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An Elementary Proof of Chang's Completeness Theorem for the Infinite-valued Calculus of Lukasiewicz

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Abstract

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.

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Cignoli, R., Mundici, D. An Elementary Proof of Chang's Completeness Theorem for the Infinite-valued Calculus of Lukasiewicz. Studia Logica 58, 79–97 (1997). https://doi.org/10.1023/A:1004991931741

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  • DOI: https://doi.org/10.1023/A:1004991931741

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