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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.20932 |
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| _version_ | 1866916267681644544 |
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| author | Coniglio, Marcelo E. Figallo, Martín Rodrigues, Abilio |
| author_facet | Coniglio, Marcelo E. Figallo, Martín Rodrigues, Abilio |
| contents | In this paper, we investigate proof-theoretic aspects of the logics of evidence and truth LETJ and LETF. These logics extend, respectively, Nelson's logic N and the logic of first-degree entailment FDE, also known as Belnap-Dunn four-valued logic, with a classicality operator that recovers classical logic for formulas in its scope. We will present natural deduction and sequent systems for LETJ and LETF, together with proofs of normalization and cut-elimination theorems, respectively. As a corollary, we obtain decidability for both logics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_20932 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Normalization and cut-elimination theorems for some logics of evidence and truth Coniglio, Marcelo E. Figallo, Martín Rodrigues, Abilio Logic In this paper, we investigate proof-theoretic aspects of the logics of evidence and truth LETJ and LETF. These logics extend, respectively, Nelson's logic N and the logic of first-degree entailment FDE, also known as Belnap-Dunn four-valued logic, with a classicality operator that recovers classical logic for formulas in its scope. We will present natural deduction and sequent systems for LETJ and LETF, together with proofs of normalization and cut-elimination theorems, respectively. As a corollary, we obtain decidability for both logics. |
| title | Normalization and cut-elimination theorems for some logics of evidence and truth |
| topic | Logic |
| url | https://arxiv.org/abs/2405.20932 |