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).
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?
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,
Ummm. 
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?
@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.
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Tavros:
No vote, at the moment. I’d like to get some idea of where this dynasty is headed,