[DL] validity of laws of predicate logic under CWA and NAF

[Uli Sattler]

On 20 Feb 2009, at 15:27, Ankesh Khandelwal wrote:

> Dear DL-members,
>
> I have a knowledge base and a set of rules written under closed world
> assumption that use negation only as negation as failure.
>


Dear Ankesh,

which semantics do you use? Can you give us a reference for where it  
is defined? Cheers, Uli
>

> 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
>
> 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.
>
> Thank you,
> Ankesh
>
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