Light has long been investigated as a medium in which to realize logic. The invention of the laser in 1958 generated great interest in optical logic, as a source of coherent light was now available. Various implementations of optical logic have since been proposed. An all-optical logic paradigm could in principle offer advantages over electronics. However, semiconductor electronics remain the dominant method of conducting logical operations. In this work, a novel means of realizing optical logic, called interference logic, using passive silicon-on-insulator waveguiding elements is described and demonstrated. The origins of the paradigm are discussed, as well as the method by which an arbitrary Boolean logic function can be realized. The results of the design, simulation, fabrication, and test of rib waveguides and multi-mode interference devices used to construct the logic are presented. Additional optical logic device designs are proposed and are demonstrated through the use of computer simulation.