
Re: set builder notation
Posted:
Aug 17, 2013 7:34 AM


On Saturday, August 17, 2013 4:12:34 AM UTC7, lite.o...@gmail.com wrote: > S = {x /in A  P(x) } > > > > For the set builder notation above, what we really means is: > > > > all things x, such that "x is element of A *and* P(x) is true" correct? > > > > The vertical bar is essentially conjunction, correct?/
No, consider
S = { x /in A  P(a,b,x,y,z) }
there is an implicit ALL(x) by placing x on the left of the bar.
x is no longer free in P
the conjunction A&B just returns a value of true or false.
S = {x  p(x)}
is shorthand for
ALL(x) xeS <> p(x)
Putting complex expressions before the bar is a different shorthand...
it's really
S = { x  xeA & P(x) }
Set Specification increases the level of the logic above FOL.
Now you can solve S UNION T
using the predesignated parameter in p(...)
X e ( S U T ) < X e S X e ( S U T ) < X e T
so to test for UNION it will then backward chain to a direct element check on one or both of the unioned sets
...via how they were specified... and then call p()
X e S < p(X)
Herc
 www.phpPROLOG.com
www.tinyurl.com/HowPrologWorks

