Re: pc answers

[jorge@phyast.pitt.edu]

la djer cusku di'e

> 1. (z1)(w1)  t(z1,w1).    For each z1, For each w1, touches( z1,w1).
> 2. E(z1)(w1) t(z1,w1).    For some z1, For each w1, touches(z1, w1).
> 3. E(w1)(z1) t(z1,w1).    etc.
> 4. (z1)E(w1) t(z1,w1).
> 5. (w1)E(z1) t(z1,w1).
> 6. E(z1)E(w1)t(z1,w1).
>
> As I understand it the order here in the prenex does not matter; so
> 2. is equivalent to 5; and 3. is equivalent to 4.

Actually, the order does matter.

2. says that there is at least one man, such that he touches each
   of the three dogs.
5. says that each of the three dogs is touched by at least one man.

In 2., it has to be the same man that does the touching, while in 5.
it can be a different one for each dog.

> This yields only 4 distinct forms.
>
> This is reasonable because the form p[Q{w1}, Q{z1}] where p is a
> predicate and Q a quantifier (either the universal or the existential),
> has exactly 4 permutations.

It has 8 permutations (two possibilities for each Q, times two possible
orders of the arguments, 2^3=8). But since (z1)(w1) is equivalent
to (w1)(z1), and E(z1)E(w1) is the same as E(w1)E(z1) there are left
only six that are different.

The order of universal and existential quantifier matters. The order
of two universals or two existentials doesn't.

All this still doesn't tell us what does {ci nanmu cu pencu ci gerku}
mean.

Jorge