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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.
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]
Type-theoretical foundations of mathematics are generally not extensional in this sense, and setoids are commonly used to maintain a difference between intensional equality and a more general equivalence relation (which generally has poor constructibility or decidability properties).
If present, a dagger (†) indicates the usage of a nautical time zone letter outside of the standard geographic definition of that time zone. Some zones that are north/south of each other in the mid-Pacific differ by 24 hours in time – they have the same time of day but dates that are one day apart. The two extreme time zones on Earth (both ...
Such designations can be ambiguous; for example, "CST" can mean China Standard Time (UTC+08:00), Cuba Standard Time (UTC−05:00), and (North American) Central Standard Time (UTC−06:00), and it is also a widely used variant of ACST (Australian Central Standard Time, UTC+9:30). Such designations predate both ISO 8601 and the internet era; in ...
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.
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 ]