Demonstrates an algebraic framework for truth values in the complex plane, suggesting profound implications for understanding belief dynamics.
Standard TRALSE logic assigns truth values in [0,1] — a real-valued spectrum between classical True (1) and False (0). This paper extends TRALSE to the complex plane, introducing **Tralse Wave Algebra (TWA)**: a complete algebraic system in which truth values are complex numbers τ = r + iφ (r = real truth magnitude, φ = imaginary truth phase), and logical operations are defined as wave interactions. The central insight: truth is not a static magnitude but a wave — it oscillates, interferes, propagates, and decays. Classical logic treats truth as DC (zero-frequency); TRALSE Wave Algebra treats truth as AC (finite frequency), with the classical case as the zero-frequency limit. This unlocks: (1) truth interference — two beliefs can constructively or destructively cancel each other; (2) truth resonance — related beliefs can amplify each other through phase alignment; (3) truth decay — isolated beliefs lose coherence over time; and (4) the Tralse Fourier Transform — any complex belief state can be decomposed into fundamental truth frequencies. Applications include belief dynamics modeling, LCC-based epistemics, and the formal grounding of Myrion Resolution as wave convergence.
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Brandon Charles Emerick (2026) studied this question.
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