Subtleties with Stratified Rules

Example:

p(X) :- r(X)

q(X) :- s(X) & NOT p(X).

Suppose: r = {1}, and s = {1,2}

One solution: p = {1} and q = {2}

Another solution: p={1,2} and q={}.

Perfect model semantics: apply the rules stratum after stratum.