Figure 2 description

A square with the four corners labeled in clockwise order as Necessary, Impossible, Non-Necessary, and Possible. The legend describes four types of lines:

• Implication [arrowed line],
• Contraries [dotted blue line],
• Subcontraries [green line],
• Contradictories [dashed purple lines].

Implication lines connect Necessary to Possible and Impossible to Non-Necessary. A Contraries line connects Necessary and Impossible. A Subcontraries line connects Possible and Non-Necessary. Contradictories lines connect Necessary and Non-Necessary and also Impossible and Possible.

Figure 4 description

A square with the four corners labeled in clockwise order as Obligatory, Impermissible, Omissible, and Permissible. Assuming the legend from figure 2 Implication lines connect Obligatory to Permissible and Impermissible to Omissible. A Contraries line connects Obligatory and Impermissible. A Subcontraries line connects Permissible and Omissible. Contradictories lines connect Obligatory and Omissible and also Impermissible and Permissible.

Figure 5 description

A hexagon with the corners labeled clockwise as

1. $\OB p$
2. $\IM p$
3. $\NO p$
4. $\OM p$
5. $\PE p$
6. $\OP p$

Using the same legend as figure 2, the following lines connect each corner to all the others

• Implication [arrowed line],
  • $\OB p$ (corner 1) to $\NO p$ (corner 3)
  • $\OB p$ (corner 1) to $\PE p$ (corner 5)
  • $\IM p$ (corner 2) to $\NO p$ (corner 3)
  • $\IM p$ (corner 2) to $\OM p$ (corner 4)
  • $\OP p$ (corner 6) to $\OM p$ (corner 4)
  • $\OP p$ (corner 6) to $\PE p$ (corner 5)
• Contraries [dotted blue line],
  • $\OB p$ and $\IM p$ (corners 1 and 2)
  • $\OB p$ and $\OP p$ (corners 1 and 6)
  • $\IM p$ and $\OP p$ (corners 2 and 6)
• Subcontraries [green line],
  • $\NO p$ and $\OM p$ (corners 3 and 4)
  • $\NO p$ and $\PE p$ (corners 3 and 5)
  • $\PE p$ and $\OM p$ (corners 4 and 5)
• Contradictories [dashed purple lines].
  • $\OB p$ and $\OM p$ (corners 1 and 4)
  • $\IM p$ and $\PE p$ (corners 2 and 5)
  • $\NO p$ and $\OP p$ (corners 3 and 6)

Figure 6 description

A square with the four corners labeled in clockwise order as

1. All $x:p$
2. No $x:p$
3. Some $x:p$
4. Some $x: \neg p$

Assuming the legend from figure 2 Implication lines connect corner 1 to corner 4 and corner 2 to corner 3. A Contraries line connects corners 1 and 2. A Subcontraries line connects corners 3 and 4. Contradictories lines connect corners 1 and 3 and also corners 2 and 4.

Figure 7 description

Three boxes containg respectively the phrases:

1. All $x:p$
2. Some $x: p$ & Some $x: \neg p$
3. No $x: p$

The first and second are braced as “Some $x: p$”. The second and third are braced as “Some $x: \neg p$”.

Figure 8 description

A diagram of six boxes in a row. All boxes have a blue dot at the bottom and $A^i$ below.

1. first box is labeled “$\OB p$:” and contains “All $p$”
2. second box is labeled “$\PE p$:” and contains “Some $p$”
3. third box is labeled “$\IM p$:” and contains “No $p$”
4. fourth box is labeled “$\OM p$:” and contains “Some $\neg p$”
5. fifth box is labeled “$\OP p$:” and contains “Some $p$ and Some $\neg p$”
6. sixth box is labeled “$\NO p$:” and contains “All $p$ or No $p$”

Figure 10 description

A vertical bar with three vertical dots below it. The top of the bar is labelled $\OB p:$ and an arrow pointing to the top of the bar is labelled “all $p$-worlds here”. A brace encloses both the bar and the dots and is labelled “the $i$-ranked worlds (the higher the level, the better the worlds within it, relative to $i$)”.

Figure 11 description

A diagram of two boxes in a row. All boxes have $R^i$ below.

1. The first box has “NEC$p$;” above and “All $p$” inside.
2. The second box has “POS$p$;” above and “Some $p$” inside.

Figure 12 description

A diagram of one box which has “$d$: DEM” above and a blue dot labelled $j$ inside.

Figure 13 description

Two overlapping blue boxes. In the intersection of the two boxes is a blue dot. Above both is “POS$d$: DEM”; below both is “$R^i$”.

Figure 14 description

Six pairs of two overlapping blue boxes. Below each pair is “$R^i$”. Each pair also has a blue dot in the intersection of the two boxes.

1. first pair is labelled “$\OB p:$ DEM” and has the blue dot labelled “All $p$”.
2. second pair is labelled “$\PE p:$ DEM” and has the blue dot labelled “Some $p$”.
3. third pair is labelled “$\IM p:$ DEM” and has the blue dot labelled “No $p$”.
4. fourth pair is labelled “$\OM p:$ DEM” and has the blue dot labelled “Some $\neg p$”.
5. fifth pair is labelled “$\OP p:$ DEM” and has the blue dot labelled “Some $p$ and Some $\neg p$”.
6. sixth pair is labelled “$\NO p:$ DEM” and has the blue dot labelled “All $p$ or No $p$”.

Figure D.1 description

A graph of three dots: $i, j, k$.

1. first dot is labelled $i$. There is the comment “So $\neg\OB(\OB p \rightarrow p)$”.
2. second dot is labelled $j$ and has $\neg p$ above it. There is the comment “So $\OB p$ and $\neg(\OB p \rightarrow p)$”.
3. third dot is labelled $k$ and has $p$ above it. There is no comment.

An arrow points from dot $i$ to dot $j$ and another from dot $j$ to dot $k$. An arrow also points from dot $k$ back to itself.

Figure D.2 description

A graph of four dots: $i, j, k, l$. Similar to figure D.1.

1. first dot is labelled $i$. There is the comment “So $\OB \OB p \rightarrow \OB p$ and $\neg\OB(\OB p \rightarrow p)$”.
2. second dot is labelled $j$ and has $\neg p$ above it. There is the comment “So $\neg(\OB p \rightarrow p)$”.
3. third dot is labelled $k$ and has $p$ above it. There is no comment.
4. fourth dot is labelled $l$.

An arrow points from dot $i$ to dot $j$ and another from dot $j$ to dot $k$. An arrow also points from dot $k$ back to itself. In addition an arrow points from dot $i$ to dot $l$ and another from dot $l$ to dot $j$.