We propose a method to design two-dimensional photonic crystal all-optical logic gates based on the linear interference effect and ring resonators. The phase difference is generated by introducing the optical path difference in the ring cavity, which leads to the constructive or destructive interference of light waves. Thus, optical logic gates, such as OR, AND, XOR, NOT, NOR, and NAND, are realized. The plane-wave expansion and time-domain finite-difference methods are used to simulate the logic devices and verify the logic functions. The results demonstrate that small-sized devices can be realized. In addition, the devices have a high transmittance rate, high contrast ratio, and fast response time(less than 218 fs). The design has potential application in the field of integrated optics.