An Elementary Proof of Chang's Completeness Theorem for the Infinite-valued Calculus of Lukasiewicz |
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Authors: | Cignoli Roberto Mundici Daniele |
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Institution: | (1) Departamento de Matemática Facultad de Ciencias Exactas, Ciudad Universitaria, 1428 Buenos Aires, Argentina;(2) Department of Computer Science, University of Milan, Via Comelico 39-41, 20135 Milan, Italy |
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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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Keywords: | MV algebra completeness of the Lukasiewicz calculus infinite-valued logic |
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