A Quantum-Inspired Multi-Valued Logic for Resolving Paradoxes

This paper extends the framework of single-valued (S), multi-valued (M), and no-valued (N) numbers introduced by Towne (2024) into a quantum-inspired logical system to address classical paradoxes. We introduce a Möbius strip model to formalize undecidable propositions, such as Gödel's "This proposition cannot be proven," as non-collapsible multi-valued states. Collapsible multi-valued states resolve paradoxes like Russell’s, the Barber, the Liar, and the Absence-Presence paradox through a collapse mechanism akin to quantum measurement. Building on Towne’s resolutions of Russell’s and Barber paradoxes using Axiom 5.5 (Towne, 2024), we refine the axioms and provide detailed proofs to demonstrate the system’s consistency and broader applicability.