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If a class does not satisfy this condition, then it is intensional.
English, in common with every other natural language, is an intensional language.
Note that it also creates a class from the extension of the intensional set.
Functors for which this assumption does not hold are called intensional.
We shall consider in Section 4.2 what precisely is the intensional structure for this interpretation.
For example, an intensional definition of bachelor is 'unmarried man'.
An expression such as "believes that" is said to introduce an intensional context.
An intensional description of a cluster is developed during the clustering process.
Intensional descriptions are usually invented by some sort of generalizing method.
The classes of an ontology may be extensional or intensional in nature.
In other words, these first-order interpretations are extensional not intensional.
An intensional description provides a way to decide whether any particular thing is in the cluster by examining its properties.
I shall assume that all intensional descriptions are classical.
She was an internationally recognized scholar of Leibniz and intensional logic.
As mentioned, motivations for settling problems that belong today to intensional logic have a long past.
The notation with braces may also be used in an intensional specification of a set.
Under intensional equality, two functions f and g are considered equal if they have the same "internal structure".
There are some intensional logic systems that claim to fully analyze the common language:
Already in 1951, Alonzo Church had developed an intensional calculus.
Intensional attributes can resemble, but are not identical to, the properties perceived by the five senses.
One way is by intensional definition, using a rule or semantic description:
Initial values can be given in intensional definition, as in:
This is a type of intensional definition.
It will be noted that the intensional statements above feature expressions like "knows", "possible", and "pleased".
This is because 'believes' is typically an intensional context.