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arXiv · 2601.10026

A New Overture to Classical Simple Type Theory, Ketonen-type Gentzen and Tableau Systems

Tadayoshi Miwa·Takao Inoué
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Abstract

In this paper, we introduce a Ketonen-type Gentzen-style classical simple type theory $\bf KCT$. Also the tableau system $\bf KCTT$ corresponding to $\bf KCT$ is introduced. Further inference-preserving Gentzen system $\bf KCT_h$ (equivalent to $\bf KCT$) and tableau system $\bf KCTT_h$ (equivalent to $\bf KCTT$) is introduced. We introduce the notion of Hintikka sequents for $\bf KCTT_h$.The completeness theorem and Takahashi-Prawitz's theorem are proved for $\bf KCTT_h$.

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BibTeXRIS

Tadayoshi Miwa, Takao Inoué. 2026-01-15. A New Overture to Classical Simple Type Theory, Ketonen-type Gentzen and Tableau Systems. https://arxiv.org/abs/2601.10026

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