The Theory of Non-Knowledge as a Meta-Logical Framework for Optimality: A Formal Application to the Traveling Salesman Problem

This paper proposes a formal application of the Theory of Non-Knowledge (TNK) to the Traveling Salesman Problem (TSP), a canonical case in combinatorial optimization. It is argued that the nullification operator (∿), as introduced by Souza (2025), provides a meta-logical mechanism to eliminate epistemic contradictions and isolate the admissible statements that survive nullification. When TNK is applied to the corpus of tour-cost statements and certificates of a TSP instance, the optimal solution coincides with the subset of propositions that remain non-nullified. The study integrates classical results from complexity theory and operations research, showing that TNK serves as a reference for “optimality” and enables formal proofs of suboptimality