@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} } @article {74, title = {Local Closed World Reasoning with Description Logics under the Well-Founded Semantics}, journal = {Artificial Intelligence}, volume = {175}, year = {2011}, pages = {1528{\textendash}1554}, abstract = {

An important question for the upcoming Semantic Web is how to best combine open world ontology languages, such as the OWL-based ones, with closed world rule-based languages. One of the most mature proposals for this combination is known as hybrid MKNF knowledge bases [52], and it is based on an adaptation of the Stable Model Semantics to knowledge bases consisting of ontology axioms and rules. In this paper we propose a well-founded semantics for nondisjunctive hybrid MKNF knowledge bases that promises to provide better efficiency of reasoning, and that is compatible with both the OWL-based semantics and the traditional Well-Founded Semantics for logic programs. Moreover, our proposal allows for the detection of inconsistencies, possibly occurring in tightly integrated ontology axioms and rules, with only little additional effort. We also identify tractable fragments of the resulting language.

}, keywords = {Description Logic, Knowledge representation, Logic Programming, Non-monotonic reasoning, Ontologies, Semantic Web}, doi = {10.1016/j.artint.2011.01.007}, url = {http://dx.doi.org/10.1016/j.artint.2011.01.007}, author = {Matthias Knorr and Jos{\'e} J{\'u}lio Alferes and Pascal Hitzler} } @article {80, title = {Concept learning in description logics using refinement operators}, journal = {Machine Learning}, volume = {78}, year = {2010}, pages = {203{\textendash}250}, abstract = {

With the advent of the Semantic Web, description logics have become one of the most prominent paradigms for knowledge representation and reasoning. Progress in research and applications, however, is constrained by the lack of well-structured knowledge bases consisting of a sophisticated schema and instance data adhering to this schema. It is paramount that suitable automated methods for their acquisition, maintenance, and evolution will be developed. In this paper, we provide a learning algorithm based on refinement operators for the description logic ALCQ including support for concrete roles. We develop the algorithm from thorough theoretical foundations by identifying possible abstract property combinations which refinement operators for description logics can have. Using these investigations as a basis, we derive a practically useful complete and proper refinement operator. The operator is then cast into a learning algorithm and evaluated using our implementation DL-Learner. The results of the evaluation show that our approach is superior to other learning approaches on description logics, and is competitive with established ILP systems.

}, keywords = {description logics, Inductive logic programming, OWL, refinement operators, Semantic Web, Structured Machine Learning}, url = {http://springerlink.metapress.com/content/c040n45u15qrnu44/}, author = {Jens Lehmann and Pascal Hitzler} } @article {78, title = {A Reasonable Semantic Web}, journal = {Semantic Web}, volume = {1}, year = {2010}, pages = {39{\textendash}44}, abstract = {

The realization of Semantic Web reasoning is central to substantiating the Semantic Web vision. However, current mainstream research on this topic faces serious challenges, which forces us to question established lines of research and to rethink the underlying approaches. We argue that reasoning for the Semantic Web should be understood as "shared inference," which is not necessarily based on deductive methods. Model-theoretic semantics (and sound and complete reasoning based on it) functions as a gold standard, but applications dealing with large-scale and noisy data usually cannot afford the required runtimes. Approximate methods, including deductive ones, but also approaches based on entirely different methods like machine learning or natureinspired computing need to be investigated, while quality assurance needs to be done in terms of precision and recall values (as in information retrieval) and not necessarily in terms of soundness and completeness of the underlying algorithms.

}, keywords = {Automated Reasoning, Formal Semantics, Knowledge representation, Linked Open Data, Semantic Web}, doi = {10.3233/SW-2010-0010}, url = {http://dx.doi.org/10.3233/SW-2010-0010}, author = {Pascal Hitzler and Frank van Harmelen} }