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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.25880 |
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| _version_ | 1866911185731846144 |
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| author | Bayzid, Luke Madeira, Alexandre Martins, Manuel A. |
| author_facet | Bayzid, Luke Madeira, Alexandre Martins, Manuel A. |
| contents | Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results between these representations can be non-trivial, as different frameworks are used for different contexts. We present a general structure based on set-theoretic concepts that accommodates many situations related to logical and semantic frameworks. We show the versatility of this approach by presenting alternative constructions of modal logic; in particular, all modal logics can be represented within the framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_25880 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Function-Set Framework: General Properties and Applications to Modal Logic Bayzid, Luke Madeira, Alexandre Martins, Manuel A. Logic in Computer Science Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results between these representations can be non-trivial, as different frameworks are used for different contexts. We present a general structure based on set-theoretic concepts that accommodates many situations related to logical and semantic frameworks. We show the versatility of this approach by presenting alternative constructions of modal logic; in particular, all modal logics can be represented within the framework. |
| title | A Function-Set Framework: General Properties and Applications to Modal Logic |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2509.25880 |