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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

 Messages: [ Previous | Next ]
 Graham Cooper Posts: 4,421 Registered: 5/20/10
SET THEORY and QUANTIFIER LOGIC are SUPERFLUOUS! You only need
1 or the other!

Posted: Nov 20, 2012 4:09 AM

The notation in

{ x | p(x) }

stands for ALL VALUES OF x
that are satisfied in p(x)

This is the SAME 'ALL' as ALL(x) ....predicate(..predicate...
x ...) ...)

ALL is merely SUBSET!

ALL(n):N n+1 > n

is just

{ n | neN } C { n | n+1>n }

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

ALL(x):N xeR

is just

{ x | xeN } C { x | xeR }

Naturals are a subset of Reals!

All Naturals are elements of Reals!
A(x):N xeR

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

This is good news for me since I'm adding breadth first functionality
to microPROLOG (sets of results) so I just have to figure out a set
notation with { }.

e.g.
union( { 1 2 3 } , { 3 4 } , X }

X = { 1 2 3 4 }

So I can avoid the horrors of eliminating quantifiers by making you
write the theorems in set theory notation instead! Haha!

Herc

--
www.microPROLOG.com
if( if(t(S),f(R)) , if(t(R),f(S)) ).
if it's sunny then it's not raining
ergo
if it's raining then it's not sunny

Date Subject Author
11/20/12 Graham Cooper
11/20/12 Frederick Williams
11/20/12 Charlie-Boo
11/20/12 Frederick Williams
11/22/12 Dan Christensen
11/22/12 Graham Cooper
11/22/12 Graham Cooper
11/22/12 Graham Cooper