Paraconsistency in the Logic sqŁ<sup>*</sup>
The logic sqŁ<sup>*</sup> is closely related to complex fuzzy sets. In this paper, we continue our study on sqŁ<sup>*</sup> by establishing a system that includes all formulas with values <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" disp...
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MDPI AG
2025-03-01
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| author | Lei Cai Wenjuan Chen |
| author_facet | Lei Cai Wenjuan Chen |
| author_sort | Lei Cai |
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| description | The logic sqŁ<sup>*</sup> is closely related to complex fuzzy sets. In this paper, we continue our study on sqŁ<sup>*</sup> by establishing a system that includes all formulas with values <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mn mathvariant="bold">0</mn></semantics></math></inline-formula> in sqŁ<sup>*</sup>. This system has paraconsistent formulas within sqŁ<sup>*</sup>. Moreover, we show that this logical system is both sound and weakly complete. |
| format | Article |
| id | doaj-art-65ef46c3192a4aa89b9a77d6b58ac6ce |
| institution | OA Journals |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
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| series | Axioms |
| spelling | doaj-art-65ef46c3192a4aa89b9a77d6b58ac6ce2025-08-20T02:17:14ZengMDPI AGAxioms2075-16802025-03-0114424110.3390/axioms14040241Paraconsistency in the Logic sqŁ<sup>*</sup>Lei Cai0Wenjuan Chen1School of Mathematical Sciences, University of Jinan, No. 336, West Road of Nan Xinzhuang, Jinan 250022, ChinaSchool of Mathematical Sciences, University of Jinan, No. 336, West Road of Nan Xinzhuang, Jinan 250022, ChinaThe logic sqŁ<sup>*</sup> is closely related to complex fuzzy sets. In this paper, we continue our study on sqŁ<sup>*</sup> by establishing a system that includes all formulas with values <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mn mathvariant="bold">0</mn></semantics></math></inline-formula> in sqŁ<sup>*</sup>. This system has paraconsistent formulas within sqŁ<sup>*</sup>. Moreover, we show that this logical system is both sound and weakly complete.https://www.mdpi.com/2075-1680/14/4/241strong quasi-Wajsberg* algebrasstrong quasi-MV* algebrasMV*-algebrasparaconsistency |
| spellingShingle | Lei Cai Wenjuan Chen Paraconsistency in the Logic sqŁ<sup>*</sup> Axioms strong quasi-Wajsberg* algebras strong quasi-MV* algebras MV*-algebras paraconsistency |
| title | Paraconsistency in the Logic sqŁ<sup>*</sup> |
| title_full | Paraconsistency in the Logic sqŁ<sup>*</sup> |
| title_fullStr | Paraconsistency in the Logic sqŁ<sup>*</sup> |
| title_full_unstemmed | Paraconsistency in the Logic sqŁ<sup>*</sup> |
| title_short | Paraconsistency in the Logic sqŁ<sup>*</sup> |
| title_sort | paraconsistency in the logic sql sup sup |
| topic | strong quasi-Wajsberg* algebras strong quasi-MV* algebras MV*-algebras paraconsistency |
| url | https://www.mdpi.com/2075-1680/14/4/241 |
| work_keys_str_mv | AT leicai paraconsistencyinthelogicsqłsupsup AT wenjuanchen paraconsistencyinthelogicsqłsupsup |