The higher dimensional propositional calculus
Fuente:
arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866929336996593664 |
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| author | Bucciarelli, Antonio Curien, Pierre-Louis Ledda, Antonio Paoli, Francesco Salibra, Antonino |
| author_facet | Bucciarelli, Antonio Curien, Pierre-Louis Ledda, Antonio Paoli, Francesco Salibra, Antonino |
| contents | In recent research, some of the present authors introduced the concept of an n-dimensional Boolean algebra and its corresponding propositional logic nCL, generalising the Boolean propositional calculus to n>= 2 perfectly symmetric truth values. This paper presents a sound and complete sequent calculus for nCL, named nLK. We provide two proofs of completeness: one syntactic and one semantic. The former implies as a corollary that nLK enjoys the cut admissibility property. The latter relies on the generalisation to the n-ary case of the classical proof based on the Lindenbaum algebra of formulas and Boolean ultrafilters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_00435 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The higher dimensional propositional calculus Bucciarelli, Antonio Curien, Pierre-Louis Ledda, Antonio Paoli, Francesco Salibra, Antonino Logic in Computer Science In recent research, some of the present authors introduced the concept of an n-dimensional Boolean algebra and its corresponding propositional logic nCL, generalising the Boolean propositional calculus to n>= 2 perfectly symmetric truth values. This paper presents a sound and complete sequent calculus for nCL, named nLK. We provide two proofs of completeness: one syntactic and one semantic. The former implies as a corollary that nLK enjoys the cut admissibility property. The latter relies on the generalisation to the n-ary case of the classical proof based on the Lindenbaum algebra of formulas and Boolean ultrafilters. |
| title | The higher dimensional propositional calculus |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2204.00435 |