TY - JOUR T1 - Complexities of Horn Description Logics JF - ACM Trans. Comput. Log. Y1 - 2013 A1 - Markus Krötzsch A1 - Sebastian Rudolph A1 - Pascal Hitzler KW - computational complexity KW - description logics KW - Horn logic AB - Description Logics (DLs) have become a prominent paradigm for representing knowledge bases in a variety of application areas. Central to leveraging them for corresponding systems is the provision of a favourable balance between expressivity of the knowledge representation formalism on the one hand, and runtime performance of reasoning algorithms on the other. Due to this, Horn description logics (Horn DLs) have attracted attention since their (worst-case) data complexities are in general lower than their overall (i.e. combined) complexities, which makes them attractive for reasoning with large sets of instance data (ABoxes). However, the natural question whether Horn DLs also provide advantages for schema (TBox) reasoning has hardly been addressed so far. In this paper, we therefore provide a thorough and comprehensive analysis of the combined complexities of Horn DLs. While the combined complexity for many Horn DLs studied herein turns out to be the same as for their non-Horn counterparts, we identify subboolean DLs where Hornness simplifies reasoning. We also provide convenient normal forms for Horn DLs. VL - 14 UR - http://doi.acm.org/10.1145/2422085.2422087 ER - TY - CONF T1 - Recent Advances in Integrating OWL and Rules T2 - Web Reasoning and Rule Systems - 6th International Conference, RR 2012, Vienna, Austria, September 10-12, 2012. Proceedings Y1 - 2012 A1 - Matthias Knorr A1 - David Carral A1 - Pascal Hitzler A1 - Adila Krisnadhi A1 - Frederick Maier A1 - Cong Wang ED - Markus Krötzsch ED - Umberto Straccia KW - description logics KW - OWL KW - Rules AB - As part of the quest for a unifying logic for the Semantic Web Technology Stack, a central issue is finding suitable ways of integrating description logics based on the Web Ontology Language (OWL) with rule-based approaches based on logic programming. Such integration is difficult since naive approaches typically result in the violation of one or more desirable design principles. For example, while both OWL 2 DL and RIF Core (a dialect of the Rule Interchange Format RIF) are decidable, their naive union is not, unless carefully chosen syntactic restrictions are applied. We report on recent advances and ongoing work by the authors in integrating OWL and rulesWe take an OWL-centric perspective, which means that we take OWL 2 DL as a starting point and pursue the question of how features of rulebased formalisms can be added without jeopardizing decidability. We also report on incorporating the closed world assumption and on reasoning algorithms. This paper essentially serves as an entry point to the original papers, to which we will refer throughout, where detailed expositions of the results can be found. JF - Web Reasoning and Rule Systems - 6th International Conference, RR 2012, Vienna, Austria, September 10-12, 2012. Proceedings PB - Springer CY - Austria, Vienna VL - 7497 UR - http://dx.doi.org/10.1007/978-3-642-33203-6_20 ER - TY - JOUR T1 - Type-Elimination-Based Reasoning for the Description Logic SHIQbs using Decision Diagrams and Disjunctive Datalog JF - Logical Methods in Computer Science Y1 - 2012 A1 - Sebastian Rudolph A1 - Markus Krötzsch A1 - Pascal Hitzler KW - datalog KW - decision diagrams KW - description logics KW - type elimination AB - We propose a novel, type-elimination-based method for standard reasoning in the description logic SHIQbs 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 SHIQbs, we provide a stepwise reduction from SHIQbs 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. VL - 8 UR - http://dx.doi.org/10.2168/LMCS-8(1:12)2012 ER - TY - CONF T1 - A Better Uncle for OWL: Nominal Schemas for Integrating Rules and Ontologies T2 - Proceedings of the 20th International Conference on World Wide Web, WWW 2011, Hyderabad, India, March 28 - April 1, 2011 Y1 - 2011 A1 - Markus Krötzsch A1 - Frederick Maier A1 - Adila Krisnadhi A1 - Pascal Hitzler ED - Sadagopan Srinivasan ED - Krithi Ramamritham ED - Arun Kumar ED - M. P. Ravindra ED - Elisa Bertino ED - Ravi Kumar KW - datalog KW - Description Logic KW - Semantic Web Rule Language KW - SROIQ KW - tractability KW - Web Ontology Language AB - We propose a description-logic style extension of OWL 2 with nominal schemas which can be used like "variable nominal classes" within axioms. This feature allows ontology languages to express arbitrary DL-safe rules (as expressible in SWRL or RIF) in their native syntax. We show that adding nominal schemas to OWL 2 does not increase the worst-case reasoning complexity, and we identify a novel tractable language SROELV3(\cap, x) that is versatile enough to capture the lightweight languages OWL EL and OWL RL. JF - Proceedings of the 20th International Conference on World Wide Web, WWW 2011, Hyderabad, India, March 28 - April 1, 2011 PB - ACM SN - 978-1-4503-0632-4 UR - http://doi.acm.org/10.1145/1963405.1963496 ER -