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