Intension

In philosophy, the word intension (with an s — not intention) refers to definitions in terms of properties, or "necessary and sufficient conditions", rather than extension, a direct enumeration of referents.

For example, "a prime number less than 10" is an intensional definition, wheres "one of {2, 3, 5, 7}" is extensional.

By extension, in semantics, an intensional interpretation of a phrase is one that retains the sense of the words used, whereas an extensional interpretation is one that directly gets at the referent.

For example, consider the phrase Clark Kent is Superman. If both phrases are given an extensional interpretation, the phrase's denotation collapses to $x=x$ for the man $x$ denoted by "Clark Kent" and by "Superman". Handling noun phrases this way is the easiest option, but as we can see, it fails to capture the "intensional" essence of this sentence (an equality of two descriptions) and collapses it down to a tautology (an equality between $x$ and itself).

To handle a noun phrase like "Superman" intensionally, we need a denotation that can still access the descriptor used. The Kuna way to do this is to denote noun phrases with an effect Int. Under the hood, it's not an entity directly, but a function from worlds to entities; mí Superman refers not directly to that man $x$ but to something like λw. superman(w) — that is, whoever is called "Superman" in the world the clause is to be evaluated in.

A real-life example: in a conversation on Discord about a now-defunct social media platform that changed its name from Calckey to Firefish, Kıa said:

duashao jí, mä taoshao nhána, ꝡä sıu chúa shú Firefox
I wonder if they intend for the name to resemble "Firefox"

This only makes sense if chúa is given an intensional interpretation: it must refer to whatever name the platform has, rather than to the word Calckey or the word Firefish for the sentence to really work.