
258 Chakravarthy, Grant, and Minker
axiom for a given integrity constraint. We also define the notion of merge
compatibility between an axiom and an integrity constraint.
DEFINITION
1
An integrity constraint IC partially subsumes an axiom A if IC does not sub-
sume the body of A but a subclause of IC+ subsumes the body of A. •
To define the notion of a residue we need first the notion of back substitu-
tion. We mentioned earlier, that when the subsumption algorithm is applied to
check if C subsumes D, a substitution θ is applied first to transform D to a
ground clause. Since this transformation assigns a new constant to each vari-
able, it is