The Bayesian Description Logic BALC

Description Logics (DLs) that support uncertainty are not as well studied as their crisp alternatives, thereby limiting their use in real world domains. The Bayesian DL BEL and its extensions have been introduced to deal with uncertain knowledge without assuming (prob- abilistic) independence between axioms. In this paper we combine the classical DL ALC with Bayesian Networks. Our new DL includes a so- lution to the consistency checking problem and changes to the tableaux algorithm that are not a part of BEL. Furthermore, BALC also supports probabilistic assertional information which was not studied for BEL. We present algorithms for four categories of reasoning problems for our logic; two versions of concept satisfiability (referred to as total concept satis- fiability and partial concept satisfiability respectively), knowledge base consistency, subsumption, and instance checking. We show that all rea- soning problems in BALC are in the same complexity class as their classical variants, provided that the size of the Bayesian Network is included in the size of the knowledge base