Proof-Theoretic Functional Completeness for the Connexive Logic C
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913933906935808 |
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| author | Ayhan, Sara Oddsson, Hrafn Valtýr |
| author_facet | Ayhan, Sara Oddsson, Hrafn Valtýr |
| contents | We show the functional completeness for the connectives of the non-trivial negation inconsistent logic C by using a well-established method implementing purely proof-theoretic notions only. Firstly, given that C contains a strong negation, expressing a notion of direct refutation, the proof needs to be applied in a bilateralist way in that not only higher-order rule schemata for proofs but also for refutations need to be considered. Secondly, given that C is a connexive logic we need to take a connexive understanding of inference as a basis, leading to a different conception of (higher-order) refutation than is usually employed. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_06854 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Proof-Theoretic Functional Completeness for the Connexive Logic C Ayhan, Sara Oddsson, Hrafn Valtýr Logic in Computer Science Logic We show the functional completeness for the connectives of the non-trivial negation inconsistent logic C by using a well-established method implementing purely proof-theoretic notions only. Firstly, given that C contains a strong negation, expressing a notion of direct refutation, the proof needs to be applied in a bilateralist way in that not only higher-order rule schemata for proofs but also for refutations need to be considered. Secondly, given that C is a connexive logic we need to take a connexive understanding of inference as a basis, leading to a different conception of (higher-order) refutation than is usually employed. |
| title | Proof-Theoretic Functional Completeness for the Connexive Logic C |
| topic | Logic in Computer Science Logic |
| url | https://arxiv.org/abs/2507.06854 |