DFKI Research Report-91-02
by Francesco Donini, Bernhard Hollunder, Maurizio Lenzerini, Alberto Marchetti Spaccamela, Daniele Nardi, Werner Nutt
The Complexity of Existential Quantification in Concept Languages
Much of the research on concept languages, also called terminological languages, has focused on the computational complexity of subsumption. The intractability results can be divided into two groups. First, it has been shown that extending the basic language - with constructs containing some form of logical disjunction leads to co-NP-hard subsumption problems. Second, adding negation to - makes subsumption PSPACE-complete.The main result of this paper is that extending - with unrestricted existential quantification makes subsumption NP-complete. This is the first proof of intractability for a concept language containing no construct expressing disjunction--whether explicitly or implicitly. Unrestricted existential quantification is therefore, alongside disjunction, a source of computational complexity in concept languages.
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