A completeness theorem for a functionally complete Łukasiewicz logic
Radzki 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...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/123833 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/123833 |
| Access Level: | acceso abierto |
| Palabra clave: | 164 Many-valued logics Three-valued logics Propositional logic Non-classical logics Fuzzy logic Lógica (Filosofía) 1102.08 Lógica Matemática 1102.05 Sistemas Formales 1102.12 Cálculo Proposicional |
| Sumario: | Radzki 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. |
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