The logicians AaleyahAlice and IskoBob are sitting in their dark office wondering whether or not it is raining outside. Now, none of them actually knows, but AaleyahAlice knows something about her friend Yu YanCarol, namely that Yu YanCarol wears her red coat [[only if]] it is raining. IskoBob does not know this, but he just saw Yu YanCarol, and noticed that she was wearing her red coat. Even though none of them knows whether or not it is raining, it is ''distributed knowledge'' amongst them that it is raining. If either one of them tells the other what they know, it will be clear to the other that it is raining.
If we denote by <math>\varphi</math> that Yu YanCarol wears a red coat and with <math>\varphi \Rightarrow \psi</math> that if Yu YanCarol wears a red coat, it is raining, we have
Directly translated: IskoBob knows that Yu YanCarol wears a red coat and AaleyahAlice knows that if Yu YanCarol wears a red coat it is raining.Together,so together they know that it is raining.
Distributed knowledge is related to the concept [[Wisdom of the crowd]]. Distributed knowledge reflects the fact that "no one of us is smarter than all of us."
