Xjyuk

Suppose someone asked me the question, "Have you completed the project?". A standard response would be "I have". Why does the equivalent "I've" sound so strange and never used as a replacement?

I am also trying to think of other responses where contractions are used as a complete sentence, but I can't think of something concrete.

Not sure if this even works, but for example, if I were to ask "I am going to pick you up after work", an accepted response could be "Don't. I'm already on my way home". Even if it isn't a complete sentence, it still sounds a lot cleaner than the "I've" response.

Is there a linguistical reason for this?

English syntax makes a distinction between auxiliary verbs and full verbs. (Note that this answer is only talking about English; other languages do things differently.)

"Auxiliary" verbs have a few special properties in English; the most famous one is that they swap places with the subject when asking a direct question. For example, can is an auxiliary verb in the sentence he can swim, so if you turn it into a question, it moves to the front: can he swim? The verb likes seems similar on the surface, but is not an auxiliary: he likes to swim, but not *likes he to swim? Instead, an extra auxiliary is added for the question: does he like to swim?

Things get trickier when using verbs like "have", which can be either auxiliaries or full verbs, depending on their meaning. Compare you have finished ~ have you finished? against you have a cat ~ *have you a cat? In the first case, it's an auxiliary marking what linguists call "perfective aspect"; in the second case, it's a full verb indicating ownership. This is why do you have a cat? *I've is ungrammatical: only auxiliary verbs can contract.

And on top of that, there's an additional rule. Auxiliary verbs usually come attached to the full verb, but sometimes that full verb disappears if it's clear from context. This is called verbal ellipsis, and is extremely common: Have you finished? I have. Do you take this woman to be your wife? I do. But, crucially, auxiliary verbs cannot contract when there is verbal ellipsis. This is why your first example (have you completed the project? *I've) is ungrammatical.

These rules together can be summed up as: certain verbs in English can contract together with the preceding word, but only when acting as auxiliaries, and not if the following full verb is elided.

P.S. An extra point was added while I was writing!

Not sure if this even works, but for example, if I were to ask "I am going to pick you up after work", an accepted response could be "Don't. I'm already on my way home". Even if it isn't a complete sentence, it still sounds a lot cleaner than the "I've" response.

This is a different type of contraction. Another feature of auxiliaries in English is that they can be negated by putting "not" directly after them; full verbs can't do that without sounding extremely archaic (*he completed not the task!).

When this happens, the "not" can sometimes contract to "n't", losing its vowel. But this is separate from the auxiliary itself getting contracted, which is what was happening up above. "Not"-contraction isn't subject to the same restrictions, which is why I didn't is a valid sentence, but *I'dn't isn't.

P.P.S. If you look into this further on your own, be aware that there are two competing definitions of "auxiliary" in English! One definition, the one I'm using, is: auxiliary verbs are the ones that can swap places with the subject in negation. Another definition is: auxiliary verbs are the ones that have no semantic meaning, only grammatical meaning. Some people use the term "modal verbs" for the second meaning, but that term can also have different definitions…welcome to the wonderful world of linguistics terminology!

There are multiple technical explanations, depending on theoretical framework, but one non-technical way to look at it is that you have to include an "actual verb" in the response, where the verb is "stressed" (emphasized, put in focus). You can't say "*I'll", but you can say "I will"; you can also say "I'll go", "I won't, so it's not that you can't do contractions in such responses. One popular analysis is that contraction involves a morphosyntactic process of cliticization, where an apparent full word can also be realized as a phrasal affix on some preceding word. Despite appearances, "*I'd; *I'll" doesn't have a verb. But "I would" does.

There is more to it than that, since you can't say "*I'd have" (as in "I would have gone"). This has to do with the stress requirement (which is about semantics – what you are focusing on). Notice that there is a subtle difference between (1) "I would have sold it" and (2) "I would have sold it", and that (3) "I would have sold it" is kind of bizarre. (1) focuses on the fact that you did not actually sell it and suggests there are other reasons for not selling it; (2) focuses on the choice of selling versus some other action. I cannot conjure up any sensible thing that you'd be contrasting in emphasizing "have" in 3.

You can't delete a vowel and also stress it. That's obvious. So deleting a vowel prevents stressing it, and stressing a vowel prevents deleting it. A principle of English stress is that the last stressed vowel in the last word of a phrase bears the main stress in that phrase -- this is the Nuclear Stress Rule, or NSR.

Putting these two things together, we can predict that you can't delete the last stressed vowel in the last word of a phrase. In your example, answering the question "Have you completed the project?" with "I have completed the project" leaves the vowel of "have" in a vulnerable position for contraction, since "have" is not at the end of a phrase, and the NSR is inapplicable to its vowel. In the shortened answer "I have", however, the NSR requires stress on the vowel of "have", since it is at the end of its phrase (the sentence), thus preventing contraction.