Dear Ontolog-members,  (01)
I have a knowledge base and a set of rules written under closed world
assumption that use negation only as negation as failure.  (02)
Under these circumstances are the laws of quantifier movement valid?
Laws of Quantifier movements:
1. '(all x.P(x)) --> Q' equivalent-to 'exists x.(P(x)-->Q)', provided x is
not free in Q
2. '(exisits x.P(x)) --> Q' equivalent-to 'all x.(P(x)-->Q)', provided x
is not free in Q
3. 'P --> (all x.Q(x))' equivalent-to 'all x.(P --> Q(x))', provided x is
not free in P
4. 'P --> (exists x.Q(x))' equivalent-to 'exists x.(P --> Q(x))', provided
x is not free in P  (03)
And/ Or are the following laws valid?
1. 'not(all x. P(x))' equivalent-to 'exists x.(not P(x))', where not has
the Negation as Failure semantics.
2. 'not(exists x. P(x))' equivalent-to 'all x.(not P(x))', where not has
the Negation as Failure semantics.  (04)
Thank you,
Ankesh  (05)
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