Belle trades Beau an potato for an apple.
Languages are usually limited to only a certain number of nouns or cases. Most languages handle ditransitives, but there are still occasional verbs that seem to need four places. This is especially an issue for loglangs where arity is more firmly encoded. How does your language handle quaternary verbs ?
Common approaches
If you haven't thought about this before, here are some common approaches in case you need some inspiration. This is just optional reading for the curious.
Adpositions
This is an common approach particularly in natlangs and naturalistic languages, and is in fact the approach used in English ! Just use some relevant adposition to indicate the fourth argument. From a logical perspective, these can coordinate through the event variable.
Four cases or four nouns
Alternatively, just have enough cases for four arguments even if these verbs are rare. This is Lojban's approach. There aren't any well known quinary concepts, so this should be enough for everything.
Respective coordination
Now we get into the more loglang pedantry. Another approach is to use respective coordination. This is, coordinate the traders and the items being trade, and mark for respectivity. In English this would look something like:
Belle and Beau trade a potato and an apple respectively.
Some languages even have a respective coordinator (again, Lojban has this, though it's not used here). For example, let's pretend this was spelled "resp" in English, then:
Belle resp Beau trade a potato resp an apple.
Tuples
This similar to respective coordination, but slightly different at the type level. Instead, make the argument of "trade" two 2-tuples. Assuming you have some predicate in your language like
twople(t, a, b) ⇔ t = (a, b)
Then, you can define "trade" as
trade(traders, items) ⇔ ∃ a b x y. twople(traders, a, b) ∧ twople(items, x, y) ∧ trade'(a, b, x, y)
Then you can build the tuple with link args or subordinate clauses or something similar.
the twople of Beau and of Belle trade the twople of a potato and of an apple
Split predicates
The most complex solution is to split the predicate into two ternary predicates that coordinate through the third argument. This is, for example, one would have traders predicate with frame [c c 1] and a trade'with predicate with frame [c c c] where the first argument of trade'with is some opaque trade coordination object and traders's third argument is a unary lambda that varies in this opaque object. Then a trade would be something like:
traders Belle Beau λ x. trade'with x a potato an apple
Note we use a pseudo syntax here since we're far beyond anything English can do. Note that traders can also have frame [c c c] if the language has a way to link two arguments similar to Eberban "hinging".
Have fun
So how does your language handle this ?