A recent question used the abbreviations "NP" (noun phrase) and "AP" (adjective phrase) without expansion. A commenter objected, recommending that such abbreviations always be expanded for the benefit of those who may not be familiar with them.
A list of commonly used abbreviations currently exists on ELU Meta: List of common abbreviations and acronyms (NOAD, ESL, PIE...). Apparently the list is useful, because both the question proposing it and the answer containing the actual list have several dozen upvotes. Furthermore, ELU's help pages link to that list; I assume that this confers some sort of official (or semi-official?) imprimatur upon it.
That list does not contain abbreviations commmonly used for various sentence constituents and parts of speech. Should we add abbreviations such as "NP" and "AP" (and "Det", "PP", etc.)? If so, would it be best for them to be in a separate section? I was going to go ahead and just do it, but there would be quite a few terms to add, so I thought it would be best to gauge interest before making such a big edit.
Also of interest:
A question asked whether we should discourage the use of "argot": Should we discourage the use of argot such as AmE, BrE, ELU, ...?. That suggestion doesn't seem to have gotten much traction. The most upvoted answer notes: "Rather than asking these specialists to abandon the very way they communicate, it makes more sense to me to make sure the site helps anyone who is not familiar by documenting common jargon, including abbreviations, in the online help." It then links to the list of abbreviations.
A more popular suggestion (postdating the list of abbreviations) asks for a glossary of terms, including abbreviations. I searched ELU for "glossary" and found nothing like that, so I assume that nothing came of it.