This message can mean different problems and then different solutions.
First try to shutdown completely the computer and restart.
Can you start Logic directly from the Applications folder? If it works, then you may have a corrupt link in the Dock.
Also, if you do some search on the Web, you will find hints related to clearing some folders in /var/folders. Below an example.
Damaged or Incomplete - Apple Community
It is for Sierra but it may apply to Catalina too. I don't know and no guarantee it will works. Better know what you're doing.
Hope that helps,
WD