentiation, powers of a binomial (polynomial), binomial. According to the theorem, it is possible to expand the polynomial into a summati ...
is a generalization of the formula for $\left(1+x\right)^n$.

{{wikiquote * Categorical imperative (ethical generalization) * ''
Ceteris paribus ' or ' () is a Latin phrase meaning "other things equal"; English translations of the phrase include "all other things being equal" or "other things held constant" or "all else unchanged". A prediction or a statement about a ontic, causal, episte ...
'' *
Class diagram In software engineering, a class diagram in the Unified Modeling Language The Unified Modeling Language (UML) is a general-purpose, developmental, modeling language in the field of software engineering that is intended to provide a standard way t ...

*
External validityExternal validity is the validity of applying the conclusions of a scientific study outside the context of that study. In other words, it is the extent to which the results of a study can be generalized to and across other situations, people, stimuli ...
(scientific studies) *
Faulty generalization A faulty generalization is an informal fallacy Informal fallacies are a type of incorrect argument In logic Logic (from Ancient Greek, Greek: grc, wikt:λογική, λογική, label=none, lit=possessed of reason, intellectual, dialecti ...
* Generic (disambiguation) *
Critical thinking Critical thinking is the analysis of facts to form a judgment. The subject is complex; several different Critical thinking#Definitions, definitions exist, which generally include the rational, skepticism, skeptical, and unbiased analysis or evalu ...
*
Generic antecedent Generic or generics may refer to: In business * Generic term, a common name used for a range or class of similar things not protected by trademark * Generic brand, a brand for a product that does not have an associated brand or trademark, other ...
*
Hasty generalization In logic Logic (from Ancient Greek, Greek: grc, wikt:λογική, λογική, label=none, lit=possessed of reason, intellectual, dialectical, argumentative, translit=logikḗ)Also related to (''logos''), "word, thought, idea, argument, ac ...
*
Inheritance (object-oriented programming) In object-oriented programming Object-oriented programming (OOP) is a programming paradigm based on the concept of "Object (computer science), objects", which can contain data and code: data in the form of Field (computer science), fields (oft ...
, * '''' *
-onym The suffix ''-onym'' (from grc, ὄνυμα / name) is a bound morpheme, that is attached to the end of a root word, thus forming a new compound word that designates a particular ''class'' of names. In linguistic terminology, compound words that a ...
*
Ramer–Douglas–Peucker algorithmThe Ramer–Douglas–Peucker algorithm, also known as the Douglas–Peucker algorithm and iterative end-point fit algorithm, is an algorithm that decimates a curve composed of line segments to a similar curve with fewer points. It was one of the ea ...
* Semantic compression *
Specialization (logic) Specialization or Specialized may refer to: Academia * Academic specialization, may be a course of study or major at an academic institution or may refer to the field in which a specialist practices * Specialty (medicine), a branch of medical ...
, the opposite process *
Inventor's paradoxThe inventor's paradox is a phenomenon that occurs in seeking a solution to a given problem. Instead of solving a specific type of problem, which would seem intuitively easier, it can be easier to solve a more general problem, which covers the specif ...

# References

Generalizations Critical_thinking Inductive_reasoning