@article {60,
	title = {Complexities of Horn Description Logics},
	journal = {ACM Trans. Comput. Log.},
	volume = {14},
	year = {2013},
	pages = {2},
	abstract = {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.},
	keywords = {computational complexity, description logics, Horn logic},
	doi = {10.1145/2422085.2422087},
	url = {http://doi.acm.org/10.1145/2422085.2422087},
	author = {Markus Kr{\"o}tzsch and Sebastian Rudolph and Pascal Hitzler}
}
@book {290,
	title = {语义Web技术基础},
	year = {2013},
	publisher = {Tsinghua University Press},
	organization = {Tsinghua University Press},
	author = {Pascal Hitzler and Markus Kr{\"o}tzsch and Sebastian Rudolph}
}
@article {303,
	title = {OWL 2 Web Ontology Language: Primer (Second Edition)},
	year = {2012},
	month = {12/11/2012},
	pages = {W3C Recommendation},
	url = {http://www.w3.org/TR/owl2-primer},
	author = {Pascal Hitzler and Markus Kr{\"o}tzsch and Bijan Parsia and Peter F. Patel-Schneider and Sebastian Rudolph}
}
@conference {124,
	title = {Recent Advances in Integrating {OWL} and Rules},
	booktitle = {Web Reasoning and Rule Systems - 6th International Conference, RR 2012, Vienna, Austria, September 10-12, 2012. Proceedings},
	volume = {7497},
	year = {2012},
	month = {09/2012},
	pages = {225-228},
	publisher = {Springer},
	organization = {Springer},
	address = {Austria, Vienna},
	abstract = {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.},
	keywords = {description logics, OWL, Rules},
	doi = {10.1007/978-3-642-33203-6_20},
	url = {http://dx.doi.org/10.1007/978-3-642-33203-6_20},
	author = {Matthias Knorr and David Carral and Pascal Hitzler and Adila Krisnadhi and Frederick Maier and Cong Wang},
	editor = {Markus Kr{\"o}tzsch and Umberto Straccia}
}
@conference {19,
	title = {A Tableau Algorithm for Description Logics with Nominal Schemas},
	booktitle = {Web Reasoning and Rule Systems, 6th International Conference, RR2012, Vienna, Austria, September 10-12, 2012, Proceedings},
	volume = {7497},
	year = {2012},
	month = {09/2012},
	pages = {234-237},
	publisher = {Springer},
	organization = {Springer},
	abstract = {<p>We present a tableau algorithm for the description logic\&nbsp;ALCOV. This description logic is obtained by extending the description\&nbsp;logic ALCO with the expressive nominal schema construct that enables\&nbsp;DL-safe datalog with predicates of arbitrary arity to be covered within\&nbsp;the description logic framework. The tableau algorithm provides a basis to implement a delayed grounding strategy which was not facilitated\&nbsp;by earlier versions of decision procedures for satisfiability in expressive\&nbsp;description logics with nominal schemas.</p>
},
	doi = {10.1007/978-3-642-33203-6_22},
	author = {Adila Krisnadhi and Pascal Hitzler},
	editor = {Markus Kr{\"o}tzsch and Umberto Straccia}
}
@article {65,
	title = {Type-Elimination-Based Reasoning for the Description Logic SHIQbs using Decision Diagrams and Disjunctive Datalog},
	journal = {Logical Methods in Computer Science},
	volume = {8},
	year = {2012},
	abstract = {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.},
	keywords = {datalog, decision diagrams, description logics, type elimination},
	doi = {10.2168/LMCS-8(1:12)2012},
	url = {http://dx.doi.org/10.2168/LMCS-8(1:12)2012},
	author = {Sebastian Rudolph and Markus Kr{\"o}tzsch and Pascal Hitzler}
}
@conference {139,
	title = {A Better Uncle for {OWL}: Nominal Schemas for Integrating Rules and Ontologies},
	booktitle = {Proceedings of the 20th International Conference on World Wide Web, WWW 2011, Hyderabad, India, March 28 - April 1, 2011},
	year = {2011},
	month = {03/2011},
	pages = {645-654},
	publisher = {ACM},
	organization = {ACM},
	abstract = {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.},
	keywords = {datalog, Description Logic, Semantic Web Rule Language, SROIQ, tractability, Web Ontology Language},
	isbn = {978-1-4503-0632-4},
	doi = {10.1145/1963405.1963496},
	url = {http://doi.acm.org/10.1145/1963405.1963496},
	author = {Markus Kr{\"o}tzsch and Frederick Maier and Adila Krisnadhi and Pascal Hitzler},
	editor = {Sadagopan Srinivasan and Krithi Ramamritham and Arun Kumar and M. P. Ravindra and Elisa Bertino and Ravi Kumar}
}
@book {291,
	title = {Logik und Logikprogrammierung Band 2: Aufgaben und L{\"o}sungen},
	year = {2011},
	publisher = {Synchron Verlag},
	organization = {Synchron Verlag},
	address = {Heidelberg, Germany},
	issn = {978-3-935025-85-0},
	author = {Steffen H{\"o}lldobler and Sebastian Bader and Bertram Fronh{\"o}fer and Ursula Hans and Pascal Hitzler and Markus Kr{\"o}tzsch and Tobias Pietzsch}
}
@conference {142,
	title = {Nominal Schemas for Integrating Rules and Description Logics},
	booktitle = {Proceedings of the 24th International Workshop on Description Logics (DL 2011), Barcelona, Spain, July 13-16, 2011},
	volume = {745},
	year = {2011},
	month = {07/2011},
	publisher = {CEUR-WS.org},
	organization = {CEUR-WS.org},
	abstract = {We propose an extension of SROIQ with nominal schemas which can be used like {\textquotedblleft}variable nominal concepts{\textquotedblright} within axioms. This feature allows us to express arbitrary DL-safe rules in description logic
syntax. We show that adding nominal schemas to SROIQ does not increase its worst-case reasoning complexity, and we identify a family of tractable DLs SROELVn that allow for restricted use of nominal
schemas.},
	url = {http://ceur-ws.org/Vol-745/paper_39.pdf},
	author = {Markus Kr{\"o}tzsch and Frederick Maier and Adila Krisnadhi and Pascal Hitzler},
	editor = {Riccardo Rosati and Sebastian Rudolph and Michael Zakharyaschev}
}
@book {293,
	title = {Foundations of Semantic Web Technologies},
	series = {Textbooks in Computing},
	year = {2009},
	pages = {455},
	publisher = {Chapman and Hall/CRC Press},
	organization = {Chapman and Hall/CRC Press},
	issn = {9781420090505},
	author = {Pascal Hitzler and Markus Kr{\"o}tzsch and Sebastian Rudolph}
}
@article {304,
	title = {OWL 2 Web Ontology Language: Primer},
	year = {2009},
	month = {10/27/2009},
	pages = {W3C Recommendation},
	url = {http://www.w3.org/TR/2009/REC-owl2-primer-20091027},
	author = {Pascal Hitzler and Markus Kr{\"o}tzsch and Bijan Parsia and Peter F. Patel-Schneider and Sebastian Rudolph}
}
@book {294,
	title = {Semantic Web Grundlagen},
	year = {2008},
	pages = {277},
	publisher = {Springer textbook},
	organization = {Springer textbook},
	issn = {978-3-540-33993-9},
	author = {Pascal Hitzler and Markus Kr{\"o}tzsch and Sebastian Rudolph and York Sure}
}
