a amp b a b true if a or b true or missing a amp b true if a and b true or missing assert mia assert mib gen byte c a b gen byte c a b if mia amp mib ab true if either a or b is true regardless of what the other is ID: 783990
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Slide1
MULTI-valued logic
Slide2a | b
a & b
Slide3a | b -– true if a or b true or missing
a & b – true if a and b true or missing
Slide4assert ~mi(a)
assert ~mi(b)
gen byte c = a | b
Slide5gen byte c = a | b if ~mi(a) & ~mi(b)
Slide6a|b
-- true if either a or b is true, regardless of what the other is
a&b
-- false if either a or b is false, regardless of what the other is
Slide7Three-valued logic
or
0
1
.
0
0
1
.
1111..1.
and01.0000101..0..
a
not a
0
1
1
0
.
.
Slide8Three-valued logic, Liberal protocol
or
0
1
.
0
0
1
0
1111.01.
and01.00001011.01.
a
not a
0
1
1
0
.
.
Slide9or
0
1
.
0
0
1
.
1
11.....
and01.000.101.....
a
not a
0
1
1
0
.
.
Three-valued logic, Draconian protocol
Slide101 | .
0 | .
1 & .
0 & .
Slide11a|b
-- true if either a or b is true, regardless of what the other is
a&b
-- false if either a or b is false, regardless of what the other is
Slide121 | .
0 | .
1 & .
0 & .
Slide13Draconian: .b
Unknown: .u
Liberal: .v
Slide14(1 | .u) & .v = 1
(1 | .u) & .u = .u
(1 | .b) & .U = .b
Slide15|
0
1
.u
.v
.b
0
0
1
.u0.b11111.b.u
.u1.u.u.b.v01.u.v.b.b.b.b.b.b.b
&
0
1
.u
.v
.b
0
0000.b1
0
1
.u
1
.b
.u
0
.u
.u.u.b.v01.u.v.b.b.b.b.b.b.b
Or
And
a~a0110.u.u.v.v.b.b
Not
Slide16At least one child is female:
f1 | f2 | f3 | f4 | f5 | f6 | f7 | f8
Every child is female:
f1 & f2 & f3 & f4 & f5 & f6 & f7 & f8
At least one child is male:
~f1 | ~f2 | ~f3 | ~f4 | ~f5 | ~f6 | ~f7 | ~f8
Every child is male:
~f1 & ~f2 & ~f3 & ~f4 & ~f5 & ~f6 & ~f7 & ~f8
Slide173 + .
7 + .
0 * .
12 / .
sum(4, 17, 30, 12, .)
mean(4, 17, 30, 12, .)
Slide183 + .v = 3
3 + .b = .b
Mean((4, 17, 30, 12, .u) = .u
Mean((4, 17, 30, 12, .v) = 15.75
Mean((4, 17, 30, 12, .b) = .b
Slide190 * .u = 0
12 / .u = .b
Slide20(12 + 3 + .v) * 2 = 30
(12 + 3 + .v) * .u = .u
((7 + .v) * 2 – 14) * .u = 0
Slide21.b
.u
Normal values
.v
Slide22.b
0
.u
All other numbers
.v
.b
1
.u
0
.v
.b0.u1.vOrAnd
Multiplication
Slide23Sup n
Sup n-1
…
Sup 2
Sup 1
Normal values
Inf
1
Inf
2…Inf k