Paraconsistent algebras

The prepositional calculiC_n, 1 n introduced by N.C.A. da Costa constitute special kinds of paraconsistent logics. A question which remained open for some time concerned whether it was possible to obtain a Lindenbaum's algebra forC_n. C. Mortensen settled the problem, proving that no equivalence relation forC_n. determines a non-trivial quotient algebra.The concept of da Costa algebra, which reflects most of the logical properties ofC_n, as well as the concept of paraconsistent closure system, are introduced in this paper.We show that every da Costa algebra is isomorphic with a paraconsistent algebra of sets, and that the closure system of all filters of a da Costa algebra is paraconsistent.