It's been a while since I've used my iMac. But I updated it to 10.9 to test before upgrading my main machines.
Anyway I tried to launch Logos today and it is crashing immediately. Sometimes I see the signing in screen, other times I don't. If I disable my wifi and get the log in screen, if I choose to work off line Logos crashes immediately after the screen.
Here are the logs I believe.
7317.LogosLogs.DaveSmith.20131104-192957.zip