On the unification problem for GLP
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911829709553664 |
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| author | Beklemishev, Lev D. |
| author_facet | Beklemishev, Lev D. |
| contents | We show that the polymodal provability logic GLP, in a language with at least two modalities and one variable, has nullary unification type. More specifically, we show that the formula [1]p does not have maximal unifiers, and exhibit an infinite complete set of unifiers for it. Further, we discuss the algorithmic problem of whether a given formula is unifiable in GLP and remark that this problem has a positive solution. Finally, we state the arithmetical analogues of the unification and admissibility problems for GLP and formulate a number of open questions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04893 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the unification problem for GLP Beklemishev, Lev D. Logic 03B45, 03F45 We show that the polymodal provability logic GLP, in a language with at least two modalities and one variable, has nullary unification type. More specifically, we show that the formula [1]p does not have maximal unifiers, and exhibit an infinite complete set of unifiers for it. Further, we discuss the algorithmic problem of whether a given formula is unifiable in GLP and remark that this problem has a positive solution. Finally, we state the arithmetical analogues of the unification and admissibility problems for GLP and formulate a number of open questions. |
| title | On the unification problem for GLP |
| topic | Logic 03B45, 03F45 |
| url | https://arxiv.org/abs/2404.04893 |