A Tractable Paraconsistent Fuzzy Description Logic

In this paper, we introduce the tractable pf-EL++ logic, a paraconsistent version of the fuzzy logic f-EL++. Within pf-EL++, it is possible to tolerate contradictions under incomplete and vague knowledge. pf-EL++ extends the f-EL++ language with a paraconsistent negation in order to represent contradictions. This paraconsistent negation is defined under Belnap's bilattices. It is important to observe that pf -EL++ is a conservative extension of f-EL++, thus assuring that the polynomial-time reasoning algorithm used in f-EL++ can also be used in pf -EL++.