I've been trying to think of how to complete this with a single query,
but my knowledge of exactly which function would be useful here is
limited.

The situation:
I have an indexed table that refers to two other tables, call it
'INSTALLS'. INSTALLS contains two indexed columns, SYSTEM and
SOFTWARE, which point to their respective tables.

What I want to do, is for a given SYSTEM ID, return all SOFTWARE IDs
which are *not* listed in INSTALLS.

The query so far:
SELECT sw.*, i.*
FROM `SOFTWARE` sw
LEFT OUTER JOIN `INSTALLS` i ON i.`software` = sw.`id`
OR i.`system` IS NULL OR (NOT i.`system` = {id}) ;

The problem with this is that if the software is listed as installed
on another system, it will always be returned, even if it is already
installed on the system with ID {id}.

I'm sorry if this is a bit confusing, it's hard to wrap my head
around, but I'll try to clarify if needed.