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In '''6. IMPLEMENTATION''', the authors de … In '''6. IMPLEMENTATION''', the authors describe their algorithm for determining the fixedpoint of a graph/view. They write, "In some more details, the procedure starts with the true statements, which are extensionally lister, or which can be derived from views, which do not use negation. //Though, I thought that views ''could'' use negation…// We call this underestimate ''U''<sub>1</sub>. Statements in ''U''<sub>1</sub> are known to be true. ''U''<sub>1</sub> is used to compute an overestimate ''O''<sub>1</sub> by evaluating all views against this set of true statements. '''The result will be an overestimate, because ''U''<sub>1</sub> was still incomplete and therefore bound negation will succeed in too many cases.''' //So views ''can'' contain negation…//" (emphasis added) I do not see how they can guarantee that ''O''<sub>1</sub> will be an overestimate. It is generated based on ''U''<sub>1</sub> whose elements are known to be true, but which is not yet the set of all true statements. Then if ''O''<sub>1</sub> does not depend on views using negation, it would seem that ''O''<sub>1</sub> could be another underestimate. In '''5.1 Requirements …, RDF Schema''' the authors state "that NGs are expressive enough to alternatively model the RDFS inference rules as view definitions." I imagine a a ''U''<sub>1</sub> containing "X rdf:type A", "A rdf:subClassOf B", and "B rdf:subClassOf C", which would lead to an ''O''<sub>1</sub> containing ''U''<sub>1</sub> as a subset, and also "X rdf:type B", and perhaps "X rdf:type C". Yet ''O''<sub>1</sub> is clearly not an overestimate. What am I missing here? t an overestimate. What am I missing here?
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