
Shepherdson
It is worth noting also that these nice properties of Horn clauses all depend
on an asymmetry in the treatment of positive and negative information: in the
closed world assumption a ground atom is supposed false unless it can be
proved true; in a generic model it is ground atoms (not their negations) that are
true iff they are true in all models; and in a homomorphism, it is the basic rela-
tions (not their negations) whose truth is preserved.
(Sato [1982] considers a negative closed world assumption, where ground
atoms are considered to be true if they cannot be proved false. However, he
shifts his ground from requiring "proved