Effects of the Strict-Tolerant Approach on Intuitionistic and Minimal Logic
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918139944501248 |
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| author | Barroso-Nascimento, Victor Mejia, German |
| author_facet | Barroso-Nascimento, Victor Mejia, German |
| contents | This paper extends the literature on the strict-tolerant logical approach by applying its methods to intuitionistic and minimal logic. In short, the strict-tolerant approach modifies the usual notion of logical consequence by stipulating that, in order for an inference to be valid, from the truth of the premises must follow the non-falsity of the conclusion. This notion can also be generalized to define strict-tolerant metainferences, metametainferences and so on, which may or may not generate logics distinct from those obtained on the inferential level. It is already known that strict-tolerant definitions can make the notion of inference for non-classical logics collapse into the classical notion, but the strength of this effect is not yet fully known. This paper shows that intuitionistic strict-tolerant inferences also collapse into classical ones, but minimal ones do not. However, minimal strict-tolerant logic has the property that no inferences are valid (which is not carried over to the metainferential level). Additionally, it is shown that the logics obtained from intuitionistic, minimal and classical logic at the metainferential level are distinct from each other. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_10322 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Effects of the Strict-Tolerant Approach on Intuitionistic and Minimal Logic Barroso-Nascimento, Victor Mejia, German Logic in Computer Science This paper extends the literature on the strict-tolerant logical approach by applying its methods to intuitionistic and minimal logic. In short, the strict-tolerant approach modifies the usual notion of logical consequence by stipulating that, in order for an inference to be valid, from the truth of the premises must follow the non-falsity of the conclusion. This notion can also be generalized to define strict-tolerant metainferences, metametainferences and so on, which may or may not generate logics distinct from those obtained on the inferential level. It is already known that strict-tolerant definitions can make the notion of inference for non-classical logics collapse into the classical notion, but the strength of this effect is not yet fully known. This paper shows that intuitionistic strict-tolerant inferences also collapse into classical ones, but minimal ones do not. However, minimal strict-tolerant logic has the property that no inferences are valid (which is not carried over to the metainferential level). Additionally, it is shown that the logics obtained from intuitionistic, minimal and classical logic at the metainferential level are distinct from each other. |
| title | Effects of the Strict-Tolerant Approach on Intuitionistic and Minimal Logic |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2509.10322 |