Optical logic gates are elementary components for optical network and optical computing. In this paper, we propose a structure for AND, NAND, XNOR and NOR logic gates in the two dimensional photonic crystal which utilizes the dispersion based self-collimation effect. The self-collimated beam is splitted by the line defect and interfered with other self-collimated beam. This interference may be constructive or destructive based on their phase difference. This phenomenon is employed to realize all-optical logic gates. The gates are demonstrated numerically by computing electromagnetic field distribution using the finite difference time domain (FDTD) method. The results ensure that this design can function as AND, NAND, XNOR and NOR logic gates. The size of the structure is about 10 μm×10 μm which in turn results in an increase in the speed and all the gates are realized in the same configuration. The ON-OFF contrast ratio is about 6 dB.