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May 30, 2011 11:58AM
(i) r --> (q & ~s)
(ii) If he does not give her flowers nor chocolates, then she does not eat chocolates.

(i) For all x[S(x) --> there exists y(P(y) & F(x,y))[
(ii) If every x feeds every y, then x is a student and p is a parrot.

(i) (K1p & K2p) & (~K1K2p & ~K2K1p)
(ii) If agent 1 knows that agent 2 knows p, then agent 2 knows that agent 1 knows that agent 2 knows p
avatar Re: Q1
May 30, 2011 01:36PM
i. Same.
ii. Same. (But either goes with or, and neither goes with nor, if you want to nit pick).

i. (I think I'm wrong)... I get forall-x forall-y (S(x) & P(y) & F(x,y))
<< !!!! Grab your copy of LPL, and look up "translation ... at least ..."
You need to specify "Not at most two" in such a case... or do I have that backward. Point is it's not as innocent as it pretends to be.
ii. It's probably safer to avoid x's in the English, so what I had (after deleting my x version) was "If something feeds something, then the former is a student, and the latter is a parrot."

"Something" is a very thin disguise for an x.

i. Basically the same. I just used the other De Morgan form, where the negation is not pushed inside the bracket. I used brackets round the inside terms, too, which is too conservative. (Could well be marked wrong).
ii. smile Yes. (What a tangle, eh?)
Re: Q1
May 30, 2011 03:42PM
Is this equivalent?:
A bird is fed by someone only if that someone is a student and the bird is a parrot.
avatar Re: Q1
May 30, 2011 03:57PM
It would be if a parrot was a bird.

However, in this particular question the kind of "parrot" they're talking about is the locomotive (which is fed coal by apprentice stokers - also referred to as "students".)

No hang on that was what the symbol "parrot" meant in 2007. Last year it had an almost natural meaning. It was a short form for "parrot fish", which are fed only by the marine biology students assigned to the aquarium..

Or the short version: "Very much, No, No, No."
Re: Q1
May 30, 2011 05:03PM
My bad, however we will have to find a more natural way to express such sentences..I can't see that x's and somethings will cut it in normal conversation (but maybe they will award points regardless)
avatar Re: Q1
May 30, 2011 05:33PM
For me the most natural way to think about it is actually with x's. However, I think that's a way to lose a mark or two, so the "least onerous alternative" is all we need find.

"Something" is about as "x" as I can get in English.

So the procedure would be to say "if x is a student and y is a parrot, then x feeds y", and then translate that to something more English-sounding?

" if something ... and something ... then something feeds something"... Not surprising that it sounds a little artificial, but at least the x has vanished. Of course one should always be on the lookout for something (anotherX!) less forced than "something" if possible.
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