Common Knowledge Always, Forever
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918339524165632 |
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| author | Diéguez, Martín Fernández-Duque, David |
| author_facet | Diéguez, Martín Fernández-Duque, David |
| contents | There has been an increasing interest in topological semantics for epistemic logic, which has been shown to be useful for, e.g., modelling evidence, degrees of belief, and self-reference. We introduce a polytopological PDL capable of expressing common knowledge and various generalizations and show it has the finite model property over closure spaces but not over Cantor derivative spaces. The latter is shown by embedding a version of linear temporal logic with `past', which does not have the finite model property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13914 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Common Knowledge Always, Forever Diéguez, Martín Fernández-Duque, David Logic in Computer Science Artificial Intelligence There has been an increasing interest in topological semantics for epistemic logic, which has been shown to be useful for, e.g., modelling evidence, degrees of belief, and self-reference. We introduce a polytopological PDL capable of expressing common knowledge and various generalizations and show it has the finite model property over closure spaces but not over Cantor derivative spaces. The latter is shown by embedding a version of linear temporal logic with `past', which does not have the finite model property. |
| title | Common Knowledge Always, Forever |
| topic | Logic in Computer Science Artificial Intelligence |
| url | https://arxiv.org/abs/2602.13914 |