Single-track conical nanopores functionalized with polyprotic acid chains have pH-sensitive fixed charge groups and show three levels of conductance that allow integrating several functions on a single nanofluidic diode. Nanometer-scaled pores have previously been employed in separation and sensing but not in logic devices, despite the fact that biological ion channels with pH-dependent fixed charges are known to be responsible for information processing in biophysical structures. As a preliminary application, we propose a logic gate scheme where binary and multivalued logical functions are implemented.