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Cyclic Nonassociative Bilinear Logic With Additive Constants as Extension of Full Nonassociative Lambek Calculus — arXiv:2610.40817

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.40817
License (as archived): CC0-1.0
Archived: 2026-11-02T08:06:53.671Z
SHA-256 of the archived text: a6df84b774908bfba53ec55238196085f35d1c61a6bcf64f22d58f70372d7776
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How to cite

Cyclic Nonassociative Bilinear Logic With Additive Constants as Extension of Full Nonassociative Lambek Calculus — arXiv:2610.40817 — arXiv (en), https://arxiv.org/abs/2610.40817 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_2a136bbf4254 (Metraipolis archive dc_2a136bbf4254, sha256 a6df84b774908bfba53ec55238196085f35d1c61a6bcf64f22d58f70372d7776)

BibTeX

@misc{dc2a136bbf4254,
  title = {Cyclic Nonassociative Bilinear Logic With Additive Constants as Extension of Full Nonassociative Lambek Calculus — arXiv:2610.40817},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.40817},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_2a136bbf4254; sha256 a6df84b774908bfba53ec55238196085f35d1c61a6bcf64f22d58f70372d7776},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.40817. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Cyclic Linear Logic (CyMALL, CyBL) is a compromise between Commutative Linear Logic (MALL) and Noncommutative Linear Logic (Bilinear Logic, BL). We do not admit commutativity of the tensor, but we still admit only one De Morgan negation. MALL and its variants are natural extensions of Full Lambek Calculus (FL). Abrusci proved that CyBL is not a conservative extension of FL, if we admit additive constants in these logics. In this paper we show that Cyclic Nonassociative Bilinear Logic (CyNBL) with both additive constants is a strongly conservative extension of Full Nonassociative Lambek Calculus with only one additive constant - the upper bound - and that this holds even in the presence of an arbitrary set of nonlogical axioms.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv cs.LO, nuovi lavori del giorno).
Categorie arXiv: Logic in Computer Science (cs.LO).
Pagina del lavoro: https://arxiv.org/abs/2610.40817 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-02T07:45:30.642Z dalla pagina https://arxiv.org/list/cs.LO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).