1. Accelerating Inferencing

2. Assertion Efficient inferencing using taxonomies require fast computation of subsumption, disjointness, least common ancestors, and other properties The basic primitive required is the fast computation (preferably in constant time) of is-a queries R. Agrawal, A. Borgida, H.V. Jagadish: Efficient Management of Transitive Relationship in Large Data Bases. Sigmod 89.

3. Compressed Transitive Closure of Tree Graphs Number each node to reflect its postorder traversal position Assign to each node an index consisting of the lowest postorder number amongst its descendents A node with postorder number k is-a node with postorder number j and index i iff i <= k < j. 12 11 6 451109 32 78 23 8 7 1257 71 1 2 is-a 6 but not 11

4. Observations We require O(n) storage and can determine is-a with only one range comparison. Compressed closure is incrementally maintainable. Generalizes to directed acyclic graphs See the Sigmod paper for details