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An extensional definition gives meaning to a term by specifying its extension, that is, every object that falls under the definition of the term in question.. For example, an extensional definition of the term "nation of the world" might be given by listing all of the nations of the world, or by giving some other means of recognizing the members of the corresponding class.
There are multiple versions of the type theory: Martin-Löf proposed both intensional and extensional variants of the theory and early impredicative versions, shown to be inconsistent by Girard's paradox, gave way to predicative versions. However, all versions keep the core design of constructive logic using dependent types.
In logic, extensionality, or extensional equality, refers to principles that judge objects to be equal if they have the same external properties. It stands in contrast to the concept of intensionality , which is concerned with whether the internal definitions of objects are the same.
An extensional statement is a non-intensional statement. Substitution of co-extensive expressions into it always preserves logical value. A language is intensional if it contains intensional statements, and extensional otherwise. All natural languages are intensional. [4]
See also extensionality, and also intensional definition versus extensional definition; Intensional logic embraces the study of intensional languages: at least one of their functors is intensional. It can be contrasted to extensional logic; Intensional fallacy, committed when one makes an illicit use of Leibniz's law in an argument; See also ...
Intensional definitions vs extensional definitions Main articles: Intension and Extension (semantics) An intensional definition , also called a connotative definition, specifies the necessary and sufficient conditions for a thing to be a member of a specific set . [ 3 ]
This list covers optical lens designs grouped by tasks or overall type. The field of optical lens designing has many variables including the function the lens or group of lenses have to perform, the limits of optical glass because of the index of refraction and dispersion properties, and design constraints including realistic lens element center and edge thicknesses, minimum and maximum air ...
Intensional logic is an approach to predicate logic that extends first-order logic, which has quantifiers that range over the individuals of a universe , by additional quantifiers that range over terms that may have such individuals as their value .
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