"Smoking" is the noun form of the verb "to smoke", also known as a gerund.
"No" is an adjective (quantity) modifying "smoking".
In the unintended misinterpretation, the phrase "no smoking" is an action that is permitted. The misinterpretation is possible because the negative is an adjective on the gerund which allows for ambiguity with regard to the sentence's predicate.
This is a feature of the English language. Colloquially, most English speakers understand the intended meaning.
The ambiguity can be removed by 1) writing "Smoking [is] not allowed" thus asserting the negative as an adverb in the predicate, 2) removing the predicate nominative "[is] allowed" (leaving only a gerundive phrase, not a full sentence), and/or 3) using a diagram like a prohibition symbol atop a burning cigarette [0]
EDIT: grammar and sense (this is getting complicated!)
I think the point of this conversation thread was to split hairs. :)
> "Smoking" is the noun form of the verb "to smoke", also known as a gerund.
Yes.
> "No" is an adjective (quantity) modifying "smoking".
Yes.
> "no smoking" is an action
That does not fit with my understanding. "Uncle Bob is no smoking." is not valid English. "No" is a word used when talking about sets of things/actions. To make an action that is the opposite of smoking, you have to use "not".
FWIW, I agree with Dylan16807. Compare "quickly planning" to "quick planning". Why are both an adjective and an adverb allowed in the same position? Because the adverb is part of the subordinate clause implied by the gerund (where it's treated as a verb), while the adjective is part of the main clause and modifies the gerund (as a noun). "No" is (syntactically) an adjective, so unless it fits into a known colloquialism or special case that bends grammar rules for the sake of brevity, its role in "no smoking" must be the latter - part of the main clause. But then the gerund is treated no differently from any other noun, and "no" does the same trick it always does: "no X does Y" is (always) shorthand for "(an X which does Y) does not exist". "No smoking is allowed" is no different from "no help is available" or "no money has been taken".
(edit: changed first example to something more idiomatic)
"Smoking" is the noun form of the verb "to smoke", also known as a gerund.
"No" is an adjective (quantity) modifying "smoking".
In the unintended misinterpretation, the phrase "no smoking" is an action that is permitted. The misinterpretation is possible because the negative is an adjective on the gerund which allows for ambiguity with regard to the sentence's predicate.
This is a feature of the English language. Colloquially, most English speakers understand the intended meaning.
The ambiguity can be removed by 1) writing "Smoking [is] not allowed" thus asserting the negative as an adverb in the predicate, 2) removing the predicate nominative "[is] allowed" (leaving only a gerundive phrase, not a full sentence), and/or 3) using a diagram like a prohibition symbol atop a burning cigarette [0]
EDIT: grammar and sense (this is getting complicated!)
[0] http://images.mydoorsign.com/img/lg/S/no-smoking-sign-s-9584...