Automata can show PSpace results for description logics

  • Authors:

  • Franz Baader;Jan Hladik;Rafael Peòaloza

  • Affiliations:

  • Theoretical Computer Science, TU Dresden, 01062 Dresden, Germany;Theoretical Computer Science, TU Dresden, 01062 Dresden, Germany;Intelligent Systems, University of Leipzig, Germany

  • Venue:
  • Information and Computation
  • Year:
  • 2008

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Abstract

In the area of Description Logic (DL), both tableau-based and automata-based algorithms are frequently used to show decidability and complexity results for basic inference problems such as satisfiability of concepts. Whereas tableau-based algorithms usually yield worst-case optimal algorithms in the case of PSpace-complete logics, it is often very hard to design optimal tableau-based algorithms for ExpTime-complete DLs. In contrast, the automata-based approach is usually well-suited to prove ExpTime upper-bounds, but its direct application will usually also yield an ExpTime-algorithm for a PSpace-complete logic since the (tree) automaton constructed for a given concept is usually exponentially large. In the present paper, we formulate conditions under which an on-the-fly construction of such an exponentially large automaton can be used to obtain a PSpace-algorithm. We illustrate the usefulness of this approach by proving a new PSpace upper-bound for satisfiability of concepts with respect to acyclic terminologies in the DL SI, which extends the basic DL ALC with transitive and inverse roles.