IKTω and Łukasiewicz-Models

IF 0.6 3区 数学 Q2 LOGIC
Andreas Fjellstad, Jan-Fredrik Olsen
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引用次数: 2

Abstract

In this note, we show that the first-order logic IKω is sound with regard to the models obtained from continuum-valued Łukasiewicz-models for first-order languages by treating the quantifiers as infinitary strong disjunction/conjunction rather than infinitary weak disjunction/conjunction. Moreover, we show that these models cannot be used to provide a new consistency proof for the theory of truth IKTω obtained by expanding IKω with transparent truth, because the models are inconsistent with transparent truth. Finally, we show that whether or not this inconsistency can be reproduced in the sequent calculus for IKTω depends on how vacuous quantification is treated.
在本文中,我们通过将量词视为无限强析取/连接而不是无限弱析取/连接,证明了一阶逻辑IKω对于一阶语言的连续值Łukasiewicz-models得到的模型是健全的。此外,由于这些模型与透明真值不一致,我们证明了这些模型不能用于为用透明真值展开ikm而得到的真值理论IKTω提供新的一致性证明。最后,我们表明,这种不一致是否可以在IKTω的后续演算中再现取决于如何处理空洞量化。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.00
自引率
14.30%
发文量
14
审稿时长
>12 weeks
期刊介绍: The Notre Dame Journal of Formal Logic, founded in 1960, aims to publish high quality and original research papers in philosophical logic, mathematical logic, and related areas, including papers of compelling historical interest. The Journal is also willing to selectively publish expository articles on important current topics of interest as well as book reviews.
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