Paraconsistent circumscription: first-order case

In this paper we describe paraconsistent circumscription by application of predicate circumscription in a paraconsistent logic. In addition to circumscribe the predicates, we also circumscribe the inconsistency. Paraconsistent circumscription can be well characterized by the minimal semantics that is both nonmonotonic and paraconsistent. It brings us advantages at least in two respects: nonmonotonic logic would be nontrivial while there was a contradiction, and paraconsistent logic would be equivalent to classical logic while there was no direct effect of a contradiction