Chrysippus’ Logic in a Natural Deduction Setting

In this paper, we zoom in on some important features of Chrysippus’ logic by framing them in a natural deduction system for relevant logic. Our view is alternative to other recent reconstructions of Chrysippus’ view based on the sequent calculus. We show how, adding suitable elimination rules (akin to the five indemonstrables) that are missing in the Chrysippean system, one automatically obtains classical logic as a kind of deductive upper bound.