The most natural paradefinite logic relative to classical logic
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915792261480448 |
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| author | Middelburg, C. A. |
| author_facet | Middelburg, C. A. |
| contents | A paradefinite logic is a logic that can serve as the underlying logic for theories that are inconsistent or incomplete. A well-known paradefinite logic is Belnap-Dunn logic. Various expansions of Belnap-Dunn logic have been studied in the literature. In this note, it is argued that the most natural paradefinite logic relative to classical logic is the expansion of Belnap-Dunn logic with a falsity connective and an implication connective for which the standard deduction theorem holds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04081 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The most natural paradefinite logic relative to classical logic Middelburg, C. A. Logic Logic in Computer Science 03B50 (Primary) 03B05, 03B53 (Secondary) A paradefinite logic is a logic that can serve as the underlying logic for theories that are inconsistent or incomplete. A well-known paradefinite logic is Belnap-Dunn logic. Various expansions of Belnap-Dunn logic have been studied in the literature. In this note, it is argued that the most natural paradefinite logic relative to classical logic is the expansion of Belnap-Dunn logic with a falsity connective and an implication connective for which the standard deduction theorem holds. |
| title | The most natural paradefinite logic relative to classical logic |
| topic | Logic Logic in Computer Science 03B50 (Primary) 03B05, 03B53 (Secondary) |
| url | https://arxiv.org/abs/2601.04081 |