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Topic: PREDICATE CALCULUS 2
Replies: 23   Last Post: Nov 29, 2012 1:13 AM

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 Graham Cooper Posts: 4,417 Registered: 5/20/10
Re: PREDICATE CALCULUS 2
Posted: Nov 27, 2012 9:29 PM

>
> {(Y1,Y2)|r(X,Y1)^r(X,Y2)} C {(Y1,Y2)|r(X,Y1)^r(X,Y2)->Y1=Y2}
> DETECTING r is a FUNCTION without QUANTIFIERS!
>

This simplifies to..

{(Y1,Y2) | r(X,Y1)^r(X,Y2)} C {(Y,Y) | r(X,Y)}

which simply guarantees only 1 Y value for any X value.

So it switches from Quantifier ALL(X) P(...) HOLDS
to ALL VALUES OF X SATISFYING { X | P(...) }

which is a different type of result, a SET
but SET1 C SET2
then returns the same Boolean type as Quantifier ALL(X)

Herc

Date Subject Author
11/25/12 Graham Cooper
11/27/12 Dan Christensen
11/27/12 Graham Cooper
11/27/12 Dan Christensen
11/27/12 Dan Christensen
11/27/12 Dan Christensen
11/27/12 Graham Cooper
11/27/12 Graham Cooper
11/27/12 Graham Cooper
11/27/12 Dan Christensen
11/28/12 Graham Cooper
11/28/12 Dan Christensen
11/28/12 Graham Cooper
11/28/12 Virgil
11/28/12 Dan Christensen
11/28/12 Graham Cooper
11/28/12 Dan Christensen
11/28/12 Graham Cooper
11/28/12 Dan Christensen
11/29/12 Graham Cooper
11/29/12 Dan Christensen
11/28/12 Frederick Williams
11/28/12 Dan Christensen
11/28/12 Dan Christensen