Memristive stateful logic refers to a form of computational logic in which memristors both store logic values and perform logical operations on these values. We present a generalized form of memristive stateful logic and define the logic operations realizable in this form. We also consider the CMOS circuitry required for reliable implementation of memristive stateful logic. Furthermore, synthesis of arbitrary Boolean functions and the parallelization of stateful logic to memristive crossbars is presented.