Nonlinear optics has been of increased interest for all-optical signal, data and image processing in high speed photonic networks. The application of multi-valued (nonbinary) digital signals can provide considerable relief in transmission, storage and processing of a large amount of information in digital signal processing. Here, we propose the design of an all-optical system for some basic tri-state logic operations (trinary OR, trinary AND, trinary XOR, Inverter, Truth detector, False detector) which exploits the polarization properties of light. Nonlinear material based optical switch can play an important role. Tri-state logic can play a significant role towards carry and borrow free arithmetic operations. The principles and possibilities of the design of nonlinear material based tri-state logic circuits are proposed and described.