Sette’s calculus P1 and some hierarchies of paraconsistent systems

The necessary condition for a calculus to be paraconsistent is that its consequence relation is not explosive. This results in rejection of the principle of ex contradictione sequitur quodlibet. In 1973, Sette presented a calculus, denoted as P^1 which is paraconsistent only at the atomic level, i.e. \alpha and {\sim }\alpha yield any \beta if, and only if the formula \alpha is not a propositional variable. The calculus has been...