<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Shasha Huang</style></author><author><style face="normal" font="default" size="100%">Qingguo Li</style></author><author><style face="normal" font="default" size="100%">Pascal Hitzler</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Reasoning with Inconsistencies in Hybrid MKNF Knowledge Bases</style></title><secondary-title><style face="normal" font="default" size="100%">Logic Journal of the IGPL</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">Data complexity</style></keyword><keyword><style  face="normal" font="default" size="100%">Description logics and rules</style></keyword><keyword><style  face="normal" font="default" size="100%">Knowledge representation</style></keyword><keyword><style  face="normal" font="default" size="100%">Non-monotonic reasoning</style></keyword><keyword><style  face="normal" font="default" size="100%">Paraconsistent reasoning</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2013</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://dx.doi.org/10.1093/jigpal/jzs043</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">21</style></volume><pages><style face="normal" font="default" size="100%">263–290</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">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.</style></abstract></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>47</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Shasha Huang</style></author><author><style face="normal" font="default" size="100%">Qingguo Li</style></author><author><style face="normal" font="default" size="100%">Pascal Hitzler</style></author></authors><secondary-authors><author><style face="normal" font="default" size="100%">Sebastian Rudolph</style></author><author><style face="normal" font="default" size="100%">Claudio Gutierrez</style></author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Paraconsistent Semantics for Hybrid MKNF Knowledge Bases</style></title><secondary-title><style face="normal" font="default" size="100%">Web Reasoning and Rule Systems - 5th International Conference, RR 2011</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2011</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://dx.doi.org/10.1007/978-3-642-23580-1_8</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">Springer</style></publisher><pub-location><style face="normal" font="default" size="100%">Galway, Ireland</style></pub-location><volume><style face="normal" font="default" size="100%">6902</style></volume><pages><style face="normal" font="default" size="100%">93–107</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;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.&lt;/p&gt;
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