A Tableau Decision Procedure for $\mathcal{SHOIQ}$

OWL DL, a new W3C ontology language recommendation, is based on the expressive description logic $\mathcal{SHOIN}$. Although the ontology consistency problem for $\mathcal{SHOIN}$ is known to be decidable, up to now there has been no known “practical” decision procedure, that is, a goal-directed procedure that is likely to perform well with realistic ontology derived problems. We present such a decision procedure for $\mathcal{SHOIQ}$, a slightly more expressive logic than $\mathcal{SHOIN}$, extending the well-known algorithm for $\mathcal{SHIQ}$, which is the basis for several highly successful implementations.

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