Intensional Definition

An Intensional Definition is a Definition of a Concept Class that is based on a description of the (Necessary and Condition) Conditions that a Concept must satisfy to be a member of the Concept Class.

• AKA: Connotative Definition.
• Context:
  • .
• Example(s):
  • z=PositiveNumber(x) → z=1 if x > 0; else z=0. (A Unary Relation)
  • z=GreaterThan(x,y) → z=TRUE if x>y; else z=FALSE. (A binary Semantic Relation)
  • “A bachelor is an unmarried man.”
  • Hyponym(X,Y) iff F(X) entails, but is not entailed by F(Y).
• See: Extensional Definition.

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References

• Misc
  • An intensional definition lists the attributes or characteristics of the concept.
• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Intensional_definition
  • In logic and mathematics, an intensional definition gives the meaning of a term by specifying all the properties required to come to that definition, that is, the necessary and sufficient conditions for belonging to the set being defined.
  • For example, an intensional definition of "bachelor" is "unmarried man." Being an unmarried man is an essential property of something referred to as a bachelor. It is a necessary condition: one cannot be a bachelor without being an unmarried man. It is also a sufficient condition: any unmarried man is a bachelor.
  • This is the opposite approach to the extensional definition, which defines by listing everything that falls under that definition — an extensional definition of "bachelor" would be a listing of all the unmarried men in the world.
• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Definiendum#Intension_and_extension
  • An intensional definition, also called a connotative definition, specifies the necessary and sufficient conditions for a thing being a member of a specific set. Any definition that attempts to set out the essence of something, such as that by genus and differentia, is an intensional definition.
  • An extensional definition, also called a denotative definition, of a concept or term specifies its extension. It is a list naming every object that is a member of a specific set.

2002

• (Cruse, 2002) ⇒ D. Alan Cruse. (2002). “Hyponymy and its Varieties.” In: (Green et al., 2002).
  • Taking a logical approach, we can define hyponymy either extensionally or intensionally.
  • One extensional definition is the following, after Cann (1994), but modified to exclude synonymy:
    • X is a hyponym of Y iff there exists a meaning postulate relation X' and Y' of the form:
    • ∀x[X'(x) → Y'(x)], but none of the form: ∀x[Y'(x) → X'(x)].
  • (Here, X' and Y' are the logical constants corresponding to the lexical items X and Y, and the definition states, effectively, that for X to be a hyponym of Y, the extension of X' must be included in the extension of Y'.)
  • An example of an intensional definition is the following:
    • X is a hyponym of Y iff F(X) entails, but is not entailed by F(Y).

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