Monday, June 17, 2013

A Tern for the Worse

Fails 3-5 / Skju

Adminned at 19 Jun 2013 17:42:58 UTC

Add the following to the list of axioms

[>>a] = b
[>>b] = c
[>>c] = a
FAX[[[[~[X = a]] && [~[X = b]]] && [~[X = c]]] -> [[>>X] = φ]]
FAX[[<<X] = [[>>[>>X]]]]

Adding the option to use ternary logic (with a, b and c) and φ as the general “error” result.

Could also maybe force everything to be a, b, or c but then we run into issues where = would no longer commute (unless a = b = c).

Comments

Tavros:

06-18-2013 00:39:52 UTC

No vote, at the moment. I’d like to get some idea of where this dynasty is headed,

kikar:

06-18-2013 00:42:31 UTC

imperial As a, b, and, c are already defined as variables, I’m not sure that this works completely. For clarity, maybe you should define a,b, and c in a dynastic rule?

Tavros:

06-18-2013 01:51:03 UTC

It’s currently unclear whether free Variables in Formulae refer to constants (“global variables”), or to Variables implicitly universally quantified over (“local variables”),

By the way, since a, b, and c are Variables, and Variables are considered equal whenever they have the same truth value, it can be shown that a, b, and c must all have the same truth value and therefore be equal; otherwise, one of the first three axioms would be violated. Maybe they should be Identifiers instead,

Ienpw III:

06-18-2013 02:10:17 UTC

imperial

RaichuKFM:

06-18-2013 02:40:48 UTC

against

Skju:

06-18-2013 03:13:19 UTC

Ummm. against Since you frame it as an “option”, I elect to not take it, especially because of the variable confusion and messiness. Shouldn’t we be heading towards first-order logic already?

Larrytheturtle:

06-18-2013 04:03:30 UTC

against

Clucky:

06-18-2013 05:35:45 UTC

@skju - first order logic is already well researched. Dynasty will be super boring if we don’t add other stuff to our logics.

@Travos I mean, I guess that assumes that if a is true and b is true then a = b? Do we actually know that? But yeah, the fact that ‘a’ itself is a formula and so has to have a truth value kinda breaks this… I missed that. not really sure what variables can actually be used for then.

Ienpw III:

06-18-2013 14:57:15 UTC

cov for

quirck:

06-18-2013 15:11:49 UTC

imperial arrow

quirck:

06-18-2013 15:12:26 UTC

Oh, it’s a proof, have to be explicit against

Murphy:

06-19-2013 19:26:11 UTC

for