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5 Dec 2000

Ignore truth tables for finitely valued logics 2 reduced

 

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

at

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