Automata can show PSpace results for description logics

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 ExpTimecomplete 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.

DOI: 10.1016/j.ic.2008.03.006

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Cite this paper

@article{Baader2008AutomataCS, title={Automata can show PSpace results for description logics}, author={Franz Baader and Jan Hladik and Rafael Pe{\~n}aloza}, journal={Inf. Comput.}, year={2008}, volume={206}, pages={1045-1056} }