About Opposition and Duality in Paraconsistent Type Theory

Abstract

A paraconsistent type theory (an extension of a fragment of intuitionistic type theory by adding opposite types) is here extended by adding co-function types. It is shown that, in the extended paraconsistent type system, the opposite type constructor can be viewed as an involution operation that transforms each type into its dual type. Moreover, intuitive interpretations of opposite and co-function types under different interpretations of types are discussed.