Tense logics based on posets
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929402899595264 |
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| author | Chajda, Ivan Länger, Helmut Ledda, Antonio Paseka, Jan Vergottini, Gandolfo |
| author_facet | Chajda, Ivan Länger, Helmut Ledda, Antonio Paseka, Jan Vergottini, Gandolfo |
| contents | Not all logical systems can be captured using algebras. We see this in classical logic (formalized by Boolean algebras) and many-valued logics (like Lukasiewicz logic with MV-algebras). Even quantum mechanics, initially formalized with orthomodular lattices, benefits from a simpler approach using just partially ordered sets (posets). This paper explores how logical connectives are introduced in poset-based logics. Building on prior work by the authors, we delve deeper into "dynamic" logics where truth values can change over time. We consider time sets with a preference relation and propositions whose truth depends on time. Tense operators, introduced by J.Burgess and extended for various logics, become a valuable tool. This paper proposes several approaches to this topic, aiming to inspire a further stream of research. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_20034 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tense logics based on posets Chajda, Ivan Länger, Helmut Ledda, Antonio Paseka, Jan Vergottini, Gandolfo Logic 03B44, 03G12, 03G25, 06A11, 08A55 Not all logical systems can be captured using algebras. We see this in classical logic (formalized by Boolean algebras) and many-valued logics (like Lukasiewicz logic with MV-algebras). Even quantum mechanics, initially formalized with orthomodular lattices, benefits from a simpler approach using just partially ordered sets (posets). This paper explores how logical connectives are introduced in poset-based logics. Building on prior work by the authors, we delve deeper into "dynamic" logics where truth values can change over time. We consider time sets with a preference relation and propositions whose truth depends on time. Tense operators, introduced by J.Burgess and extended for various logics, become a valuable tool. This paper proposes several approaches to this topic, aiming to inspire a further stream of research. |
| title | Tense logics based on posets |
| topic | Logic 03B44, 03G12, 03G25, 06A11, 08A55 |
| url | https://arxiv.org/abs/2406.20034 |