The Theory of Non-Knowledge as a Meta-Logical Framework for Optimality: A Formal Application to the Traveling Salesman Problem
Year: 2025
Type: article
Abstract: 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
Author: Souza, Euclides
Institution: Universidade Federal da Paraíba
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7095065463
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