An elementary proof of chang's completeness theorem for the infinite-valued calculus of Łukasiewicz
The interpretation of propositions in Łukasiewicz's infinite-valued calculus as answers in Ulam's game with lies-the Boolean case corresponding to the traditional Twenty Questions game-gives added interest to the completeness theorem. The literature contains several different proofs, but t...
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todo:paper_00393215_v58_n1_p79_Cignoli2023-10-03T14:49:41Z An elementary proof of chang's completeness theorem for the infinite-valued calculus of Łukasiewicz Cignoli, R. Mundici, D. Completeness of the Łukasiewicz calculus Infinite-valued logic MV algebra The interpretation of propositions in Łukasiewicz's infinite-valued calculus as answers in Ulam's game with lies-the Boolean case corresponding to the traditional Twenty Questions game-gives added interest to the completeness theorem. The literature contains several different proofs, but they invariably require technical prerequisites from such areas as model-theory, algebraic geometry, or the theory of ordered groups. The aim of this paper is to provide a self-contained proof, only requiring the rudiments of algebra and convexity in finite-dimensional vector spaces. © 1997 Kluwer Academic Publishers. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00393215_v58_n1_p79_Cignoli |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Completeness of the Łukasiewicz calculus Infinite-valued logic MV algebra |
| spellingShingle |
Completeness of the Łukasiewicz calculus Infinite-valued logic MV algebra Cignoli, R. Mundici, D. An elementary proof of chang's completeness theorem for the infinite-valued calculus of Łukasiewicz |
| topic_facet |
Completeness of the Łukasiewicz calculus Infinite-valued logic MV algebra |
| description |
The interpretation of propositions in Łukasiewicz's infinite-valued calculus as answers in Ulam's game with lies-the Boolean case corresponding to the traditional Twenty Questions game-gives added interest to the completeness theorem. The literature contains several different proofs, but they invariably require technical prerequisites from such areas as model-theory, algebraic geometry, or the theory of ordered groups. The aim of this paper is to provide a self-contained proof, only requiring the rudiments of algebra and convexity in finite-dimensional vector spaces. © 1997 Kluwer Academic Publishers. |
| format |
JOUR |
| author |
Cignoli, R. Mundici, D. |
| author_facet |
Cignoli, R. Mundici, D. |
| author_sort |
Cignoli, R. |
| title |
An elementary proof of chang's completeness theorem for the infinite-valued calculus of Łukasiewicz |
| title_short |
An elementary proof of chang's completeness theorem for the infinite-valued calculus of Łukasiewicz |
| title_full |
An elementary proof of chang's completeness theorem for the infinite-valued calculus of Łukasiewicz |
| title_fullStr |
An elementary proof of chang's completeness theorem for the infinite-valued calculus of Łukasiewicz |
| title_full_unstemmed |
An elementary proof of chang's completeness theorem for the infinite-valued calculus of Łukasiewicz |
| title_sort |
elementary proof of chang's completeness theorem for the infinite-valued calculus of łukasiewicz |
| url |
http://hdl.handle.net/20.500.12110/paper_00393215_v58_n1_p79_Cignoli |
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