Of or pertaining to intension.
Used in a Sentence
intensional
Definition, parts of speech, synonyms, and sentence examples for intensional.
Editorial note
In type theory the equality is intensional and thus preserved by structure.
Examples17
Definitions1
Parts of speech1
Quick take
Of or pertaining to intension.
Meaning at a glance
The clearest senses and uses of intensional gathered in one view.
Definitions
Core meanings and parts of speech for intensional.
adjective
Of or pertaining to intension.
Example sentences
In type theory the equality is intensional and thus preserved by structure.
Most of the really interesting modern work is just building on top of some form intensional Martin-Löf theory.
For instance, in some systems (such as Intensional Type Theory), type checking is decidable, which is really nice.
The former is extensional, the latter intensional.
No, HoTT is not based on the Calculus of Constructions, but instead on intensional Martin-Loef type theory with identity typed.
The novelty of HoTT, and only extension over intensional Martin-Loef type-theory, is the univalence axiom.
This was all considered theoretical and impractical--until someone noticed that the logic provided by Intensional Type Theory (as implemented in e.g.
One of the things that was a mess at Google was an intensional/extensional conflict.
The problem seems to stem from the tension between intensional and extensional definitions.
In fact, whether intensional or not, it's a trick with statistics itself.
As for equality (i.e., intensional equality) itself, I think memberwise equality (or perhaps even equivalence?) is a perfectly reasonable definition.
You have to make a distinction between the intensional and extensional domain.
Quote examples
I think you've confused "intensional" and "extensional".
("Intensional" means "identity determined by structure"; "extensional" means "identity determined by behavior".
I would say the first two are "instances" of the same principle (in the same way that, for example, intensional equality can be "instantiated" for integers, arrays, matrices, etc.).
("I believe X means nothing more or less than that I am disposed to behave in certain ways under certain conditions" – where "certainty" involves pre-theoretical commitments emergent by our own evolutionary tract.) The intensional-extensional domain distinction of the number theory is directly structurally relevant to the discussion of inside-outside (internal-external) behavior of neuroscience.
Proper noun examples
Intensional type theory is a theory of formal proof, where the terms are literally proofs of judgement: it's pretty dead in there.
Frequently asked questions
Short answers drawn from the clearest meanings and examples for this word.
How do you use intensional in a sentence?
In type theory the equality is intensional and thus preserved by structure.
What does intensional mean?
Of or pertaining to intension.
What part of speech is intensional?
intensional is commonly used as adjective.