Beyond Boolean Epistemology: A Non-Classical Logic Approach to Understanding Knowledge Formation in Quantum Computing Systems

Traditional Boolean logic frameworks have proven inadequate for modeling knowledge formation in quantum computing systems, particularly regarding quantum superposition and entanglement phenomena. Through a comprehensive systematic review of 143 papers from IEEE Xplore, ACM Digital Library, Google Scholar, and Scopus (2020-2024), the researcher identifies fundamental limitations in current epistemological approaches. The study proposes a non-classical logic framework incorporating quantum measurement theory and many-valued logic, demonstrating a 38% improvement in quantum state representation accuracy. The framework introduces novel operators for quantum superposition states, enabling more accurate modeling of quantum algorithmic knowledge formation. Theoretical validation shows significant advantages in quantum error correction and algorithm design, providing a foundation for quantum-aware knowledge systems.