Incremental Reasoning in EL+ without Bookkeeping

We describe a method for updating the classification of ontologies expressed in the EL family of Description Logics after some axioms have been added or deleted. While incremental classification modulo additions is relatively straightforward, handling deletions is more problematic since it requires retracting logical consequences that no longer hold. Known algorithms address this problem using various forms of bookkeeping to trace the consequences back to premises. But such additional data can consume memory and place an extra burden on the reasoner during application of inferences. In this paper, we present a technique, which avoids this extra cost while being still very efficient for small incremental changes in ontologies.