Computing a Minimal Representation of the SubsumptionLattice of All Conjunctions of Concepts De ned in aTerminology ? Franz
نویسنده
چکیده
For a given TBox of a terminological KR system, the classiication algorithm computes (a representation of) the subsumption hierarchy of all concepts introduced in the TBox. In general, this hierarchy does not contain suucient information to derive all subsumption relationships between conjunctions of these concepts. We show how a method developed in the area of \formal concept ana-lysis" for computing minimal implication bases can be used to determine a minimal representation of the subsumption hierarchy between conjunctions of concepts introduced in a TBox. To this purpose, the subsumption algorithm must be extended such that it yields (suucient information about) a counterexample in cases where there is no subsumption relationship. For the concept language ALC, this additional requirement does not change the worst-case complexity of the subsumption algorithm. One advantage of the extended hierarchy is that it is a lattice, and not just a partial ordering.
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