TYPE-ELIMINATION-BASED REASONING FOR THE DESCRIPTION LOGIC SHIQb(s) USING DECISION DIAGRAMS AND DISJUNCTIVE DATALOG
We propose a novel, type-elimination-based method for standard reasoning in the description logic SHIQb(s) extended by DL-safe rules. To this end, we first establish a knowledge compilation method converting the terminological part of an ALCIb knowledge base into an ordered binary decision diagram (OBDD) that represents a canonical model. This OBDD can in turn be transformed into disjunctive Datalog and merged with the assertional part of the knowledge base in order to perform combined reasoning. In order to leverage our technique for full SHIQb(s), we provide a stepwise reduction from SHIQb(s) to ALCIb that preserves satisfiability and entailment of positive and negative ground facts. The proposed technique is shown to be worst-case optimal w.r.t. combined and data complexity.
description logics decision diagrams datalog type elimination