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x
| A | B | A | ∧ | ¬ | A | ⊨ | B |
| 1 | 1 | 1 | 0 | 0 | 1 | N | 1 |
| 1 | 0 | 1 | 0 | 0 | 1 | N | 0 |
| 0 | 1 | 0 | 0 | 1 | 0 | N | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 | N | 0 |
x
x
| A | B | A | ∧ | ¬ | A | ⊨ | B |
| 1 | 1 | 1 | 0 | 0 | 1 | N | 1 |
| 1 | 0 | 1 | 0 | 0 | 1 | N | 0 |
| 0 | 1 | 0 | 0 | 1 | 0 | N | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 | N | 0 |
x
x
| A | B | A | ∧ | ¬ | A | ⊨ | B |
| 1 | 1 | 1 | 0 | 0 | 1 | N | 1 |
| 1 | 0 | 1 | 0 | 0 | 1 | N | 0 |
| 0 | 1 | 0 | 0 | 1 | 0 | N | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 | N | 0 |
x
x
| A | B | A | ∧ | ¬ | A | ⊨ | B |
| 1 | 1 | 1 | 0 | 0 | 1 | N | 1 |
| 1 | 0 | 1 | 0 | 0 | 1 | N | 0 |
| 0 | 1 | 0 | 0 | 1 | 0 | N | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 | N | 0 |
x
CLASSICAL LOGIC
| ¬ | |
| 1 | 0 |
| 0 | 1 |
| ∧ | 1 | 0 |
| 1 | 1 | 0 |
| 0 | 0 | 0 |
| ∨ | 1 | 0 |
| 1 | 1 | 1 |
| 0 | 1 | 0 |
| ⊃ | 1 | 0 |
| 1 | 1 | 0 |
| 0 | 1 | 1 |
xxx
Neither valued
| ¬ | |
| 1 | 0 |
| n | n |
| 0 | 1 |
| ∧ | 1 | n | 0 |
| 1 | 1 | n | 0 |
| n | n | n | 0 |
| 0 | 0 | 0 | 0 |
| ∨ | 1 | n | 0 |
| 1 | 1 | 1 | 1 |
| n | 1 | n | n |
| 0 | 1 | n | 0 |
| ⊃ | 1 | n | 0 |
| 1 | 1 | n | 0 |
| n | 1 | 1 | n |
| 0 | 1 | 1 | 1 |
xxx
LP Priest Both value
| ¬ | |
| 1 | 0 |
| b | b |
| 0 | 1 |
| ∧ | 1 | b | 0 |
| 1 | 1 | b | 0 |
| b | b | b | 0 |
| 0 | 0 | 0 | 0 |
| ∨ | 1 | b | 0 |
| 1 | 1 | 1 | 1 |
| b | 1 | b | b |
| 0 | 1 | b | 0 |
| ⊃ | 1 | b | 0 |
| 1 | 1 | b | 0 |
| b | 1 | b | b |
| 0 | 1 | 1 | 1 |
| ⊃ | 1 | b | 0 |
| 1 | 1 | 0 | 0 |
| b | 1 | b | o |
| 0 | 1 | 1 | 1 |
xxx
four valued FDE
¬ 1 0 b b n n o 1
∧ 1 b n o 1 1 b n 0 b b b 0 0 n n 0 n 0 o 0 0 0 0 x
∨ 1 b n o 1 1 1 1 1 b 1 b 1 b n 1 1 n n o 1 b n 0
x
⊃ 1 b n o 1 1 0 n 0 b 1 b n 0 n 1 n 1 n o 1 1 1 1
xxx
fuzzy tables
x
x
¬ 1 0 0.75 0.25 0.5 0.5 0.25 0.75 o 1 x
x
| ∧ | 1 | 0.75 | 0.5 | 0.25 | o |
| 1 | 1 | 0.75 | 0.5 | 0.25 | 0 |
| 0.75 | 0.75 | 0.75 | 0.5 | 0.25 | 0 |
| 0.5 | 0.5 | 0.5 | 0.5 | 0.25 | 0 |
| 0.25 | 0.25 | 0.25 | 0.25 | 0.25 | 0 |
| o | 0 | 0 | 0 | 0 | 0 |
x
x
| ∨ | 1 | 0.75 | 0.5 | 0.25 | o |
| 1 | 1 | 1 | 1 | 1 | 1 |
| 0.75 | 1 | 0.75 | 0.75 | 0.75 | 0.75 |
| 0.5 | 1 | 0.75 | 0.5 | 0.5 | 0.5 |
| 0.25 | 1 | 0.75 | 0.5 | 0.25 | 0.25 |
| o | 1 | 0.75 | 0.5 | 0.25 | 0 |
x
x
| ⊃ | 1 | 0.75 | 0.5 | 0.25 | o |
| 1 | 1 | 0.75 | 0.5 | 0.25 | 0 |
| 0.75 | 1 | 1 | 0.75 | 0.5 | 0.25 |
| 0.5 | 1 | 1 | 1 | 0.75 | 0.5 |
| 0.25 | 1 | 1 | 1 | 1 | 0.75 |
| o | 1 | 1 | 1 | 1 | 1 |
x
x
| ∧ | 1 | 0.75 | 0.5 | 0.25 | o |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0.75 | 0 | 0 | 0 | 0 | 0 |
| 0.5 | 0 | 0 | 0 | 0 | 0 |
| 0.25 | 0 | 0 | 0 | 0 | 0 |
| o | 0 | 0 | 0 | 0 | 0 |
x
INTUITIONISM
x
| ¬ | in w1 |
| 1 in w1 1 in w2 | 0 |
| 1 in w1 0 in w2 | [Cannot Be] |
| 0 in w1 1 in w2 | 0 |
| 0 in w1 0 in w2 | 1 |
x
∧ 1 0 1 1 0 0 0 0
∨ 1 0 1 1 1 0 1 0
⊃ 1 0 1 1 0 0 1 1
xxxx
x
| ⊃ | 1 in w1 1 in w2 | 1 in w1 0 in w2 | 0.5 | 0.25 | o |
| 1 in w1 1 in w2 | 0 | 0 | 0 | 0 | 0 |
| 0 in w1 1 in w2 | 0 | 0 | 0 | 0 | 0 |
| 0 in w1 0 in w2 | 0 | 0 | 0 | 0 | 0 |
| 0 in w1 0 in w2 | 0 | 0 | 0 | 0 | 0 |
x
zzzzz
| A ⊃ B | B=1, w1 B=1, w2 | B=0, w1 B=1, w2 | B=0, w1 B=0, w2 |
| A=1, w1 A=1, w2 | 1, w1 | 1, w1 | 0, w1 |
| A=0, w1 A=1, w2 | 1, w1 | 1, w1 | 1, w1 |
| A=0, w1 A=0, w2 | 1, w1 | 1, w1 | 1, w1 |
x
x
| ¬ | in w1 |
| 1 in w1 1 in w2 | 0 |
| 0 in w1 1 in w2 | 0 |
| 0 in w1 0 in w2 | 1 |
x
