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In-Depth Information
Table 2.1 The currently existing 45 negations
¬
x
,
b
,
a
1
¬
x
,
sg
(
a
),
sg
(
a
)
2
x , b , a . b + a 2
¬ 3
¬
x
,
b
,
1
b
4
¬
x
,
sg
(
1
b
),
sg
(
1
b
)
5
¬ 6
x ,
(
b ),
( a )
sg
1
sg
¬
x
,
sg
(
1
b
),
a
7
¬
x
,
1
a
,
a
8
¬ 9
x ,
sg
( a ), a
¬
x
,
sg
(
1
b
),
1
b
10
¬ 11
x , sg ( b ), sg ( b )
b 2
¬ 12
x
,
b
.(
b
+
a
),
min
(
1
,
a
.(
+
a
+
b
.
a
))
¬
x
,
sg
(
1
a
),
sg
(
1
a
)
13
¬ 14
x , sg ( b ), sg ( 1 a )
¬
x
,
sg
(
1
b
),
sg
(
1
a
)
15
¬
x
,
sg
(
a
),
sg
(
1
a
)
16
¬ 17
x , sg ( 1 b ), sg ( b )
¬
x
,
b
.
sg
(
a
),
a
.
sg
(
b
)
18
¬
x
,
b
.
sg
(
a
),
0
19
¬ 20
x , b , 0
¬
x
,
min
(
1
a
,
sg
(
a
)),
min
(
a
,
sg
(
1
a
))
21
¬
x
,
min
(
1
a
,
sg
(
a
)),
0
22
¬ 23
x , 1 a , 0
¬
x
,
min
(
b
,
sg
(
1
b
)),
min
(
1
b
,
sg
(
b
))
24
¬
x
,
min
(
b
,
sg
(
1
b
)),
0
25
¬ 26
x , b , a . b + sg ( 1 a )
¬
x
,
1
a
,
a
.(
1
a
) +
sg
(
1
a
)
27
¬
x
,
b
,(
1
b
).
b
+
sg
(
b
)
28
¬ 29
x ,
(
, b . a +
(
b )),
(
, a .( b . a +
(
b )) +
(
a ))
max
0
sg
1
m in
1
sg
1
sg
1
¬
x
,
a
.
b
,
a
.(
a
.
b
+
sg
(
1
b
)) +
sg
(
1
a
)
30
¬
x
,
max
(
0
,(
1
a
).
a
+
sg
(
a
)),
min
(
1
,
a
.((
1
a
).
a
+
sg
(
a
)) +
sg
(
1
a
))
31
¬ 32
x ,(
1
a ). a , a .((
1
a ). a +
sg
( a )) +
sg
(
1
a )
¬
x
,
b
.(
1
b
) +
sg
(
1
b
), (
1
b
).(
b
.(
1
b
) +
sg
(
1
b
)) +
sg
(
b
))
33
¬ 34
x , b .( 1 b ), ( 1 b ).( b .( 1 b ) + sg ( 1 b )) + sg ( b )
b
2
1
+
a
¬
,
35
2
b
3
2
+
a
¬ 36
,
3
2 b
3
2 a
+
1
¬
,
37
3
1
a
2
+
a
¬
,
38
3
3
b
3
3
b
¬ 39
,
3
2 2 a
3
1 + 2 a
3
¬
,
40
(continued)
 
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