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Abstract:

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.

Registro:

Documento: Artículo
Título:An elementary proof of chang's completeness theorem for the infinite-valued calculus of Łukasiewicz
Autor:Cignoli, R.; Mundici, D.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas, Ciudad Universitaria, 1428 Buenos Aires, Argentina
Department of Computer Science, University of Milan, Via Comelico 39-41, 20135 Milan, Italy
Palabras clave:Completeness of the Łukasiewicz calculus; Infinite-valued logic; MV algebra
Año:1997
Volumen:58
Número:1
Página de inicio:79
Página de fin:97
DOI: http://dx.doi.org/10.1023/A:1004991931741
Título revista:Studia Logica
Título revista abreviado:Stud. Logica
ISSN:00393215
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393215_v58_n1_p79_Cignoli

Referencias:

  • Chang, C.C., Algebraic analysis of many-valued logics (1958) Trans. Amer. Math. Soc., 88, pp. 467-490
  • Chang, C.C., A new proof of the completeness of the Łukasiewicz axioms (1959) Trans. Amer. Math. Soc., 93, pp. 74-80
  • 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
  • Mangani, P., On certain algebras related to many-valued logics (1973) Bollettino Unione Matematica Italiana, 8, pp. 68-78
  • Mundici, D., Interpretation of AF C-algebras in Łukasiewicz sentential calculus (1986) J. Functional Analysis, 65, pp. 15-63
  • Mundici, D., Ulam game, Łukasiewicz logic, and AF C -algebras (1993) Fundamenta Informaticae, 18, pp. 151-161
  • Panti, G., A geometric proof of the completeness of the calculus of Łukasiewicz (1995) J. Symbolic Logic, 60, pp. 563-578
  • Rose, A., Rosser, J.B., Fragments of many-valued statement calculi (1958) Trans. Amer. Math. Soc., 87, pp. 1-53
  • 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
  • Ulam, S.M., (1976) Adventures of A Mathematician, , Scribner's, New York

Citas:

---------- APA ----------
Cignoli, R. & Mundici, D. (1997) . An elementary proof of chang's completeness theorem for the infinite-valued calculus of Łukasiewicz. Studia Logica, 58(1), 79-97.
http://dx.doi.org/10.1023/A:1004991931741
---------- CHICAGO ----------
Cignoli, R., Mundici, D. "An elementary proof of chang's completeness theorem for the infinite-valued calculus of Łukasiewicz" . Studia Logica 58, no. 1 (1997) : 79-97.
http://dx.doi.org/10.1023/A:1004991931741
---------- MLA ----------
Cignoli, R., Mundici, D. "An elementary proof of chang's completeness theorem for the infinite-valued calculus of Łukasiewicz" . Studia Logica, vol. 58, no. 1, 1997, pp. 79-97.
http://dx.doi.org/10.1023/A:1004991931741
---------- VANCOUVER ----------
Cignoli, R., Mundici, D. An elementary proof of chang's completeness theorem for the infinite-valued calculus of Łukasiewicz. Stud. Logica. 1997;58(1):79-97.
http://dx.doi.org/10.1023/A:1004991931741