Figure 1 description

The diagram consists of three horizontal points labeled (left to right) as \(w\), \(v\), and \(u\). A red rectangle labeled \(A\) encloses \(u\). A green rectangle labeled \(C\) encloses \(v\). A blue rectangle labeled \(B\) encloses the red and the green rectangles. Point \(w\) is outside all these rectangles. An arrow points from \(u\) to \(v\) and another from \(v\) to \(w\).

Figure 2 description

The diagram consists of two equations with rectangles around them with an arrow pointing to a comment for each. The red rectangle encloses \(\Gamma(w)\bot A = \{\{A\supset B,\, A\supset \neg C\}\}\) with the comment “For the single \(X\) in \(\Gamma(w)\bot A\), \(X \cup \{A\}\) implies \(B\wedge \neg C\)”. The blue rectangle encloses \(\Gamma(w)\bot B = \{\Gamma(w)\}\) with the comment “For the single \(Y\) in \(\Gamma(w)\bot B\), \(Y \cup \{B\}\) implies \(\neg A\wedge C\)”.

Figure 3 description

The diagram consists of a blue rectangle labeled \(B\) with a small circle labeled \(A\) inside the rectangle at the left edge. The rectangle is divided into two pieces: the left portion has area \(\delta\) and contains the circle; the right portion has area \(1 - \delta\) and is, itself contained in a larger green rectangle labeled \(C\).

Figure 4 description

Two separate but similar diagrams. Both consist of two blue rectangles, one above the other. The upper rectangle is divided down the middle with a dashed line. The left half of this rectangle is labeled \(A\) and has two vertical dots. The right half is labeled \(\neg A\) and has one dot. The lower rectangle is similar to the left side of the upper rectangle in being labeled \(A\) and having two vertical dots. An arrow points from the upper rectangle to the lower.

In addition diagram 4a has in the upper rectangle in the left half the upper dot labeled with a \(p\) and a \(u\) and the lower dot with a \(q\) and a \(v\). The right half has the dot labeled \(r\) and \(w\) with the dot and labels crossed out. In the lower rectangle, the upper dot is labeled \(\frac{p}{p+q}\) and \(u\) and the lower dot labeled \(\frac{q}{p+q}\) and \(v\).

Diagram 4b has in the upper rectangle in the left half the upper dot labeled with a \(p\) and a \(u\) and the lower dot with a \(q\) and a \(v\); a red dashed arrow goes loops from each dot back to itself. The right half has the dot labeled \(r\) and \(w\) with with a red dashed arrow going from it to the upper dot on the left half. In the lower rectangle, the upper dot is labeled \(p+r\) and \(u\) and the lower dot labeled \(q\) and \(v\).