Is asking a question with intonation {rather than the usual inversion} grammatically correct?

Is asking a question with intonation only grammatically correct? I had a discussion with colleague about the correct formal way to ask a question in English language. The usual, formal way:

• "Is that your mug?"

However, someone claimed that

• "That is your mug?"

is grammatically correct, despite the fact that it has the form of a statement, and that intonation alone can be used to indicate the question. So, is the latter grammatically correct in formal language?

Solution 1:

There is a term for the non-inverted interrogative sentence: the declarative question. It is marked with a question mark in print and by intonation in speech. From Richard Nordquist at Grammar About.com:

A [declarative question is a] yes-no question that has the form of a declarative sentence but is spoken with rising intonation at the end.

Declarative sentences are commonly used in informal speech to express surprise or [to] ask for verification. The most likely response to a declarative question is agreement or confirmation.

example [in this case showing a pugnacious attitude rather than a casual enquiry]: "You think I'm kidding you? You think it's a joke to have to walk home on a clear night with an umbrella? You think that because I'm quirky I don't hurt? You've got it backwards. I'm quirky because I hurt." (Jack Weston as Danny in The Four Seasons, 1981)

I'd say they're much more appropriate in casual conversation or when about to hit someone than in formal writing. It's probably not helpful to argue about their grammaticality; this probably varies according to the grammarian.