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Here is an artificial intelligence problem waiting for an algorithm.  Would
make a great but hard quiz problem.

Given that you can only use the rules of
1. De Morgans Law [(A v B) <~A & ~B],
2. Material Implication [A -> B <~A v B],
3. Distribution [A v (B & C) <(A v B) & (A v C) or A & (B v C) <(A &
B) v (A & C)],
4. Simplification [A & B A, and A & B B], and
5. Double Negative [A <~~A]
construct an algorithm that will solve by Resolution any symbolic logic
problem, with one or more stated propositions to reach a solvable stated
goal by using the negative of the goal and creating a contradiction.

If you get stuck, you might also use the rule of Co-imply [A v A <A, or A
& A <A].

For example, prove that (~P & Q) v (P & ~P) can result in Q as a stated goal
with the same truth value.  So (~P & Q) v (P & ~P)  and the negative of the
goal, ~Q are your two propositions (statements) you use to reach the
contradition.

Do NOT use truth tables.

That is a algorithm worthy of working on.  And, yes, it is programmable.

If you are not familiar with the symbolism, a "v" means OR.  The rest is
self evident.

No Sam

On Sun, Oct 4, 2009 at 6:57 PM, Martin DeMello <martindemello / gmail.com>wrote:

> I've noticed that the ruby quiz has been getting few responses of
> late. In one sense I'm part of the problem; I seldom do the quizzes
> myself. However, I do like setting them, and have fun thinking up
> quizzes that are (reasonably) quick and (hopefully) enjoyable. So I
> put it to you - what sort of quizzes do you enjoy? More
> algorithm-based? More focused on a fun result (a game, some pretty
> pictures, etc)? Something "real world" that gives you the satisfaction
> of writing a useful program? Something that encourages you to explore
> the libraries out there? Something competitive? Pick out one or two
> quizzes that you enjoyed doing and say why.
>
> martin
>
>

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