This paper presents fundamental logic structures designed using novel quantum dot gate FETs with three-state characteristics. This three-state FET manifests itself as a transistor with a stable "intermediate" state, where the drain current remains constant over a range of input gate voltages due to a change in the threshold voltage over this range. We have developed a simplified circuit model that accounts for this intermediate state. Using this model, we have designed rudimentary logic circuits for use in multiple-valued logic circuits.