Finite Hilbert systems for Weak Kleene logics
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914721412677632 |
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| author | Greati, Vitor Marcelino, Sérgio Rivieccio, Umberto |
| author_facet | Greati, Vitor Marcelino, Sérgio Rivieccio, Umberto |
| contents | Multiple-conclusion Hilbert-style systems allow us to finitely axiomatize every logic defined by a finite matrix. Having obtained such axiomatizations for Paraconsistent Weak Kleene and Bochvar-Kleene logics, we modify them by replacing the multiple-conclusion rules with carefully selected single-conclusion ones. In this way we manage to introduce the first finite Hilbert-style single-conclusion axiomatizations for these logics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03265 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite Hilbert systems for Weak Kleene logics Greati, Vitor Marcelino, Sérgio Rivieccio, Umberto Logic Logic in Computer Science 03B22 F.4.1 Multiple-conclusion Hilbert-style systems allow us to finitely axiomatize every logic defined by a finite matrix. Having obtained such axiomatizations for Paraconsistent Weak Kleene and Bochvar-Kleene logics, we modify them by replacing the multiple-conclusion rules with carefully selected single-conclusion ones. In this way we manage to introduce the first finite Hilbert-style single-conclusion axiomatizations for these logics. |
| title | Finite Hilbert systems for Weak Kleene logics |
| topic | Logic Logic in Computer Science 03B22 F.4.1 |
| url | https://arxiv.org/abs/2401.03265 |