Multi-Valued Logic in Three-Valued Systems

Explore the intricacies of multi-valued logic in three-valued systems, including Liberal and Draconian protocols. Learn how logical assertions and byte generation are influenced by the values of variables like a, b, u, and v.

• Multi-Valued Logic
• Three-Valued Systems
• Logical Protocols
• Variable Values

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Uploaded on Oct 09, 2024 | 0 Views

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1. MULTI-VALUED LOGIC

2. a | b a & b

3. a | b - true if a or b true or missing a & b true if a and b true or missing

4. assert ~mi(a) assert ~mi(b) gen byte c = a | b

5. gen byte c = a | b if ~mi(a) & ~mi(b)

6. a|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

7. Three-valued logic or 0 1 . 0 0 1 . 1 1 1 1 . . 1 . and 0 0 1 . 1 0 1 . . 0 . . a 0 1 . not a 1 0 . 0 0 0

8. Three-valued logic, Liberal protocol or 0 1 . 0 0 1 0 1 1 1 1 . 0 1 . and 0 0 1 . 1 0 1 1 . 0 1 . a 0 1 . not a 1 0 . 0 0 0

9. Three-valued logic, Draconian protocol or 0 1 . 0 0 1 . 1 1 1 . . . . . and 0 0 1 . 1 0 1 . . . . . a 0 1 . not a 1 0 . 0 0 .

10. 1 | . 0 | . 1 & . 0 & .

11. a|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

12. 1 | . 0 | . 1 & . 0 & .

13. Draconian: .b Unknown: .u Liberal: .v

14. (1 | .u) & .v = 1 (1 | .u) & .u = .u (1 | .b) & .U = .b

15. And Or Not | 0 0 1 .u .u 1 .u .u .b .v 0 1 .u .v .b .b .b .b .b .b .b 1 .u .v .b 1 .u 0 1 1 & 0 1 .u .v .b a ~a 0 1 .u .u .v .v .b .b 1 0 0 1 .b .b 0 1 .u 0 .v 0 .b .b .b .b .b .b 0 0 0 0 1 .u 1 .u .u .u .b 1 .u .v .b 0 .b .b 1

16. At 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

17. 3 + . 7 + . 0 * . 12 / . sum(4, 17, 30, 12, .) mean(4, 17, 30, 12, .)

18. 3 + .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

19. 0 * .u = 0 12 / .u = .b

20. (12 + 3 + .v) * 2 = 30 (12 + 3 + .v) * .u = .u ((7 + .v) * 2 14) * .u = 0

21. .b .u Normal values .v

22. Multiplication Or And .b 0 .u All other numbers .v .b 1 .u 0 .v .b 0 .u 1 .v

23. Sup n Sup n-1 Sup 2 Sup 1 Normal values Inf 1 Inf 2 Inf k