8:47 AM
@AliTaghavi I would guess that if you create a chatroom and post nothing there, it is very likely that other users won't know what is a purpose of that room. (And moreover, if you don't post anything there, nobody can ping you in that room.)
But perhaps you have created that room by mistake?

12 hours later…
8:34 PM
Is this a good place to discuss fuzzy logic? I came up with a set of propositions that are paradoxical in classical logic, but which allow a solution of (1/3, 1/3, 2/3) in fuzzy logic:
x = y xor z
y = x and z
z = not x and not y
In fuzzy (or classical) logic, these can be rewritten as:
x = |y - z|
y = min(x, z)
z = min(1-x, 1-y)
The values of (1/3, 1/3, 2/3) provide the only valid solution to this.
What I'm wondering is (a) whether this is the simplest set of propositions that contain 1/3 as a solution to one of the propositions, (b) whether there is a general means for constructing such se
8:44 PM
For those who are interested in the trivial (classically non-paradoxical) example, here's the simplest version I can think of:
x = y and not z
y = (not x) and z
z = x and not y
In fuzzy (or classical) logic, these can be rewritten as:
x = min(y, 1-z)
y = min(1-x, z)
z = min(x, 1-y)
And for any alpha between 0 and 0.5 inclusive, x=y=z=alpha is a solution.
Oh wait, there's an even more trivial example: x = x and not x. As before, letting x be false is a perfectly valid solution, but if we convert it to fuzzy logic, any value between 0 and 0.5 (inclusive) works.