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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.19426 |
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| _version_ | 1866916920630968320 |
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| author | Russo, Ciro |
| author_facet | Russo, Ciro |
| contents | We define the category $\mathcal{QM}$ of quantales and their modules and prove the existence of coproducts, and the one of pushout and amalgamated coproducts under certain conditions. Then we define the non-full subcategory $\mathcal{DS}_0$, of propositional deductive systems, show that it is equivalent to the one of ``real'' propositional logics whose morphisms are interpretations (modulo a language translation, when needed), and prove that the coproduct in $\mathcal{DS}_0$ is precisely the deductive system called ``logical coproduct'' in [Russo,2022]. Last, we discuss amalgamation in $\mathcal{DS}_0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19426 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The category of propositional deductive systems Russo, Ciro Logic Category Theory We define the category $\mathcal{QM}$ of quantales and their modules and prove the existence of coproducts, and the one of pushout and amalgamated coproducts under certain conditions. Then we define the non-full subcategory $\mathcal{DS}_0$, of propositional deductive systems, show that it is equivalent to the one of ``real'' propositional logics whose morphisms are interpretations (modulo a language translation, when needed), and prove that the coproduct in $\mathcal{DS}_0$ is precisely the deductive system called ``logical coproduct'' in [Russo,2022]. Last, we discuss amalgamation in $\mathcal{DS}_0$. |
| title | The category of propositional deductive systems |
| topic | Logic Category Theory |
| url | https://arxiv.org/abs/2508.19426 |