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Recent advances in neurobiology and the biophysics of neural computation have brought to the foreground the importance of dendritic structures of neurons. These structures are now viewed as the primary basic computational units of the neuron, capable of realizing logical operations. Based on these new biophysical neural models, we develop a new paradigm for single layer perceptrons that incorporates dendritic processes. The basic computational processes in dendrites as well as neurons are based on lattice algebra. The computational capabilities of this new perceptron model is demonstrated by means of several illustrative examples and two theorems.