Logic analyzer: multiple circuits, one ground
You should not attempt to measure signals with different ground references on the same logic analayzer. It might look like it's working and it might actually be working but you can never be certain that it is. Possibly, somewhere down the line there is a common ground, or maybe there are faults in your house wiring and that's not effectively the case. At some point, something weird will happen and you'll curse at your setup until you determine that the issue was the lack of common grounds. 

Save yourself that trouble now - don't rely on a flawed test equipment configuration. There must be one ground common to all of the signals you are trying to measure on the same logic analyzer.