On the Various Translations between Classical, Intuitionistic and Linear Logic
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917069874790400 |
|---|---|
| author | Ferreira, Gilda Oliva, Paulo Protin, Clarence Lewis |
| author_facet | Ferreira, Gilda Oliva, Paulo Protin, Clarence Lewis |
| contents | Several different proof translations exist between classical and intuitionistic logic (negative translations), and intuitionistic and linear logic (Girard translations). Our aims in this paper are (1) to consider extensions of intuitionistic linear logic which correspond to each of these systems, and (2) with this common logical basis, to develop a uniform approach to devising and simplifying proof translations. As we shall see, through this process of ``simplification'' we obtain most of the well-known translations in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02249 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Various Translations between Classical, Intuitionistic and Linear Logic Ferreira, Gilda Oliva, Paulo Protin, Clarence Lewis Logic 03F52, 03B20, 03F07, 03F25 Several different proof translations exist between classical and intuitionistic logic (negative translations), and intuitionistic and linear logic (Girard translations). Our aims in this paper are (1) to consider extensions of intuitionistic linear logic which correspond to each of these systems, and (2) with this common logical basis, to develop a uniform approach to devising and simplifying proof translations. As we shall see, through this process of ``simplification'' we obtain most of the well-known translations in the literature. |
| title | On the Various Translations between Classical, Intuitionistic and Linear Logic |
| topic | Logic 03F52, 03B20, 03F07, 03F25 |
| url | https://arxiv.org/abs/2409.02249 |