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What is an intension?

What is an intension? Here are some definitions.

Noun
  1. intensity or the act of becoming intense.
  2. (logic) Any property or quality connoted by a word, phrase or other symbol, contrasted to actual instances in the real world to which the term applies.
  3. (dated) A straining, stretching, or bending; the state of being strained.
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The announcement of BP's intension to 'do the right thing' brought a battery of veiled threats from Angolan oil company, Sonangol.
From this arises the distinctive terms known as the content, extension and intension of concepts, respectively.
They provide a vehicle for the imaginative extension and intension of space beyond and within the realist scale of the city.
Typically, the intension states necessary and sufficient conditions, or conjunctions of properties, that must be present for an object to belong to the extension.
On the other hand, two sentences have the same intension if they are logically equivalent, i.e., their equivalence is due to the semantic rules of the language.
Medieval theories of ratios and proportions and of the intension and remission of forms were applied to problems of motion.

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