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Reconfigurable organic logic devices are promising candidates for next generations of efficient computing systems and adaptive electronics. Ideally, such devices would be of simple structure and design, be power efficient, and compatible with high-throughput microfabrication techniques. This work reports an organic reconfigurable logic gate based on novel dual-mode organic electrochemical transistors (OECTs), which employ a self-doped conjugated polyelectrolyte as the active material, which then allows the transistors to operate in both depletion mode and enhancement mode. Furthermore, mode switching is accomplished by simply altering the polarity of the applied gate and drain voltages, which can be done on the fly. In contrast, achieving similar mode-switching functionality with other organic transistors typically requires complex molecular design or multi-device engineering. It in shown that dual-mode functionality is enabled by the concurrent existence of anion doping and cation dedoping of the films. A device physics model that accurately describes the behavior of these transistors is developed. Finally, the utility of these dual-mode transistors for implementing reconfigurable logic by fabricating a logic gate that may be switched between logic gates AND to NOR, and OR to NAND on the fly is demonstrated.