Non-classical Reasoning With A Combination Of Ontologies And Rules In The Semantic Web

It is an important topic in Semantic Web to combine open world ontologylanguage, such as OWL-based language, with closed world rule-based language.Hybrid MKNF knowledge bases, originally based on the stable model semantics,is a mature method of combining rules and Description Logics (DLs). It has fa-vorable features, such as faithfulness, tightness, fexibility and decidability. Thewell-founded semantics for such knowledge bases has been proposed subsequentlyfor better efciency of reasoning. However, integration of rules and DLs may giverise to inconsistencies, even if they are respectively consistent. Accordingly, reason-ing systems based on the previous two semantics will break down. Moreover, theexisting semantics can not represent and reason with fuzzy information occurringin the knowledge base.In this paper, we employ the four-valued logic proposed by Belnap, and presenta paraconsistent semantics for hybrid MKNF knowledge bases (called para-MKNFknowledge bases). We also reduce this paraconsistent semantics to the stable modelsemantics via a linear transformation operator, which shows the relationship be-tween the two semantics and indicates that the data complexity in our paradigmis not higher than that of classical reasoning. Moreover, we provide fxpoint op-erators to compute paraconsistent MKNF models, each suitable to diferent kindsof rules. Besides, we present the data complexity of instance checking in diferentpara-MKNF knowledge bases.When the knowledge base contains incoherent information, reasoning systemthat is based on paraconsistent semantics will break down. Therefore, we introducea semi-S5semantics for hybrid MKNF knowledge bases on the basis of nine-valuedlattice, such that it is paraconsistent for incoherent knowledge base. It is shownthat a semi-S5model can be computed via a fxpoint operator and is in fact a para-consistent MKNF model when the knowledge base is incoherent. Also, we applysix-valued lattice to hybrid MKNF knowledge bases, present a suspicious seman-tics to distinguish diferent trust level information, and investigate the relationshipbetween suspicious semantics and paraconsistent semantics.Furthermore, we apply fuzzy set theory to hybrid MKNF knowledge bases,and establish fuzzy hybrid MKNF knowledge bases, which is sound with respectto the classical two-valued semantics. Also, we discuss fundamental properties offuzzy semantics by some examples, and characterize fuzzy MKNF models of general MKNF knowledge bases. We provide characterizations of fuzzy MKNF models ofpositive and stratifed MKNF knowledge bases in terms of a fxpoint operator andan iterative fxpoint semantics, respectively. Finally, we describe a special case offuzzy nondisjunctive positive MKNF knowledge base, in which the truth value ofa modal atom can be computed in polynomial time in the data complexity.