Ζ for the set of the variables occurring in a negative literal of the body.
We say that Ρ satisfies the strong covering axiom if for each of its clauses
XCY
and
ZQY
holds.
•
The first implication is called in Shepherdson [1984] the covering axiom.
The strong covering axiom ensures that in the SLDNF-resolution only ground
negative literals need be evaluated. We can now formulate our conjecture.
CONJECTURE 1
Let Ρ be a strict stratified program which satisfies the strong covering axiom.
Then for every ground literal L.
comp(P) f= L iff
—j
L can be refuted from Ρ by SLDNF-resolution. •
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