meaning - Adjective association

Is there a rule that states what word adjectives in a sentence will link to? If I say

I have a big cookie jar

it's still a correct sentence. The word "cookie" isn't an adjective, but "cookie jar" is a common term that represents a jar explicitly used to contain cookies.

In the phrases "dark green box" and "dark, green box" I know that with the comma, the box is dark and green, while without it, the box is dark green.

In the cookie jar sentence, is the jar explicitly used to contain "big cookies" or is the "cookie jar" big?

Answer

A sentence containing a noun with multiple modifiers would be confusing to read if there was not some common understanding regarding what modifies what.

Though it's not an absolute rule, the modifier closest to the main noun is most commonly presumed to modify that noun.

a big red silk hat is understood first and foremost as a silk hat, specifically a red one, and big in size, as one cannot modify red with big. A soft red silk hat, because soft usually doesn't modify red, would be understood as a soft silk hat which is red. One might avoid initial confusion in a bold red silk bear by hyphenating bold-red.

Similarly, a big cookie jar is understood to be, primarily, a cookie jar which is also big. A cookie jar for big cookies might be described as a wide-mouthed cookie jar just to avoid that potential ambiguity.

This is an interesting thread about adjectives.