Theoretical Foundations for BDD-based Terminological Reasoning within SHIQ Technical Report Sebastian Rudolph Institut AIFB, Universität Karlsruhe, Germany rudolph@aifb.uni-karlsruhe.de Abstract. Ordered binary decision diagrams (OBDDs) have been proven computationally advantageous in the field of model checking. In our pa- per, we propose a method to use OBDDs for TBox reasoning with the description logic SHIQ. In order to do so, we have to take several steps. After recalling the well- known reduction of SHIQ to ALCHIQ, we show that any ALCHIQ knowledge base can be translated into an equisatisfiable ALCI b knowl- edge base. Next we have to show a particular model-theoretic property for SHIQ allowing to encode a representative set of models into OBDDs. To the best of our knowledge, this is the first approach of using OBDDs for reasoning with general TBoxes. 1 Introduction In the area of Knowledge Representation, description logics have been established as a widely known and accepted paradigm, manifesing it self in the standardisa- tion of OWL DL as knowledge representation language for the Semantic Web [1]. Obvously, this trend has been substantiated and supported by the fact that DLs exhibit wanted theoretical properties (notably decidability) as well as—on the more practical side—the public availability of highly optimized implementations of decision procedures. The algorithms currently applied in those DL reason- ers can be roughly divided into two classes: tableau-based and resolution-based methods. Another reasoning paradigm that has so far received next to no attention from the DL community (for a notable exception, see [2]) is reasoning based on bi- nary decision diagrams (BDDs) [3–5]. However, those data structures have been successfully applied in other domains as model checking for hard- and software verification (citations?). A closer look reveals that certain kinds of temporal log- ics used in that domains (like CTL [5]) are closely related to modal logics which in turn are known to have strong structural similarities to DLs [6]. Hence it seems almost natural to apply BDD-based techniques also for DL reasoning. Usually, BDDs are used to represent arbitrary boolean functions. Those boolean functions are then interpreted as a kind of compressed encoding of (usually