I had the same problem and it occured directly after updating to Motion 5.2.3/FCP 10.2.3/Compressor 4.2.2/Pro Video Formats 2.0.4 today.
Logic was working fine on Friday and the machine had been shut down until I started it today and installed the above updates, so I´m quite certain the bug has something to do with the updates in my case.
When I started with CTRL held down and disabled Core Audio, Logic started.
So maybe the above mentioned update changed Core Audio?
Anyway, Tyrann0s solution by removing the folder "Databases" worked fine - Thanks a lot mate, I owe you one 🙂
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Some background info:
I use this machine (MP2013) mainly for Video & Animation and I have not installed any 3rd party instrument plugins for Logic.
The only component in the Library folder are:
AppleAES3Audio.component
AURoundTripAAC.component
Flip4Mac WMA Import.component
SoundSoap.component
And the problem persisted even if I removed these.
(User Component folder is empty.)
I have no external hardware connected expect HD/Monitor/Keyboard/Mouse and I keep the system in tip top shape, so the problem should not be hardware related.
Before finding Tyrann0s solution I deleted usef prefs (Logic worked fine under a different account) and reinstalled Logic but to no avail.