Jan Hladik

From tableaux to automata for description logics

This paper investigates the relationship between automata- and tableau-based inference procedures for description logics. To be more precise, we develop an abstract notion of what a tableau-based algorithm is, and then show, on this abstract level, how tableau-based algorithms can be converted into automata-based algorithms. In particular, this allows us to characterize a large class of tableau-based algorithms that imply an ExpTime upper-bound for reasoning in the description logics for which such an algorithm exists.

Automata can show PSpace results for description logics

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.

Implementation and Optimisation of a Tableau Algorithm for the Guarded Fragment

In this paper, we present SAGA, the implementation of a tableau-based Satisfiability Algorithm for the Guarded Fragment (GF). Satisfiability for GF with finite signature is ExpTime-complete and therefore theoretically intractable, but existingtableau-based systems for ExpTime-complete description and modal logics perform well for many realistic knowledge bases. We implemented and evaluated several optimisations used in description logic systems, and our results show that with an efficient combination, SAGA can compete with existinghig hly optimised systems for description logics and first order logic.

A Translation of Looping Alternating Automata into Description Logics

We present a translation of (one-way and two-way) alternating automata into description logics, thus reducing the emptiness problem for alternating automata to satisfiability of the target description logic. The latter problem can then be decided using highly optimised, tableau-based description logic reasoners. The translation is a step towards the understanding of the relationship between automata- and tableau-based decision procedures for description and modal logics. Moreover, it yields some by-products: (i) a program deciding the emptiness problem for alternating automata and thus the satisfiability problem for logics with automata-based decision procedures; and (ii) tight complexity bounds for the target description logic.