Can a paraconsistent differential calculus extend the classical differential calculus?

Itala M. Loffredo D'Ottaviano (Campinas) gives a talk at the Conference on Paraconsistent Reasoning in Science and Mathematics (11-13 June, 2014) titled "Can a paraconsistent differential calculus extend the classical differential calculus?". Abstract:In 2000, da Costa proposes the construction of a paraconsistent differential calculus, whose language is the language L of his known paraconsistent logic C1, extended to the language of his paraconsistent set theory CHU1, introduced in 1986. We have studied and improved the calculus proposed by da Costa, having obtained extensions of several fundamental theorems of the classical differential calculus. From the introduction of the concept of paraconsistent super-structure X over a set X of atoms of CHU1 and of the concept of monomorphism between paraconsistent super-structures, we will present a Transference Theorem that “translates” the classical differential calculus into da Costa’s paraconsistent calculus.