An elementary proof of chang's completeness theorem for the infinite-valued calculus of Łukasiewicz

被引：20

作者：

Cignoli R. ^{[1
]}

Mundici D. ^{[2
]}

机构：

[1] Departamento de Matemática, Facultad de Ciencias Exactas, Ciudad Universitaria

[2] Department of Computer Science, University of Milan, Via Comelico 39-41

来源：

Studia Logica | 1997年 / 58卷 / 1期

关键词：

Completeness of the Łukasiewicz calculus; Infinite-valued logic; MV algebra;

D O I：

10.1023/A:1004991931741

中图分类号：

学科分类号：

摘要：

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.

引用

页码：79 / 97

页数：18

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