These constructions are not appositives, and a comment (user Billj's) makes
that clear. This type of grammar is of two sorts, both having to do with the omission of text; the first is termed semantic implication and the second is reduction, the particular category of reduction concerned being ellipsis.
I
(CoGEL § 12.31) Ellipsis
The nature of ellipsis
Ellipsis may be more strictly described as 'grammatical omission', in contrast
to other kinds of omission in language. There is, for example, the phonological loss (aphaeresis) of a syllable in the familiar form of because (often spelled 'cos). In word formation […], the clipping of words (eg: flu from influenza) may well be regarded as a process of this kind: the omission is describable in terms of phonological units (syllables) rather than in terms of morphological units (morphemes) or grammatical units (words). There is
also, arguably, semantic omission. In:
- Frankly, he is very stupid.
the disjunct frankly implies a comment by the speaker on the way he is
speaking […]. But there is no one set of missing words that can be
supplied. We can expand frankly to (among many forms) I am speaking
frankly when I say . . . or If I may put it frankly I would tell you . . . Similarly, in:
- He's drunk, because I saw him staggering. [1]
there is an implicit meaning […] that might be expressed by:
- He's drunk, and I claim this because I saw him staggering. [2]
But equally we can express this understood meaning in other forms, such as
and I know, and I am sure of it, and I am convinced of it, and the proof is that. . .
In such cases it is difficult to pin down in exact words what has been omitted, so it is more appropriate to describe this phenomenon as SEMANTIC
IMPLICATION rather than as ellipsis.
The explanations given above in A Comprehensive Grammar of the English Language make the first sentence clear enough as a case of semantic omission.
- The tree fell on my brother's car, not my father's car.
"Not" can be expanded to "and not" (the car in question is not my father's), or "but not" (not both my brother's and my father's car (not parked side by side that day)).
II
The second example is a case of ellipsis because it satisfies to most of the criteria defining it.
(CoGEL § 12.32 Criteria for ellipsis
To distinguish ellipsis from other kinds of omission, it is important to
emphasise the principle of VERBATIM RECOVERABILITY that applies to ellipsis;
that is, the actual word(s) whose meaning is understood or implied must be
recoverable. Even so, like those of so many other grammatical categories,
the boundaries of ellipsis are unclear, and it is best to recognize different
degrees of 'strength' in the identification of examples of ellipsis. To be ellipsis in the strictest sense, an example must satisfy all the criteria specified in 12.33-6.
12.33 (a) The ellipted words are precisely recoverable […]
Note Verbation recovery does not necessarily mean that the items replaced are morphologically identical to the items constituting the antecedent;
12.34 (b) The elliptical construction is grammatically 'defective' […]
12.35 (c) The insertion of the missing words results in a grammatical sentence (with the same meaning as the original sentence) […]
12.36 (d) The missing word(s) are textually recoverable, and
(e) are present in the text in exactly the same form […]
(a) recoverability
- I ordered steak, not lobster.
- I ordered steak, I did not order lobster.
"I" and "ordered" are precisely recoverable, except for a change in form concerning "ordered".
(b) grammaticality
"Not lobster" is grammatically defective.
(c) grammaticality of the resulting sentence and meaning
The resulting sentence is grammatical.
- I ordered steak, I did not order lobster.
(d) textual recoverability
"I" and order are recovered from the text; therefore this criterion is satisfied.
(e) form of the antecedent
The form is different, and so this last criterion is not satisfied.
This type of ellipsis, less perfect than strict ellipsis, is termed standard ellipsis.