Aranda Utrero, Víctor2025-09-112025-09-112025Aranda, V. (2025) “A Completeness Theorem for a Functionally Complete Łukasiewicz Logic”, Logic and Logical Philosophy, pp. 1–12. doi: 10.12775/LLP.2025.014.1425-330510.12775/LLP.2025.014https://hdl.handle.net/20.500.14352/123833Radzki has recently claimed the incompleteness of the axioms given by Słupecki for the functionally complete Ł3: some of its tautologies are not provable. In this paper, we provide a new axiom system for this logic (choosing a variant with two propositional constants and the Łukasiewicz implication as primitive symbols) and prove a Completeness Theorem.engAttribution-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nd/4.0/journal article2300-9802https://doi.org/10.12775/LLP.2025.014https://apcz.umk.pl/LLP/article/view/65115open access164Many-valued logicsThree-valued logicsPropositional logicNon-classical logicsFuzzy logicLógica (Filosofía)1102.08 Lógica Matemática1102.05 Sistemas Formales1102.12 Cálculo Proposicional