Table 3.

The agents’ observations and conclusions

Agent	Assumed observation	Statement inferred via (Q)	Further implied statement	Statement inferred via (C)
$\overline{\mathrm{F}}$	$r=\mathrm{tails}\mathrm{at}\mathrm{time}n:01$	$Statement{\overline{\mathrm{F}}}^{n:02}:$ “I am certain that W will observe w = fail at time n:31.”
F	$z=+\frac{1}{2}$ at time n:11.	$Statement{\mathrm{F}}^{n:12}:$ “I am certain that $\overline{\mathrm{F}}$ knows that r = tails at time n:01.”	$Statement{\mathrm{F}}^{n:13}:$ “I am certain that $\overline{\mathrm{F}}$ is certain that W will observe w = fail at time n:31.”	$Statement{\mathrm{F}}^{n:14}:$ “I am certain that W will observe w = fail at time n:31.”
$\overline{\mathrm{W}}$	$\overline{w}=\overline{\mathrm{ok}}$ at time n:21	$Statement{\overline{\mathrm{W}}}^{n:22}:$ “I am certain that F knows that $z=+\frac{1}{2}$ at time n:11.”	$Statement{\overline{\mathrm{W}}}^{n:23}:$ “I am certain that F is certain that W will observe w = fail at time n:31.”	$Statement{\overline{\mathrm{W}}}^{n:24}:$ “I am certain that W will observe w = fail at time n:31.”
W	announcement by agent $\overline{\mathrm{W}}$ that $\overline{w}=\overline{\mathrm{ok}}$ at time n:21	$Statement{\mathrm{W}}^{n:26}:$ “I am certain that $\overline{\mathrm{W}}$ knows that $\overline{w}=\overline{\mathrm{ok}}$ at time n:21”	$Statement{\mathrm{W}}^{n:27}:$ “I am certain that $\overline{\mathrm{W}}$ is certain that I will observe w = fail at time n:31.”	$Statement{\mathrm{W}}^{n:28}:$ “I am certain that I will observe w = fail at time n:31.”

The statements that the individual agents can derive from quantum theory depend on the information accessible to them (cf. Fig. 2). Agent $\overline{\mathrm{F}}$, for instance, if she observes r = tails, can use this information to infer w, which will later be observed and announced by W