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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| Lenguaje: | Inglés |
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Springer Netherlands
1997
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| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
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| LEADER | 04009caa a22004577a 4500 | ||
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| 001 | PAPER-20118 | ||
| 003 | AR-BaUEN | ||
| 005 | 20230518205131.0 | ||
| 008 | 190411s1997 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-0002924587 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Cignoli, R. | |
| 245 | 1 | 3 | |a An elementary proof of chang's completeness theorem for the infinite-valued calculus of Łukasiewicz |
| 260 | |b Springer Netherlands |c 1997 | ||
| 270 | 1 | 0 | |m Cignoli, R.; Departamento de Matemática, Facultad de Ciencias Exactas, Ciudad Universitaria, 1428 Buenos Aires, Argentina; email: postmast@cignol.uba.ar |
| 506 | |2 openaire |e Política editorial | ||
| 504 | |a Chang, C.C., Algebraic analysis of many-valued logics (1958) Trans. Amer. Math. Soc., 88, pp. 467-490 | ||
| 504 | |a Chang, C.C., A new proof of the completeness of the Łukasiewicz axioms (1959) Trans. Amer. Math. Soc., 93, pp. 74-80 | ||
| 504 | |a Cignoli, R., Free lattice-ordered abelian groups and varieties of MV-algebras (1993) Notas de Lógica Matemática, Universidad National Del Sur, Bahía Bianca, Argentina, 38, pp. 113-118. , Proceedings of the IXth Latin American Symposium on Mathematical Logic, I | ||
| 504 | |a Mangani, P., On certain algebras related to many-valued logics (1973) Bollettino Unione Matematica Italiana, 8, pp. 68-78 | ||
| 504 | |a Mundici, D., Interpretation of AF C-algebras in Łukasiewicz sentential calculus (1986) J. Functional Analysis, 65, pp. 15-63 | ||
| 504 | |a Mundici, D., Ulam game, Łukasiewicz logic, and AF C -algebras (1993) Fundamenta Informaticae, 18, pp. 151-161 | ||
| 504 | |a Panti, G., A geometric proof of the completeness of the calculus of Łukasiewicz (1995) J. Symbolic Logic, 60, pp. 563-578 | ||
| 504 | |a Rose, A., Rosser, J.B., Fragments of many-valued statement calculi (1958) Trans. Amer. Math. Soc., 87, pp. 1-53 | ||
| 504 | |a Tarski, A., ŁUkasiewicz, J., Investigations into the Sentential Calculus (1956) Logic, Semantics, Metamathematics, pp. 38-59. , Oxford University Press, reprinted by Hackett Publishing Company, Indianapolis, 1983 | ||
| 504 | |a Ulam, S.M., (1976) Adventures of A Mathematician, , Scribner's, New York | ||
| 520 | 3 | |a 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. |l eng | |
| 593 | |a Departamento de Matemática, Facultad de Ciencias Exactas, Ciudad Universitaria, 1428 Buenos Aires, Argentina | ||
| 593 | |a Department of Computer Science, University of Milan, Via Comelico 39-41, 20135 Milan, Italy | ||
| 690 | 1 | 0 | |a COMPLETENESS OF THE ŁUKASIEWICZ CALCULUS |
| 690 | 1 | 0 | |a INFINITE-VALUED LOGIC |
| 690 | 1 | 0 | |a MV ALGEBRA |
| 700 | 1 | |a Mundici, D. | |
| 773 | 0 | |d Springer Netherlands, 1997 |g v. 58 |h pp. 79-97 |k n. 1 |p Stud. Logica |x 00393215 |w (AR-BaUEN)CENRE-365 |t Studia Logica | |
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| 856 | 4 | 0 | |u https://doi.org/10.1023/A:1004991931741 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_00393215_v58_n1_p79_Cignoli |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393215_v58_n1_p79_Cignoli |y Registro en la Biblioteca Digital |
| 961 | |a paper_00393215_v58_n1_p79_Cignoli |b paper |c PE | ||
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