Extending Paraconsistent SROIQ

The four-valued paraconsistent logic SROIQ4, originally presented by Ma and Hitzler, is extended to incorporate additional elements of SROIQ. It is shown that the modified logic is classically sound and that its embedding into classical SROIQ is consequence preserving. Furthermore, inserting special axioms into a SROIQ4 knowledge base allows additional nontrivial conclusions to be drawn, without affecting paraconsistency. It is also shown that the interaction of nominals and cardinality restrictions prevents some SROIQ4 knowledge bases from having models. For such knowledge bases, the logic remains explosive.