subsume

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--A query [P.sup.-] is the negative subsuming form of the predicate P with respect to the target system T, if ??[P.sup.-] minimally subsumes ??P with respect to T.
In the figure, an arc U [right arrow] V indicates that expression U properly subsumes V.
--A (m'N) B properly subsumes A (mN) B if m' [is greater than] m.
--A (mN) B properly subsumes A (nW) B and B (nW) A if m [is greater than or equal to] n.
--A AND B properly subsumes A (mN) B, because AND is equivalent to [infinity]N, where [infinity] is an arbitrarily large number.
On the other hand, the negative rewriting of an unsupported pattern U is the disjunction of all the supported patterns [U.sub.i] that U subsumes, i.e., U [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] v([U.sub.i]), as Figure 6 also illustrates.
In general, for an unsupported pattern U, the positive rewriting is the conjunction of all the supported patterns [U.sub.i] that subsume U, i.e., U [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] ([U.sub.i]).
Because rewritten queries (minimally) subsume original queries, the front-end needs to postfilter preliminary results that may contain extra documents with respect to the original queries.