@article {61, title = {Paraconsistent OWL and Related Logics}, journal = {Semantic Web}, volume = {4}, year = {2013}, pages = {395{\textendash}427}, abstract = {The Web Ontology Language OWL is currently the most prominent formalism for representing ontologies in Semantic Web applications. OWL is based on description logics, and automated reasoners are used to infer knowledge implicitly present in OWL ontologies. However, because typical description logics obey the classical principle of explosion, reasoning over inconsistent ontologies is impossible in OWL. This is so despite the fact that inconsistencies are bound to occur in many realistic cases, e.g., when multiple ontologies are merged or when ontologies are created by machine learning or data mining tools. In this paper, we present four-valued paraconsistent description logics which can reason over inconsistencies. We focus on logics corresponding to OWL DL and its profiles. We present the logic SROIQ4, showing that it is both sound relative to classical SROIQ and that its embedding into SROIQ is consequence preserving. We also examine paraconsistent varieties of EL++, DL-Lite, and Horn-DLs. The general framework described here has the distinct advantage of allowing classical reasoners to draw sound but nontrivial conclusions from even inconsistent knowledge bases. Truth-value gaps and gluts can also be selectively eliminated from models (by inserting additional axioms into knowledge bases). If gaps but not gluts are eliminated, additional classical conclusions can be drawn without affecting paraconsistency.}, keywords = {Automated Deduction, Complexity, Description Logic, OWL, Paraconsistency, Semantic Web, Web Ontology Language}, doi = {10.3233/SW-2012-0066}, url = {http://dx.doi.org/10.3233/SW-2012-0066}, author = {Frederick Maier and Yue Ma and Pascal Hitzler} } @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 {95, title = {Reconciling OWL and Non-monotonic Rules for the Semantic Web}, booktitle = {ECAI 2012 - 20th European Conference on Artificial Intelligence. Including Prestigious Applications of Artificial Intelligence (PAIS-2012) System Demonstrations Track}, volume = {242}, year = {2012}, pages = {474{\textendash}479}, publisher = {IOS Press}, organization = {IOS Press}, address = {Montpellier, France}, abstract = {

We propose a description logic extending SROIQ (the description logic underlying OWL 2 DL) and at the same time encompassing some of the most prominent monotonic and nonmonotonic rule languages, in particular Datalog extended with the answer set semantics. Our proposal could be considered a substantial contribution towards fulfilling the quest for a unifying logic for the Semantic Web. As a case in point, two non-monotonic extensions of description logics considered to be of distinct expressiveness until now are covered in our proposal. In contrast to earlier such proposals, our language has the {\textquotedblleft}look and feel{\textquotedblright} of a description logic and avoids hybrid or first-order syntaxes.

}, doi = {10.3233/978-1-61499-098-7-474}, url = {http://dx.doi.org/10.3233/978-1-61499-098-7-474}, author = {Matthias Knorr and Pascal Hitzler and Frederick Maier}, editor = {Luc De Raedt and Christian Bessi{\`e}re and Didier Dubois and Patrick Doherty and Paolo Frasconi and Fredrik Heintz and Peter J. F. Lucas} } @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} } @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} } @conference {140, title = {{OWL} and Rules}, booktitle = {Reasoning Web. Semantic Technologies for the Web of Data - 7th International Summer School 2011, Galway, Ireland, August 23-27, 2011, Tutorial Lectures}, volume = {6848}, year = {2011}, month = {08/2011}, pages = {382-415}, publisher = {Springer}, organization = {Springer}, abstract = {The relationship between the Web Ontology Language OWL and rule-based formalisms has been the subject of many discussions and research investigations, some of them controversial. From the many attempts to reconcile the two paradigms, we present some of the newest developments. More precisely, we show which kind of rules can be modeled in the current version of OWL, and we show how OWL can be extended to incorporate rules. We finally give references to a large body of work on rules and OWL. }, isbn = {978-3-642-23031-8}, doi = {10.1007/978-3-642-23032-5}, url = {http://dx.doi.org/10.1007/978-3-642-23032-5}, author = {Adila Krisnadhi and Frederick Maier and Pascal Hitzler}, editor = {Axel Polleres and Claudia d{\textquoteright}Amato and Marcelo Arenas and Siegfried Handschuh and Paula Kroner and Sascha Ossowski and Peter F. Patel-Schneider} } @article {167, title = {Distributed Reasoning with EL++ Using MapReduce}, year = {2010}, institution = {Wright State University}, address = {Dayton, OH, USA}, abstract = {

It has recently been shown that the MapReduce framework for distributed computation can be used effectively for large-scale RDF Schema reasoning, computing the deductive closure of over a billion RDF triples within a reasonable time [23]. Later work has carried this approach over to OWL Horst [22]. In this paper, we provide a MapReduce algorithm for classifying knowledge bases in the description logic EL++, which is essentially the OWL 2 profile OWL 2 EL. The traditional EL++ classification algorithm is recast into a form compatible with MapReduce, and it is shown how the revised algorithm can be realized within the MapReduce framework. An analysis of the circumstances under which the algorithm can be effectively used is also provided.

}, author = {Frederick Maier and Raghava Mutharaju and Pascal Hitzler} } @conference {161, title = {A MapReduce Algorithm for EL+}, booktitle = {Proceedings of the 23rd International Workshop on Description Logics (DL 2010)}, volume = {573}, year = {2010}, pages = {464-474}, publisher = {CEUR-WS.org}, organization = {CEUR-WS.org}, address = {Waterloo, Ontario, Canada}, abstract = {

Recently, the use of the MapReduce framework for distributed RDF Schema reasoning has shown that it is possible to compute the deductive closure of sets of over a billion RDF triples within a reasonable time span [22], and that it is also possible to carry the approach over to OWL Horst [21]. Following this lead, in this paper we provide a MapReduce algorithm for the description logic EL+, more precisely for the classification of EL+ ontologies. To do this, we first modify the algorithm usually used for EL+ classification. The modified algorithm can then be converted into a MapReduce algorithm along the same key ideas as used for RDF schema.

}, url = {http://ceur-ws.org/Vol-573/paper_35.pdf}, author = {Raghava Mutharaju and Frederick Maier and Pascal Hitzler}, editor = {Volker Haarslev and David Toman and Grant E. Weddell} }