Events for adverbs, adjectives and prepositions

ERG introduces events for adjectives, adverbs, and prepositions. For instance:

She saw a Jaguar speeding up on the highway.

We have 3 event variables. I know the motivation for introducing events for adjectives and adverbs, although I am still trying to find the proper reference to the explanation.

But what about the motivation for the prepositions? Can someone point me to any reference about it?

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I don’t have a reference to hand, but some thoughts: So long as we’re talking about semantically contentful adpositions (not case markers), that means they are introducing a predication, usually one that relates two (other) entities. Do you see a principled difference between the eventuality of X being on top of Y and the eventuality of X covering Y? (My point is that they are very like stative verbs at that point.)

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Thank you @ebender. As a non-native English speaker, I am not sure if this sentence below makes sense, but in

She is firmly on top of the case

I found one example where ERG understood that the adverb is modifying the preposition. The copula does not contribute to the semantics. In the Grammatical theory: From transformational grammar to constraint-based approaches. Second revised and extended edition. Vol. II. |, one sentence called my attention:

Sometimes adverbs are simply treated as a special variant of prepositions (see page 94). The explanation for this is that a prepositional phrase such as in diesem Raum ‘in this room’ shows the same syntactic distribution as the corresponding adverbs.

So the parallel of prepositions and adverbs itself may already justify the eventuality reading of prepositions?

There are at least four reasons to have prepositional phrases in English introduce events, two of which you have already noted:
(1) Copula constructions - In a sentence such as “Kim is dancing” we don’t want a separate EP for “is”, so there needs to be at least one entry for the copula “be” which does not introduce its own EP, instead having the semantic effect of constraining the tense/aspect of the event introduced by its VP complement. We use this same semantically empty copula for predicative adjectives as in “Kim was uninformed”, where the adjective, as you have noted, also introduces an event. For parsimony, we analyze predicative PPs using the same copula, so the PP has to introduce an event to give us a place to record the semantic constraints on tense and aspect provided by the auxiliaries, as in “Kim had been in the room”.
(2) Coordination - We want to treat coordinate structures as uniformly as possible, so in a sentence such as “Kim is running and in the lead” we conjoin the VP and PP, with the coordinated phrase being the complement of that same semantically empty copula. The conjunction relation takes as its two arguments the ARG0 (the inherent/intrinsic variable in an EP) of each of its two conjuncts, so the PP needs to supply one of the two events being conjoined.
(3) Absolutive constructions: In sentences modified by an absolut(iv)e construction, we again want a consistent analysis whether the predication in the modifier is a VP, an AP, or a PP, as in the following three examples:
With Kim entering the race, no one else can win.
With Kim ready to enter the race, no one else can win.
With Kim in the race, no one else can win.
Having PPs introduce an event in parallel with VPs and APs allows us to use just one construction to analyze these with-absolutives (via a suitable lexical entry for “with”), with the predicative phrase supplying the main event for the clausal meaning of the modifier.
(4) Modification of PPs - As you noted, PPs can themselves be modified by non-scopal modifiers, as in “Kim was already in the lead” and “With Kim already in the lead, no one else had a chance of winning”. We want a consistent analysis of how the adverb “already” combines semantically with the phrase it modifies, namely to take the ARG0 of that phrase as its argument and identify its label with that of the modified phrase. Assuming we use the same lexical entry for “already” in “the runner already leading” and “the runner already in the lead”, we need to have the PP “in the lead” introduce an event for “already” to use.
[Note to self: Add these comments, suitably edited/improved, to the ErgSemantics documentation, under “Semantically Vacuous Lexical Items”.]