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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.02082 |
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| _version_ | 1866911577945407488 |
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| author | Almeida, Rodrigo Nicolau Bezhanishvili, Nick Lemal, Simon |
| author_facet | Almeida, Rodrigo Nicolau Bezhanishvili, Nick Lemal, Simon |
| contents | We prove that the Fischer-Servi logic $\mathsf{IK}$ does not have the (Craig) interpolation property. This is obtained by showing that the corresponding class of modal Heyting algebras lacks the amalgamation property. We also generalize this result to some extensions of the Fischer-Servi logic such as $\mathsf{IT}$, $\mathsf{IK4}$, $\mathsf{IS4}$, and $\mathsf{IGL}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_02082 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fischer-Servi logic does not have interpolation Almeida, Rodrigo Nicolau Bezhanishvili, Nick Lemal, Simon Logic We prove that the Fischer-Servi logic $\mathsf{IK}$ does not have the (Craig) interpolation property. This is obtained by showing that the corresponding class of modal Heyting algebras lacks the amalgamation property. We also generalize this result to some extensions of the Fischer-Servi logic such as $\mathsf{IT}$, $\mathsf{IK4}$, $\mathsf{IS4}$, and $\mathsf{IGL}$. |
| title | Fischer-Servi logic does not have interpolation |
| topic | Logic |
| url | https://arxiv.org/abs/2604.02082 |