Learn English – Determining if “than” is used as conjunction or preposition

There are no special rules for rarely used prepositions. According to the Chicago Manual of Style, all prepositions should be lowercased (except when they are stressed or occur as the first or last word). But I hardly ever see this style used. The AP style is much more common. According to the AP stylebook all prepostions containing three letters or fewer should be lowercased, while the Wikipedia Manual of Style says all prepositions containing four letters or fewer should be lowercased.

However, the Wikipedia rules are not enforced, and as a result the capitalization on Wikipedia is a mess, and often in violation of the style manual (as you had observed). I think the reason for this is that the AP rules are dominant in real life, so this is what people are used to (i.e., what “looks right”). This explains many of the cases that you listed: down, over, unto, upon etc. are all capitalized according to AP style.

So regarding your examples, it depends on the style guide you choose whether the four-letter prepositions should be lowercased. Three- or two-letter prepositions like on, off, out or up should always be lowercased (if they are really used as prepositions and do not occur as first or last word). Yet should also be lowercased, if used as a conjunction.

There is no difference between book titles and song titles. The AP style for instance says that its composition title guidelines apply to book titles, movie titles, opera titles, album and song titles, radio and television program titles, and several more.

I see it as a preposition. Here’s why:

1. Subordinating conjunctions function as markers of subordination, whereas preps (inc "after") function as heads of the constituents they introduce.

2. Unlike subordinating conjunctions, preps have independent meaning ('an evident semantic content'). In the case of "after", it has a temporal meaning.

3. With items like "after" they uncontroversially occur as preps when they have an NP as complement, and there's no basis for assigning them to different categories according as they take an NP or a clause - or no complement at all.

Trad grammar has:

after the meeting: preposition + noun

after we arrived: subordinating conjunction + sub clause

I didn’t seen her after: adverb, no complement

This is just a matter of varying complementation, which is commonplace.

Compare verbs:

I know her father: verb + NP

I know that he's ill: verb + sub clause

I know: verb without complement

Or nouns:

a belief in God: noun + PP

the belief that God exists: noun + clause

her beliefs: noun without complement

Moreover, in all three constructions, "after" takes the same modifiers, e.g. a short while. We need therefore to distinguish "after" from the subordinators "that/whether", and then once we've done that "after" clearly belongs with all the other preps. For the record, Jespersen argued for treating "after" the same in all three constructions nearly a hundred years ago.