The objective of this paper is to achieve tracking control of a class of unknown nonlinear dynamical systems using a discrete-time fuzzy logic controller (FLC). Designing a discrete-time FLC is significant because almost all FLCs are implemented on digital computers. We present a repeatable design algorithm and a stability proof for an adaptive fuzzy logic controller that uses basis vectors based on the fuzzy system, unlike most standard adaptive control approaches which use basis vectors depending on the unknown plant (e.g. a tediously computed "regression matrix"). An E-modification sort of approach to adapt the fuzzy system parameters was selected. With mild assumptions on the class of discrete-time nonlinear systems, this adaptive fuzzy logic controller guarantees uniform ultimate boundedness of the closed-loop signals and that the controller achieves tracking. In fact, the fuzzy system designed is a model-free universal fuzzy controller that works for a more general class of nonlinear systems. Some new passivity properties of fuzzy logic systems are introduced.