A New Overture to Classical Simple Type Theory, Ketonen-type Gentzen and Tableau Systems
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866912825069273088 |
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| author | Miwa, Tadayoshi Inoué, Takao |
| author_facet | Miwa, Tadayoshi Inoué, Takao |
| contents | 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 $\bf KCTT_h$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10026 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A New Overture to Classical Simple Type Theory, Ketonen-type Gentzen and Tableau Systems Miwa, Tadayoshi Inoué, Takao Logic 03B38, 03F03 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 $\bf KCTT_h$. |
| title | A New Overture to Classical Simple Type Theory, Ketonen-type Gentzen and Tableau Systems |
| topic | Logic 03B38, 03F03 |
| url | https://arxiv.org/abs/2601.10026 |