We've discovered a bug in the startup of the app that may prevent you from getting past the Logging In.. stage on Alpha 2.
We've got a fix for the next Alpha, but in the mean time, this should get you going.
Try this work around and let us know if it helps.
Open "Terminal" from Applications > Utilities
Type the following two commands:
rm ~/Library/com.logos.LogosIndexer.plist
launchctl remove com.logos.LogosIndexer
Now, restart Logos 4.