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We present a novel multi-valued computation framework called Wave Interference Functions (WIF), based on emerging non-equilibrium wave phenomenon such as spin waves. WIF offers new features for data representation and computation, which can be game changing for post-CMOS integrated circuits (ICs). Information encoding wave attributes inherently leads to multi-dimensional multi-valued data representation and communication. Multi-valued computation is natively supported with wave interactions, such as wave superposition or interference. We introduce the concept of a multi-valued Interference Function that is more sophisticated than conventional Boolean and Majority functions, leading to compact circuits for logic. We present WIF implementation of multi-valued operators to realize any desired logic/arithmetic function using the Interference Function. We evaluate 2-digit to 16-digit quaternary (radix-4) full adder designs with WIF operators in terms of power, performance and area. Estimates indicate up to 63x higher density, 884x lower power and 3x better performance when compared to equivalent 45nm CMOS adders. WIF features completely change conventional assumptions on circuit design, opening new avenues to implement future nanoscale ICs for general purpose processing and other applications inherently suited to multi-valued computation.