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Topic: SET THEORY and QUANTIFIER LOGIC are SUPERFLUOUS! You only need
1 or the other!

Replies: 8   Last Post: Nov 22, 2012 4:20 PM

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Graham Cooper

Posts: 4,336
Registered: 5/20/10
Re: SET THEORY and QUANTIFIER LOGIC are SUPERFLUOUS! You only need 1
or the other!

Posted: Nov 22, 2012 4:12 PM
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On Nov 21, 7:53 am, George Greene <gree...@email.unc.edu> wrote:
> On Nov 20, 4:09 am, Graham Cooper <grahamcoop...@gmail.com> wrote:
>

> > The notation in
>
> > { x | p(x) }
>
> > stands for ALL VALUES OF x
> > that are satisfied in p(x)

>
> English is obviously not your native language.
> "x" IS NOT the KIND of thing THAT CAN *BE*satisfiED*.
> *x* is the kind of thing that CAN SATISFY.
> *p* is the kind of thing that can BE satisfied.
>



if you had a second set based on the first, say a nested forall.

{ x | xeBottles } C { x | xePrescription(S) }

ALL(x):B prescription(B,S)

prescription depends on S

ALL(S) ( ALL(x):B p(B) )

--------------

so you could nest 2 ALLS as transitive subsets.

{ S | s e S } C { x | x e B } C { x | x e P }

A(S) A(x) P(x)

in which case x is the same type as P - a predicate.

In prolog p(x(a(b))) only the leading predicate p is treated
differently in that it cannot be matched FORANY(p) to a variable.


Herc



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