Recently, negative differential resistance devices have attracted considerable attention due to their folded current-voltage characteristic, which presents multiple threshold voltage values. Because of this remarkable property, studies associated with the negative differential resistance devices have been explored for realizing multi-valued logic applications. Here we demonstrate a negative differential resistance device based on a phosphorene/rhenium disulfide (BP/ReS2) heterojunction that is formed by type-III broken-gap band alignment, showing high peak-to-valley current ratio values of 4.2 and 6.9 at room temperature and 180 K, respectively. Also, the carrier transport mechanism of the BP/ReS2 negative differential resistance device is investigated in detail by analysing the tunnelling and diffusion currents at various temperatures with the proposed analytic negative differential resistance device model. Finally, we demonstrate a ternary inverter as a multi-valued logic application. This study of a two-dimensional material heterojunction is a step forward toward future multi-valued logic device research.