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The complexity of existential quantification in concept languages. (English) Zbl 1193.68241
Summary: Much of the research on concept languages, which also are 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 $$\mathcal F\mathcal L^-$$ with constructs containing some form of logical disjunction leads to co-NP-hard subsumption problems. Secondly, adding negation to $$\mathcal F\mathcal L^-$$ makes subsumption PSPACE-complete.
The main result of this paper is that extending $$\mathcal F\mathcal L^-$$ with unrestricted existential quantification makes subsumption NP-complete. This is the proof of intractability for a concept language containing, whether explicitly or implicitly, no construct expressing disjunction. Unrestricted existential quantification is, therefore, alongside disjunction, a source of computational complexity in concept languages.

##### MSC:
 68T30 Knowledge representation 68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) 68Q25 Analysis of algorithms and problem complexity 68T27 Logic in artificial intelligence
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