An elementary proof of Chang's completeness theorem for the infinite-valued calculus of Lukasiewicz

Studia Logica 58 (1):79-97 (1997)
The interpretation of propositions in Lukasiewicz'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.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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DOI 10.1023/A:1004991931741
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Petr Hájek (1999). Ten Questions and One Problem on Fuzzy Logic. Annals of Pure and Applied Logic 96 (1-3):157-165.

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