## Long descriptions for some figures in Deontic Logic

### 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],

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 $$\PE p$$ (corner 5)
• $$\IM p$$ (corner 2) to $$\OM p$$ (corner 4)
• $$\NO p$$ (corner 3) to $$\OM p$$ (corner 4)
• $$\NO p$$ (corner 3) to $$\PE p$$ (corner 5)
• $$\OP p$$ (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 $$\NO p$$ (corners 1 and 3)
• $$\OB p$$ and $$\OP p$$ (corners 1 and 6)
• $$\IM p$$ and $$\OP p$$ (corners 2 and 6)
• Subcontraries [green line],
• $$\PE p$$ and $$\OM p$$ (corners 4 and 5)
• $$\OB p$$ 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 $$p$$”.

## Long descriptions for some figures in the supplement to Deontic Logic

### 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 $$j$$.