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BUNDER’S PARADOX
The Review of Symbolic Logic ( IF 0.6 ) Pub Date : 2019-02-06 , DOI: 10.1017/s1755020319000054
MICHAEL CAIE

Systems of illative logic are logical calculi formulated in the untyped λ-calculus supplemented with certain logical constants.1 In this short paper, I consider a paradox that arises in illative logic. I note two prima facie attractive ways of resolving the paradox. The first is well known to be consistent, and I briefly outline a now standard construction used by Scott and Aczel that establishes this. The second, however, has been thought to be inconsistent. I show that this isn’t so, by providing a nonempty class of models that establishes its consistency. I then provide an illative logic which is sound and complete for this class of models. I close by briefly noting some attractive features of the second resolution of this paradox.

中文翻译:

邦德悖论

系统照应逻辑是在 untyped 中制定的逻辑演算λ-演算补充了某些逻辑常数。1在这篇简短的论文中,我考虑了在命题逻辑中出现的一个悖论。我注意到解决这个悖论的两种表面上看起来很有吸引力的方法。众所周知,第一个是一致的,我简要概述了 Scott 和 Aczel 使用的现在标准结构,它建立了这一点。然而,第二个被认为是不一致的。我通过提供建立其一致性的非空模型类来证明事实并非如此。然后,我提供了一个对此类模型来说是合理且完整的假设逻辑。最后,我简要地指出这个悖论的第二个解决方案的一些吸引人的特征。
更新日期:2019-02-06
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