Exploiting Partial Information in Taxonomy Construction

One of the core services provided by description logic (DL) reasoners is classification: determining the subsumption quasi-ordering over the concept names occurring in a knowledge base (KB) and caching this information in the form of a directed acyclic graph known as the concept hierarchy or taxonomy. For less expressive DLs, such as members of the EL family, it may be possible to derive all the relevant subsumption relationships in a single computation [Baader et al., 2005]. In general, however, it will be necessary to “deduce” the subsumption relation by performing individual subsumption tests between pairs of concept names. For n concept names this will, in the worst case, require n tests, but for the tree-shaped hierarchies typically found in realistic KBs much better results can be achieved using algorithms that construct the taxonomy incrementally by traversing the partially-constructed taxonomy in order to find the right place to insert each concept name. This kind of algorithm suffers from two main difficulties. First, individual subsumption tests can be computationally expensive—for some complex KBs, even state-of-theart reasoners may take a long time to perform a single test. Second, even when subsumption tests themselves are very fast, a knowledge base containing a very large number of concepts1 will obviously result in a very large taxonomy, and repeatedly traversing this structure can be costly. The first difficulty is usually addressed by using an optimized construction that tries to minimize the number of subsumption tests performed in order to deduce the subsumption relation. Most implemented systems use an “enhanced traversal” algorithm due to Ellis [1991] and to Baader et al. [1994] which adds concepts to the taxonomy one at a time using a two-phase top-down and bottom-up breadth-first search of the partially-constructed taxonomy. The algorithm exploits the structure of the KB to identify “obvious” subsumers (so-called told-subsumers) of each concept, and uses this information in a heuristic that chooses the order in which concepts are added, the goal being to construct the taxonomy top-down; it also exploits information from the topdown search in order to prune the bottom-up search.2 The second difficulty can be addressed by optimizations that try to identify a subset of the concepts for which complete information about the subsumption relation can be