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Generalized methods for automated theorem proving can be used to compute formula transformations such as projection elimination and knowledge compilation. We present a framework based on clausal tableaux suited for such tasks. These tableaux are characterized independently of particular construction methods, but important features of empirically successful methods are taken into account, especially dependency directed backjumping and branch local operation. As an instance of that framework an adaption of DPLL is described. We show that knowledge compilation methods can be essentially improved by weaving projection elimination partially into the compilation phase.

Knowledge compilation is a common technique for propositional logic knowledge bases. A given knowledge base is transformed into a normal form, for which queries can be answered efficiently. This precompilation step is expensive, but it only has to be performed once. We apply this technique to concepts defined in the Description Logic ALC. We introduce a normal form called linkless normal form for ALC concepts and discuss an efficient satisability test for concepts given in this normal form. Furthermore, we will show how to efficiently calculate uniform interpolants of precompiled concepts w.r.t. a given signature.

Knowledge compilation is a common technique for propositional logic knowledge bases. The idea is to transform a given knowledge base into a special normal form ([MR03],[DH05]), for which queries can be answered efficiently. This precompilation step is very expensive but it only has to be performed once. We propose to apply this technique to knowledge bases defined in Description Logics. For this, we introduce a normal form, called linkless concept descriptions, for ALC concepts. Further we present an algorithm, based on path dissolution, which can be used to transform a given concept description into an equivalent linkless concept description. Finally we discuss a linear satisfiability test as well as a subsumption test for linkless concept descriptions.