@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}
}
@conference {98,
	title = {Paraconsistent Semantics for Hybrid MKNF Knowledge Bases},
	booktitle = {Web Reasoning and Rule Systems - 5th International Conference, RR 2011},
	volume = {6902},
	year = {2011},
	pages = {93{\textendash}107},
	publisher = {Springer},
	organization = {Springer},
	address = {Galway, Ireland},
	abstract = {<p class="rtejustify">Hybrid MKNF knowledge bases, originally based on the stable model semantics, is a mature method of combining rules and Description Logics (DLs). The well-founded semantics for such knowledge bases has been proposed subsequently for better efficiency of reasoning. However, integration of rules and DLs may give rise to inconsistencies, even if they are respectively consistent. Accordingly, reasoning systems based on the previous two semantics will break down. In this paper, we employ the four-valued logic proposed by Belnap, and present a paraconsistent semantics for Hybrid MKNF knowledge bases, which can detect inconsistencies and handle it effectively. Besides, we transform our proposed semantics to the stable model semantics via a linear transformation operator, which indicates that the data complexity in our paradigm is not higher than that of classical reasoning. Moreover, we provide a fixpoint algorithm for computing paraconsistent MKNF models.</p>
},
	doi = {10.1007/978-3-642-23580-1_8},
	url = {http://dx.doi.org/10.1007/978-3-642-23580-1_8},
	author = {Shasha Huang and Qingguo Li and Pascal Hitzler},
	editor = {Sebastian Rudolph and Claudio Gutierrez}
}
