An Alternative Definition of Quantifiers on Four-Valued Łukasiewicz Algebras
An alternative notion of an existential quantifier on four-valued Łukasiewicz algebras is introduced. The class of four-valued Łukasiewicz algebras endowed with this existential quantifier determines a variety which is denoted by M23L4. It is shown that the alternative existential quantifier is inte...
Guardado en:
| Publicado: |
2017
|
|---|---|
| Materias: | |
| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16618297_v11_n4_p439_Gonzalez http://hdl.handle.net/20.500.12110/paper_16618297_v11_n4_p439_Gonzalez |
| Aporte de: |
| Sumario: | An alternative notion of an existential quantifier on four-valued Łukasiewicz algebras is introduced. The class of four-valued Łukasiewicz algebras endowed with this existential quantifier determines a variety which is denoted by M23L4. It is shown that the alternative existential quantifier is interdefinable with the standard existential quantifier on a four-valued Łukasiewicz algebra. Some connections between the new existential quantifier and the existential quantifiers defined on bounded distributive lattices and Boolean algebras are given. Finally, a completeness theorem for the monadic four-valued Łukasiewicz predicate calculus corresponding to the dual of the alternative existential quantifier is proven. © 2017, Springer International Publishing AG, part of Springer Nature. |
|---|