A Constructively Complete Classification of Trinary Logic Within Classical Mathematics
Year: 2025
Type: article
Abstract: This work presents a constructively complete classification of trinary logic methods under classical mathematical constraints. Using only first-order logic, Peano arithmetic, and ZFC set theory, the system exhaustively enumerates 500 constructively distinct trinary logic operations defined over the truth values {0, 1, null}. Each method is deterministic, irreducible, and formally verifiable, and the classification spans 21 classical domains grouped into a layered structural framework. All methods are derived without speculative or non-classical constructs, and a formal closure argument proves that no additional distinct methods exist within the defined logical space. This work establishes a finite and exhaustive foundation for trinary logic within the bounds of classical mathematics.
Author: Daniels, Justin
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6931042085
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