Table 1 The sixteen truth value sets and their attributes

∅

0

0

0

13

None

None

{{∅}}

0

0

1

14

None

None

{{f}}

0

\(\frac {1}{1}\)

1

16

False

False

{{t}}

\(\frac {1}{1}\)

0

1

1

True

True

{{t,f}}

\( \frac {\frac {1}{2}}{1}\)

\(\frac {\frac {1}{2}}{1}\)

1

5

Both

Both

{{∅},{f}}

0

\(\frac {1}{2}\)

2

15

None

False

{{∅},{t}}

\(\frac {1}{2}\)

0

2

3

None

True

{{∅},{t,f}}

\( \frac {\frac {1}{2}}{2} \)

\( \frac { \frac {1}{2}}{2} \)

2

10

Both

Both

{{f},{t}}

\( \frac {1}{2} \)

\( \frac {1}{2} \)

2

6

Both

Both

{{f},{t,f}}

\( \frac { \frac {1}{2}}{2} \)

\( \frac { 1 + \frac {1}{2}}{2}\)

2

11

Both

Both

{{t},{t,f}}

\( \frac { 1 + \frac {1}{2}}{2}\)

\( \frac { \frac {1}{2}}{2} \)

2

2

Both

Both

{{f},{t},{t,f}}

\( \frac { 1 + \frac {1}{2}}{3}\)

\( \frac { 1 + \frac {1}{2}}{3}\)

3

7

Both

Both

{{∅},{f},{t}}

\( \frac {1}{3} \)

\( \frac {1}{3} \)

3

9

Both

Both

{{∅},{f},{t,f}}

\( \frac { \frac {1}{2}}{3} \)

\( \frac { 1 + \frac {1}{2}}{3}\)

3

12

Both

Both

{{∅},{t},{t,f}}

\( \frac { 1 + \frac {1}{2}}{3}\)

\( \frac { \frac {1}{2}}{3} \)

3

4

Both

Both

{{∅},{t},{f},{t,f}}

\( \frac { 1 + \frac {1}{2}}{4}\)

\(\frac { 1 + \frac {1}{2}}{4}\)

4

8

Both

Both