Common ground in IRC

Monk talked in his paper[1] about common ground and defined it as:

"a proposition p is only common ground if all the people conversing know p and they all knowthat they all know p."

How could this be applied to IRC conversations?

I and most of my friend run our IRC-clients in a screen, so much of the conversation takes place when we're not actually there following it. So let's say someone talks about thing A and I'm not there at the time to read it. When I later come back online, is thing A common ground to me? Of course, with screen, I could read all the backlog, and know about thing A, but having almost twenty different channels open all the time, I rarely read all the backlog. On the other hand, my friends probably know that I don't necessarily read everything discussed while I was away, but how can you know when something is common ground and when it isn't? Usually you don't even know who is really there, who isn't and who's just following conversation quietly. Interesting things to ponder.

References:
[1]Monk, A. (2009) Common ground in electronically mediated conversation. Synthesis Lectures on Human-Centered Informatics #1. Morgan & Claypool publishers.