Implicative-orthomodular lattices
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909080663097344 |
|---|---|
| author | Ciungu, Lavinia Corina |
| author_facet | Ciungu, Lavinia Corina |
| contents | Based on implicative involutive BE algebras, we redefine the orthomodular lattices, by introducing the notion of implicative-orthomodular lattices, and we study their properties. We characterize these algebras, proving that the implicative-orthomodular lattices are quantum-Wajsberg algebras. We also define and characterize the implicative-modular algebras as a subclass of implicative-orthomodular lattices. The orthomodular softlattices and orthomodular widelattices are also redefined, by introducing the notions of implicative-orthomodular softlattices and implicative-orthomodular widelattices. Finally, we prove that the implicative-orthomodular softlattices are equivalent to implicative-orthomodular lattices and that the implicative-orthomodular widelattices are special cases of quantum-Wajsberg algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12845 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Implicative-orthomodular lattices Ciungu, Lavinia Corina Rings and Algebras Based on implicative involutive BE algebras, we redefine the orthomodular lattices, by introducing the notion of implicative-orthomodular lattices, and we study their properties. We characterize these algebras, proving that the implicative-orthomodular lattices are quantum-Wajsberg algebras. We also define and characterize the implicative-modular algebras as a subclass of implicative-orthomodular lattices. The orthomodular softlattices and orthomodular widelattices are also redefined, by introducing the notions of implicative-orthomodular softlattices and implicative-orthomodular widelattices. Finally, we prove that the implicative-orthomodular softlattices are equivalent to implicative-orthomodular lattices and that the implicative-orthomodular widelattices are special cases of quantum-Wajsberg algebras. |
| title | Implicative-orthomodular lattices |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2401.12845 |