@article {62, title = {Reasoning with Inconsistencies in Hybrid MKNF Knowledge Bases}, journal = {Logic Journal of the IGPL}, volume = {21}, year = {2013}, pages = {263{\textendash}290}, abstract = {This paper is concerned with the handling of inconsistencies occurring in the combination of description logics and rules, especially in hybrid MKNF knowledge bases. More precisely, we present a paraconsistent semantics for hybrid MKNF knowledge bases (called para-MKNF knowledge bases) based on four-valued logic as proposed by Belnap. We also reduce this paraconsistent semantics to the stable model semantics via a linear transformation operator, which shows the relationship between the two semantics and indicates that the data complexity in our paradigm is not higher than that of classical reasoning. Moreover, we provide fixpoint operators to compute paraconsistent MKNF models, each suitable to different kinds of rules. At last we present the data complexity of instance checking in different paraMKNF knowledge bases.}, keywords = {Data complexity, Description logics and rules, Knowledge representation, Non-monotonic reasoning, Paraconsistent reasoning}, doi = {10.1093/jigpal/jzs043}, url = {http://dx.doi.org/10.1093/jigpal/jzs043}, author = {Shasha Huang and Qingguo Li 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 {83, title = {Computational Complexity and Anytime Algorithm for Inconsistency Measurement}, journal = {International Journal of Software and Informatics}, volume = {4}, year = {2010}, pages = {3{\textendash}21}, abstract = {

Measuring inconsistency degrees of inconsistent knowledge bases is an important problem as it provides context information for facilitating inconsistency handling. Many methods have been proposed to solve this problem and a main class of them is based on some kind of paraconsistent semantics. In this paper, we consider the computational aspects of inconsistency degrees of propositional knowledge bases under 4-valued semantics. We first give a complete analysis of the computational complexity of computing inconsistency degrees. As it turns out that computing the exact inconsistency degree is intractable, we then propose an anytime algorithm that provides tractable approximations of the inconsistency degree from above and below. We show that our algorithm satisfies some desirable properties and give experimental results of our implementation of the algorithm

}, keywords = {algorithm, computational complexity, inconsistency measurement, Knowledge representation, multi-valued logic}, url = {http://www.ijsi.org/ch/reader/view_abstract.aspx?file_no=i41\&flag=1}, author = {Yue Ma and Guilin Qi and Guohui Xiao and Pascal Hitzler and Zuoquan Lin} } @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} }