[1] Da Costa's international recognition came especially through his work on paraconsistent logic and its application to various fields such as philosophy, law, computing, and artificial intelligence.

[1] Da Costa and physicist Francisco Antônio Dória axiomatized large portions of classical physics with the help of Patrick Suppes' predicates.

Together with Francisco Antônio Dória, Da Costa published two papers with conditional relative proofs of the consistency of P = NP with the usual set-theoretic axioms ZFC.

The 2003 conditional result can be reformulated, according to da Costa and Doria 2006, as So far no formal argument has been constructed to show that ZFC + [P = NP]' is ω-consistent.

In his reviews for Mathematical Reviews of the da Costa/Doria papers on P=NP, logician Andreas Blass states that "the absence of rigor led to numerous errors (and ambiguities)"; he also rejects da Costa's "naïvely plausible condition", as this assumption is "based partly on the possible non-totality of [a certain function] F and partly on an axiom equivalent to the totality of F".