I've been reading this paper on probabilistic logic: http://ai.stanford.edu/~nilsson/OnlinePubs-Nils/PublishedPapers/problogic.pdf
On page 76 theres a 3d diagram and Nilsson mentions the bounds on P(Q) and says that P(Q) is bound by two planes.
My question: There appear to be 4 planes in the diagram? I don't exactly follow how he derived the bounds.
The vertical axis $\pi_3=p(Q)$ is being bounded. Two of the four planes are vertical and thus don't yield a bound on $\pi_3$. In any case the two vertical planes correspond to the trivial constraints $\pi_1\ge0$ and $\pi_2\le1$, and the other two are the interesting ones.