Many-valued coalgebraic logic over semi-primal varieties
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866914901676523520 |
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| author | Kurz, Alexander Poiger, Wolfgang Teheux, Bruno |
| author_facet | Kurz, Alexander Poiger, Wolfgang Teheux, Bruno |
| contents | We study many-valued coalgebraic logics with semi-primal algebras of truth-degrees. We provide a systematic way to lift endofunctors defined on the variety of Boolean algebras to endofunctors on the variety generated by a semi-primal algebra. We show that this can be extended to a technique to lift classical coalgebraic logics to many-valued ones, and that (one-step) completeness and expressivity are preserved under this lifting. For specific classes of endofunctors, we also describe how to obtain an axiomatization of the lifted many-valued logic directly from an axiomatization of the original classical one. In particular, we apply all of these techniques to classical modal logic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_14581 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Many-valued coalgebraic logic over semi-primal varieties Kurz, Alexander Poiger, Wolfgang Teheux, Bruno Logic in Computer Science Category Theory Logic We study many-valued coalgebraic logics with semi-primal algebras of truth-degrees. We provide a systematic way to lift endofunctors defined on the variety of Boolean algebras to endofunctors on the variety generated by a semi-primal algebra. We show that this can be extended to a technique to lift classical coalgebraic logics to many-valued ones, and that (one-step) completeness and expressivity are preserved under this lifting. For specific classes of endofunctors, we also describe how to obtain an axiomatization of the lifted many-valued logic directly from an axiomatization of the original classical one. In particular, we apply all of these techniques to classical modal logic. |
| title | Many-valued coalgebraic logic over semi-primal varieties |
| topic | Logic in Computer Science Category Theory Logic |
| url | https://arxiv.org/abs/2308.14581 |