A Constructively Complete Classification of Trinary Logic Within Classical Mathematics

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.