Prelinearity in (quasi-)Nelson logic
The algebraic theory of quasi-Nelson logic, a non-involutive generalization of Nelson's constructive logic with strong negation, has been shown to be surprisingly rich in a series of recent papers. In the present paper we bring quasi-Nelson logic into the fuzzy setting by adding the prelinearit...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad Nacional de Educación a Distancia |
| Repositorio: | e-spacio. Repositorio Institucional de la UNED |
| Idioma: | inglés |
| OAI Identifier: | oai:e-spacio.uned.es:20.500.14468/30671 |
| Acceso en línea: | https://hdl.handle.net/20.500.14468/30671 |
| Access Level: | acceso abierto |
| Palabra clave: | 72 Filosofía 11 Lógica (Quasi-)Nelson Weak nilpotent minimum Rotation logics Non-involutive Prelinear logics Algebraic logic |
| Sumario: | The algebraic theory of quasi-Nelson logic, a non-involutive generalization of Nelson's constructive logic with strong negation, has been shown to be surprisingly rich in a series of recent papers. In the present paper we bring quasi-Nelson logic into the fuzzy setting by adding the prelinearity axiom to it. We observe that the resulting system is an extension of the well-known Weak Nilpotent Minimum logic, as well as a rotation logic in the sense of recent work by P. Aglianò and S. Ugolini. We characterize the algebraic models of prelinear quasi-Nelson logic as twist-structures over Gödel algebras endowed with a nucleus operator and use the insight thus gained to look at subvarieties corresponding to extensions of well-known fuzzy systems. Our study of the quasi-Nelson negation in a prelinear setting also allows us to show that the variety of prelinear quasi-Nelson algebras is generated by a single standard algebra, thus obtaining a single chain completeness theorem for the logic. |
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