Complete and atomic algebras of the infinite valued Łukasiewicz logic
The infinite-valued logic of Łukasiewicz was originally defined by means of an infinite-valued matrix. Łukasiewicz took special forms of negation and implication as basic connectives and proposed an axiom system that he conjectured would be sufficient to derive the valid formulas of the logic; this...
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | JOUR |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00393215_v50_n3-4_p375_Cignoli |
| Aporte de: |
| id |
todo:paper_00393215_v50_n3-4_p375_Cignoli |
|---|---|
| record_format |
dspace |
| spelling |
todo:paper_00393215_v50_n3-4_p375_Cignoli2023-10-03T14:49:40Z Complete and atomic algebras of the infinite valued Łukasiewicz logic Cignoli, R. The infinite-valued logic of Łukasiewicz was originally defined by means of an infinite-valued matrix. Łukasiewicz took special forms of negation and implication as basic connectives and proposed an axiom system that he conjectured would be sufficient to derive the valid formulas of the logic; this was eventually verified by M. Wajsberg. The algebraic counterparts of this logic have become know as Wajsberg algebras. In this paper we show that a Wajsberg algebra is complete and atomic (as a lattice) if and only if it is a direct product of finite Wajsberg chains. The classical characterization of complete and atomic Boolean algebras as fields of sets is a particular case of this result. © 1991 Polish Academy of Sciences. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00393215_v50_n3-4_p375_Cignoli |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
The infinite-valued logic of Łukasiewicz was originally defined by means of an infinite-valued matrix. Łukasiewicz took special forms of negation and implication as basic connectives and proposed an axiom system that he conjectured would be sufficient to derive the valid formulas of the logic; this was eventually verified by M. Wajsberg. The algebraic counterparts of this logic have become know as Wajsberg algebras. In this paper we show that a Wajsberg algebra is complete and atomic (as a lattice) if and only if it is a direct product of finite Wajsberg chains. The classical characterization of complete and atomic Boolean algebras as fields of sets is a particular case of this result. © 1991 Polish Academy of Sciences. |
| format |
JOUR |
| author |
Cignoli, R. |
| spellingShingle |
Cignoli, R. Complete and atomic algebras of the infinite valued Łukasiewicz logic |
| author_facet |
Cignoli, R. |
| author_sort |
Cignoli, R. |
| title |
Complete and atomic algebras of the infinite valued Łukasiewicz logic |
| title_short |
Complete and atomic algebras of the infinite valued Łukasiewicz logic |
| title_full |
Complete and atomic algebras of the infinite valued Łukasiewicz logic |
| title_fullStr |
Complete and atomic algebras of the infinite valued Łukasiewicz logic |
| title_full_unstemmed |
Complete and atomic algebras of the infinite valued Łukasiewicz logic |
| title_sort |
complete and atomic algebras of the infinite valued łukasiewicz logic |
| url |
http://hdl.handle.net/20.500.12110/paper_00393215_v50_n3-4_p375_Cignoli |
| work_keys_str_mv |
AT cignolir completeandatomicalgebrasoftheinfinitevaluedłukasiewiczlogic |
| _version_ |
1807320515338043392 |