Extending Paraconsistent \mathcal{SROIQ}

TLDR: It is shown that the modified logic is classically sound and that its embedding into classical \(\mathcal{SROIQ}\) is consequence preserving, and inserting special axioms into a knowledge base allows additional nontrivial conclusions to be drawn, without affecting paraconsistency.

Abstract: The four-valued paraconsistent logic \(\mathcal{SROIQ}4\), originally presented by Ma and Hitzler, is extended to incorporate additional elements of \(\mathcal{SROIQ}\). It is shown that the modified logic is classically sound and that its embedding into classical \(\mathcal{SROIQ}\) is consequence preserving. Furthermore, inserting special axioms into a \(\mathcal{SROIQ}4\) 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 \(\mathcal{SROIQ}4\) knowledge bases from having models. For such knowledge bases, the logic remains explosive.