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Topic: Converting QUANTIFIER LOGIC to ATOMIC PREDICATES
Replies: 0

 Graham Cooper Posts: 4,495 Registered: 5/20/10
Converting QUANTIFIER LOGIC to ATOMIC PREDICATES
Posted: Feb 17, 2013 7:05 PM

What is the MEANING of this logical formula?

{ n | n e N } C { n | m>n }

It reduces to N C N
which is TRUE

So it MEANS --> for every n, there is a bigger m!

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

RELATION
p(a, b, e)

ATOMIC PREDICATE
p(a, b(c,d), e(f,g))

NON-ATOMIC PREDICATE
a(b) -> d(c)

NON-ATOMIC PREDICATE
All(a) p(a, b(c,d), e(f,g))

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

QUANTIFIED LOGIC
ALL(n):N EXIST(m):N m>n

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

AS A SUBSET
{ n | n e N } C { n | m>n }

every n here --> has a bigger m here

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

AS A PROLOG PREDICATE
subs( N, nat(N), bigger(M,N) )

This conversion method of

Quantifiers >> SUBSETS >> Predicates

may be used to embed deductive logic in PROLOG!

Herc
--
www.BLoCKPROLOG.com