Infinitary Cut-Elimination for Non-Wellfounded Parsimonious Linear Logic
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866918133721202688 |
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| author | Acclavio, Matteo Curzi, Gianluca Guerrieri, Giulio |
| author_facet | Acclavio, Matteo Curzi, Gianluca Guerrieri, Giulio |
| contents | We investigate non-wellfounded proof systems based on parsimonious logic, a weaker variant of linear logic where the exponential modality ! is interpreted as a constructor for streams over finite data. Logical consistency is maintained at a global level by adapting a standard progressing criterion. We present an infinitary version of cut-elimination based on finite approximations, and we prove that, in presence of the progressing criterion, it returns well-defined non-wellfounded proofs at its limit. Furthermore, we show that cut-elimination preserves the progressive criterion and various regularity conditions internalizing degrees of proof-theoretical uniformity. Finally, we provide a denotational semantics for our systems based on the relational model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_07789 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Infinitary Cut-Elimination for Non-Wellfounded Parsimonious Linear Logic Acclavio, Matteo Curzi, Gianluca Guerrieri, Giulio Logic in Computer Science We investigate non-wellfounded proof systems based on parsimonious logic, a weaker variant of linear logic where the exponential modality ! is interpreted as a constructor for streams over finite data. Logical consistency is maintained at a global level by adapting a standard progressing criterion. We present an infinitary version of cut-elimination based on finite approximations, and we prove that, in presence of the progressing criterion, it returns well-defined non-wellfounded proofs at its limit. Furthermore, we show that cut-elimination preserves the progressive criterion and various regularity conditions internalizing degrees of proof-theoretical uniformity. Finally, we provide a denotational semantics for our systems based on the relational model. |
| title | Infinitary Cut-Elimination for Non-Wellfounded Parsimonious Linear Logic |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2308.07789 |