You are allowed to be "no smoking." It doesn't say that you can't smoke, which is the only possible interpretation of the second option.

You cannot be "no smoking". You can be "not smoking". You can be "non-smoking". "no smoking" is not an adjective.

"No smoking" is a gerundive phrase which serves as the sentence's subject, with the copulative verb "is" implied: "No smoking [is] allowed".

Considered differently, the sentence is not in the imperative mood with an implied subject. The sentence is in the declarative mood with an implied verb.

The possible misunderstanding is that this declarative sentence merely identifies one action (of many) which is allowed, "no smoking", which does not necessarily prohibit other activities including "smoking", "singing", "no singing", "dancing", etc.

EDIT: grammar and readability

I strongly disagree. "not smoking" is an action. "no smoking" is not an action. You cannot parse the sentence as allowing a specific action without replacing the word "no" with something else.

Edit: Also, I treat the sentence as being declarative with an implied 'is' even when interpreting it correctly.

You are splitting hairs and are mistaken.

"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...

> You are splitting hairs

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)

This is amusing but absurd, especially if you're serious about this phrase being confusing or malformed. "You may not smoke": does this mean, to you, that either smoking or not smoking is permitted? If the answer is yes, I think the solution may be to cease applying the logical rules of programming to human languages, where it is meaning and tradition that matter.

I was going to write that the answer your question is "no" because your version is unambiguous but then I parsed it a few more times.

One way to remove the ambiguity is to recast your sentence using "must": "You must not smoke". But that version is stilted to most modern English speakers raised outside the UK.

This side-discussion is probably one of the reasons people wish HN had collapsible threads, so after this comment I will refrain from further contributing to it.

(Nice job, btw, on highlighting the ambiguity in a version where the negative is in the predicate.)

EDIT: grammar

You no smokey!

Didn't Smokey say "Only you…"? [0]

[0] https://en.wikipedia.org/wiki/File:Smokey3.jpg

He's trying to imply that one would actually read this as "no smoking [IS] allowed".

"No smoking is allowed." is the correct message.

But "smoking isn't allowed" or "smoking is prohibited" is a clearer way of putting it...