Re: pc answers

[Gerald Koenig <jlk@netcom.com>]

>
>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).
>>
>

jorge said:
>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.

djer adds:

In (2.) it does not have to be the same man [singular] that does the
touching.  (2) states, "for some z1..." where  z1 is clearly defined by
pc to be the set {x,y,z} of three men.  We have the existential
quantifier E on z1.  It is read as "for at least one..and less than
all". It does not mean only one man.  Here it can mean two men.  Some
{x,y,z}; or equivalently, E(z1) mean one only of the following list:
[x,y,z,(x,y),(x,z),(y,z)].  This is a 6 member list.

(2.) E(z1)(w1) t(z1,w1) means; select one member of the list, then pair
it with each member of {u,v,w} (dog).  Two men, for example (x,y), can
touch each dog.

E(w1) means one only of the list: [u,v,w,(u,v),(u,w),(v,w)]. This is
the list for some dogs. The double existential form, E(z1)E(w1),
requires a choice from each list to express the idea "some (of 3) men
touch some (of 3) dogs."  This yields 36 possibilities.  I am not up to
speed on default quantifiers, but if "su'o ci nanmu cu pencu su'o ci
gerku" is the default then 36 different events are possible.  The
All-All double universal combination gives only one diagram, and either
E-All or All-E each give 6 possible diagrams.

What "ci nanmu cu pencu ci gerku" means can be narrowed down by explicit
or default quantifiers; even then there is a bewildering array of
possibilites except in the All-All case. And this is for the 3-3 case
that pc provided to clarify the issues.  Perhaps only the double
universal case is useful, and beyond that we will have to describe what
we mean or be content with the incomprehensibily of so much complexity.


djer



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