1. What is the key result for their discussion of other NP-hard extensions?
The key result for their discussionof other NP-hard extensions is due to Donini et al. [DHL+92] who showed thatthe interplay of universal and existential quanti cation over attributes is a sourceof complexity that makes subsumption checking intractable.
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2. What are the only atoms allowed in this language?
The only atoms allowed in thislanguage are (x in C), denoting membership of x in class C, and (x a y), assigningy as value for attribute a to object x.
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3. What makes view maintenance methods from deductive databases?
The correspondence between concept languages and the rst-order semantics ofOODB's makes view maintenance methods from deductive databases ([UO92,CW91] applicable.
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4. What is the number of rules that add constraints?
Since each new constraint is a combination of variables and conceptor attribute expressions occurring in C, D, or , the number of rule applicationsadding constraints is polynomially bounded by the size of C, D and .
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