Strong quasi-MV* algebras and their logics
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908273116971008 |
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| author | Cai, Lei Chen, Wenjuan |
| author_facet | Cai, Lei Chen, Wenjuan |
| contents | In this paper, we introduce the subvariety of quasi-MV* algebras in order to characterize the logic which is related to complex fuzzy logic. First, we give the definitions of strong quasi-MV* algebra and strong quasi-Wajsberg* algebra and show that they are term equivalence. Second, we present the representation theorem and the standard completeness of strong quasi-MV* algebras. Moreover, we discuss the properties of terms in the language of Wajsberg* algebras and strong quasi-Wajsberg* algebras. Finally, we establish the logical system associated with strong quasi-Wajsberg* algebra and prove that the logical system is sound and complete. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_13887 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strong quasi-MV* algebras and their logics Cai, Lei Chen, Wenjuan Logic In this paper, we introduce the subvariety of quasi-MV* algebras in order to characterize the logic which is related to complex fuzzy logic. First, we give the definitions of strong quasi-MV* algebra and strong quasi-Wajsberg* algebra and show that they are term equivalence. Second, we present the representation theorem and the standard completeness of strong quasi-MV* algebras. Moreover, we discuss the properties of terms in the language of Wajsberg* algebras and strong quasi-Wajsberg* algebras. Finally, we establish the logical system associated with strong quasi-Wajsberg* algebra and prove that the logical system is sound and complete. |
| title | Strong quasi-MV* algebras and their logics |
| topic | Logic |
| url | https://arxiv.org/abs/2503.13887 |