FOL expression in Prolog

[marczoid]

Hi all, I'm trying to find a way to put the following first order logic expression into Prolog

(p(0) or p(1)) and not (p(0) and p(1))

This means that it should respond in the following way to queries:

?- p(0)
Yes.
?- p(1)
Yes.
?- p(0),p(1).
No.

I tried to translate the logical expression:

(p(0) or p(1)) and not (p(0) and p(1)) <=>
(not p(0) -> p(1)) and (p(0) -> not p(1)) <=>
p(0) <-> p(1)

Using Clarks completion (that states that every definitional theory can be put in a logical program by giving the if-halves), I can obtain:

p(0) :- p(1).

Unfortunately, this resulting theory is only sound (it will not derive false information), but not complete (for example: p(1) cannot be derived). This is a consequence of Clarks theorem.

Does anybody know if there is a better solution? Thanks!

 

[marczoid]

I made a mistake in my post, and since I don't see an edit button I will post the correction here:

The derivation of the logical expression should have: p(0) <-> not p(1) as the last formula, and the Prolog code is: p(0) :- not p(1).