The failure of cut-elimination in cyclic proof for first-order logic with inductive definitions
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2021
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916125281878016 |
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| author | Oda, Yukihiro Brotherston, James Tatsuta, Makoto |
| author_facet | Oda, Yukihiro Brotherston, James Tatsuta, Makoto |
| contents | A cyclic proof system is a proof system whose proof figure is a tree with cycles. The cut-elimination in a proof system is fundamental. It is conjectured that the cut-elimination in the cyclic proof system for first-order logic with inductive definitions does not hold. This paper shows that the conjecture is correct by giving a sequent not provable without the cut rule but provable in the cyclic proof system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_11798 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The failure of cut-elimination in cyclic proof for first-order logic with inductive definitions Oda, Yukihiro Brotherston, James Tatsuta, Makoto Logic in Computer Science Logic A cyclic proof system is a proof system whose proof figure is a tree with cycles. The cut-elimination in a proof system is fundamental. It is conjectured that the cut-elimination in the cyclic proof system for first-order logic with inductive definitions does not hold. This paper shows that the conjecture is correct by giving a sequent not provable without the cut rule but provable in the cyclic proof system. |
| title | The failure of cut-elimination in cyclic proof for first-order logic with inductive definitions |
| topic | Logic in Computer Science Logic |
| url | https://arxiv.org/abs/2106.11798 |