Normative implications
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arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866929762121809920 |
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| author | De Domenico, Andrea Farjami, Ali Manoorkar, Krishna Palmigiano, Alessandra Panettiere, Mattia Tzimoulis, Apostolos Wang, Xiaolong |
| author_facet | De Domenico, Andrea Farjami, Ali Manoorkar, Krishna Palmigiano, Alessandra Panettiere, Mattia Tzimoulis, Apostolos Wang, Xiaolong |
| contents | We continue to develop a research line initiated in \cite{wollic22}, studying I/O logic from an algebraic approach based on subordination algebras. We introduce the classes of slanted (co-)Heyting algebras as equivalent presentations of distributive lattices with subordination relations. Interpreting subordination relations as the algebraic counterparts of input/output relations on formulas yields (slanted) modal operations with interesting deontic interpretations. We study the theory of slanted and co-slanted Heyting algebras, develop algorithmic correspondence and inverse correspondence, and present some deontically meaningful axiomatic extensions and examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12965 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Normative implications De Domenico, Andrea Farjami, Ali Manoorkar, Krishna Palmigiano, Alessandra Panettiere, Mattia Tzimoulis, Apostolos Wang, Xiaolong Logic We continue to develop a research line initiated in \cite{wollic22}, studying I/O logic from an algebraic approach based on subordination algebras. We introduce the classes of slanted (co-)Heyting algebras as equivalent presentations of distributive lattices with subordination relations. Interpreting subordination relations as the algebraic counterparts of input/output relations on formulas yields (slanted) modal operations with interesting deontic interpretations. We study the theory of slanted and co-slanted Heyting algebras, develop algorithmic correspondence and inverse correspondence, and present some deontically meaningful axiomatic extensions and examples. |
| title | Normative implications |
| topic | Logic |
| url | https://arxiv.org/abs/2503.12965 |