This paper introduces a novel analytical framework based on Boolean algebra for modeling and analyzing Non-Orthogonal Multiple Access (NOMA) systems. Departing from conventional signal-to-interference-plus-noise ratio (SINR) based models, the proposed approach conceptualizes the Successive Interference Cancellation (SIC) process in a two-user interference channel as a probabilistic system of logical events. The core contribution is a systematic procedure that transforms the SIC decoding problem into a Boolean model, subsequently simplified and analyzed using techniques such as Karnaugh maps. This framework is demonstrated for systems characterized by 2, 4, and 5 elements, showcasing its capability to capture the fundamental logical interdependencies of SIC. The Boolean approach provides a new, complementary perspective for NOMA analysis, offering a structured methodology to evaluate decoding performance and system complexity in interference-limited environments.