Craig Interpolation for Decidable First-Order Fragments
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866914016280969216 |
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| author | Cate, Balder ten Comer, Jesse |
| author_facet | Cate, Balder ten Comer, Jesse |
| contents | We show that the guarded-negation fragment is, in a precise sense, the smallest extension of the guarded fragment with Craig interpolation. In contrast, we show that full first-order logic is the smallest extension of both the two-variable fragment and the forward fragment with Craig interpolation. Similarly, we also show that all extensions of the two-variable fragment and of the fluted fragment with Craig interpolation are undecidable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_08689 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Craig Interpolation for Decidable First-Order Fragments Cate, Balder ten Comer, Jesse Logic in Computer Science We show that the guarded-negation fragment is, in a precise sense, the smallest extension of the guarded fragment with Craig interpolation. In contrast, we show that full first-order logic is the smallest extension of both the two-variable fragment and the forward fragment with Craig interpolation. Similarly, we also show that all extensions of the two-variable fragment and of the fluted fragment with Craig interpolation are undecidable. |
| title | Craig Interpolation for Decidable First-Order Fragments |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2310.08689 |