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SET THEORY and QUANTIFIER LOGIC are SUPERFLUOUS! You only need
1 or the other!
Posted:
Nov 20, 2012 4:09 AM
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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
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