/prog/ - LOGIC — World4ch

Name: Anonymous 2011-01-17 16:58

Are there tautologies in ternary logic?

We all know about tertium non datur in boolean logic and other tautologies, but if we have a third value in ternary logic (e.g. "indeterminate") do these tautologies still exist?

Name: Anonymous 2011-01-17 17:05

you fail it

Name: OP 2011-01-17 17:19

(phi or not phi) can evaluate to indeterminate and true
(phi and not phi) can evaluate to indeterminate and false

so I guess all boolean tautologies don't apply to ternary logic.

Name: Anonymous 2011-01-17 20:04

>>3
“and” and “or” still only apply to “true” and “false” values. You'd need extra connectives to work with “true” and “indeterminate” together, the same for “indeterminate” and “false”.

Name: Anonymous 2011-01-18 1:23

Utrecht, gb2/bed.

Name: Anonymous 2011-01-18 2:43

Here's one:



return(x == true || x == halftrue || x == false);

Name: Anonymous 2011-01-18 3:04

>>6
In javascript:
return (x == true || x == undefined || x == false);

Name: Anonymous 2011-01-18 3:14

>>7
In perl:
$x || !defined $x || defined $x && !$x

Name: Anonymous 2011-01-18 4:31

In Haskell:
const True
Though it's not a proper tautology from the FOL/topological point of view.

Name: Anonymous 2011-01-18 4:39

(let* ((x (expt 65535 65535))

       (x (expt x x))

       (x (expt x x)))

  (ormap values (make-list (expt x x) #t)))

Name: Anonymous 2011-01-18 10:56

>>5
``homoseksueel"

Name: Anonymous 2011-01-18 12:27

>>11
no u

Name: Anonymous 2011-01-18 12:48

Boolean logic:
- ⊤ is a tautology.
- ⊥ is a contradiction.

Ternary logic:
- suggest perhaps ⊡ to be indeterminable.

Name: Anonymous 2011-01-18 13:47

⊥ gave me an erection.

Name: Anonymous 2011-01-18 14:12

_|_

LOGIC

1 Name: Anonymous 2011-01-17 16:58

2 Name: Anonymous 2011-01-17 17:05

3 Name: OP 2011-01-17 17:19

4 Name: Anonymous 2011-01-17 20:04

5 Name: Anonymous 2011-01-18 1:23

6 Name: Anonymous 2011-01-18 2:43

7 Name: Anonymous 2011-01-18 3:04

8 Name: Anonymous 2011-01-18 3:14

9 Name: Anonymous 2011-01-18 4:31

10 Name: Anonymous 2011-01-18 4:39

11 Name: Anonymous 2011-01-18 10:56

12 Name: Anonymous 2011-01-18 12:27

13 Name: Anonymous 2011-01-18 12:48

14 Name: Anonymous 2011-01-18 13:47

15 Name: Anonymous 2011-01-18 14:12