Generalization
A generalization is a form of abstraction whereby common properties of specific instances are formulated as general concepts or claims.[1] 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). As such, they are the essential basis of all valid deductive inferences (particularly in logic, mathematics and science), where the process of verification is necessary to determine whether a generalization holds true for any given situation.
For other uses, see Generalization (disambiguation).
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).[1]
In general, given two related concepts A and B, A is a "generalization" of B (equiv., B is a special case of A) if and only if both of the following hold:
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).
The is a generalization of the formula for .
