Deciding expressive description logics in the framework of resolution

We present a decision procedure for the description logic SHIQ based on the basic superposition calculus, and show that it runs in exponential time for unary coding of numbers. To derive our algorithm, we extend basic superposition with a decomposition inference rule, which transforms conclusions of certain inferences into equivalent, but simpler clauses. This rule can be used for general first-order theorem proving with any resolution-based calculus compatible with the standard notion of redundancy.