Using extensive room-temperature molecular dynamics simulations, we investigate selective aqueous cation trapping and permeation in graphene-embedded 18-crown-6 ether pores. We show that in the presence of suspended water-immersed crown-porous graphene, K<sup>+</sup> ions rapidly organize and trap stably within the pores, in contrast with Na<sup>+</sup> ions. As a result, significant qualitative differences in permeation between ionic species arise. The trapped ion occupancy and permeation behaviors are shown to be highly voltage-tunable. Interestingly, we demonstrate the possibility of performing conceptually straightforward ion-based logical operations resulting from controllable membrane charging by the trapped ions. In addition, we show that ionic transistors based on crown-porous graphene are possible, suggesting utility in cascaded ion-based logic circuitry. Our results indicate that in addition to numerous possible applications of graphene-embedded crown ether nanopores, including deionization, ion sensing/sieving, and energy storage, simple ion-based logical elements may prove promising as building blocks for reliable nanofluidic computational devices.