Abstract:This paper presents an approach to check the satisfiability of acyclic SHOIN(D)-concepts—CDNF (complete disjunctive normal form) algorithm. This calculus can make a direct judgment on the satisfiability of acyclic SHOIN(D)-concept by restructuring it into a hierarchical disjunctive normal form group on concept descriptions which is satisfiability self-telling, and reusing description clauses to block unnecessary extensions. CDNF algorithm eliminates description overlaps to the largest extent for it works on concept description directly. Therefore, CDNF algorithm has much better performance than Tableau as it saves a lot of spatial and temporal costs.