TY - JOUR T1 - Paraconsistent OWL and Related Logics JF - Semantic Web Y1 - 2013 A1 - Frederick Maier A1 - Yue Ma A1 - Pascal Hitzler KW - Automated Deduction KW - Complexity KW - Description Logic KW - OWL KW - Paraconsistency KW - Semantic Web KW - Web Ontology Language AB - 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. VL - 4 UR - http://dx.doi.org/10.3233/SW-2012-0066 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 -