Logs and objectives are revealed as the player explores derelicts. Where these refer to specific ships, systems, or galaxies, the locations will change with each reset while the logs are permanent until user data is cleared. Continuing to explore additional derelicts of the appropriate type will reveal additional main and supporting objectives.
SPOILERS AHEAD! READ AT YOUR OWN DISCRETION!!! Edit
Once unlocked, logs are stored as .bkd files (plain text) within the "\data\udata\DEFAULT\Logs" folder.
It is possible there are alternate outcomes, depending on the order in which supporting and main quests are completed. It is also possible that all the theories are related. This will require further experimentation.