When you launch Logic Pro, it may quit unexpectedly at the point where the startup screen progress indicator says "Updating Tree".
This behavior indicates an issue with the Project Manager database. Go to ~/Library/Preferences/Logic (where "~" represents your user folder) and drag the folder named "PM Data" to the Trash.
After you delete the "PM Data" folder, you'll need to rebuild the Project Manager database. See page 421 of the Logic Pro Reference manual for details.
This document will be updated as more information becomes available.