Another option would be to add another screen to the trait selection screen. When selecting a spell trait, but before you click OK, this screen would pop up. It will show you exactly what spells will become available.
The spells listed there can be clicked to be shown in hiergamemon, or hovered over to read their description. This additional screen is SCROLLABLE and DYNAMIC (think of the modders, please). Most importantly, the screen takes into account what other traits you have already, in order to show you spells that combine traits from multiple disciplines.
For example, if I have Air 2 and Fire1, and I select in the level-up screen Fire 2, the following spells should show up:
(sorry, those were fire3)
The icons in front of the spell would correctly describe what combination of traits is allowing this character to cast these spells.