On connexivity in modal and conditional contexts
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911314268389376 |
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| author | Olkhovikov, Grigory K. |
| author_facet | Olkhovikov, Grigory K. |
| contents | We define and axiomatize three new logics based on the connexive logic $\mathsf{C}$, the modal logic $\mathsf{CnK}$ and the conditional logics $\mathsf{CnCK}$ and $\mathsf{CnCK}_R$. These logics display strong connexivity properties and are connected to one another, since $\mathsf{CnCK}_R$ is the reflexive extension of $\mathsf{CnCK}$ and $\mathsf{CnK}$ is faithfully embeddable into both $\mathsf{CnCK}$ and $\mathsf{CnCK}_R$ in a multitude of natural ways. We argue that all the three logics provide (albeit in different ways) natural expansions of $\mathsf{C}$ to their respective languages that preserve and further develop several core properties of $\mathsf{C}$, especially its connexivity profile. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_10816 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On connexivity in modal and conditional contexts Olkhovikov, Grigory K. Logic 03B45, 03B53 We define and axiomatize three new logics based on the connexive logic $\mathsf{C}$, the modal logic $\mathsf{CnK}$ and the conditional logics $\mathsf{CnCK}$ and $\mathsf{CnCK}_R$. These logics display strong connexivity properties and are connected to one another, since $\mathsf{CnCK}_R$ is the reflexive extension of $\mathsf{CnCK}$ and $\mathsf{CnK}$ is faithfully embeddable into both $\mathsf{CnCK}$ and $\mathsf{CnCK}_R$ in a multitude of natural ways. We argue that all the three logics provide (albeit in different ways) natural expansions of $\mathsf{C}$ to their respective languages that preserve and further develop several core properties of $\mathsf{C}$, especially its connexivity profile. |
| title | On connexivity in modal and conditional contexts |
| topic | Logic 03B45, 03B53 |
| url | https://arxiv.org/abs/2512.10816 |