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- Łukasiewicz–Moisil_algebra abstract "Łukasiewicz–Moisil algebras (LMn algebras) were introduced in the 1940s by Grigore Moisil (initially under the name of Łukasiewicz algebras) in the hope of giving algebraic semantics for the n-valued Łukasiewicz logic. However, in 1956 Alan Rose discovered that for n ≥ 5, the Łukasiewicz–Moisil algebra does not model the Łukasiewicz logic. A faithful model for the ℵ0-valued (infinitely-many-valued) Łukasiewicz–Tarski logic was provided by C. C. Chang's MV-algebra, introduced in 1958. For the axiomatically more complicated (finite) n-valued Łukasiewicz logics, suitable algebras were published in 1977 by Revaz Grigolia and called MVn-algebras. MVn-algebras are a subclass of LMn-algebras, and the inclusion is strict for n ≥ 5. In 1982 Roberto Cignoli published some additional constraints that added to LMn-algebras produce proper models for n-valued Łukasiewicz logic; Cignoli called his discovery proper Łukasiewicz algebras.Moisil however published in 1964 a logic to match his algebra (in the general n ≥ 5 case), now called Moisil logic. After coming in contact with Zadeh's fuzzy logic, in 1968 Moisil also introduced an infinitely-many-valued logic variant and its corresponding LMθ algebras. Although the Łukasiewicz implication cannot be defined in a LMn algebra for n ≥ 5, the Heyting implication can be, i.e. LMn algebras are Heyting algebras; as a result, Moisil logics can also be developed (from a purely logical standpoint) in the framework of Brower’s intuitionistic logic.".
- Łukasiewicz–Moisil_algebra wikiPageExternalLink 1093635424.
- Łukasiewicz–Moisil_algebra wikiPageID "43613625".
- Łukasiewicz–Moisil_algebra wikiPageLength "8802".
- Łukasiewicz–Moisil_algebra wikiPageOutDegree "29".
- Łukasiewicz–Moisil_algebra wikiPageRevisionID "678514618".
- Łukasiewicz–Moisil_algebra wikiPageWikiLink Algebraic_semantics_(mathematical_logic).
- Łukasiewicz–Moisil_algebra wikiPageWikiLink Antonio_Monteiro_(mathematician).
- Łukasiewicz–Moisil_algebra wikiPageWikiLink Boolean_algebra_(structure).
- Łukasiewicz–Moisil_algebra wikiPageWikiLink Category:Algebraic_logic.
- Łukasiewicz–Moisil_algebra wikiPageWikiLink Category:Ockham_algebras.
- Łukasiewicz–Moisil_algebra wikiPageWikiLink Chen_Chung_Chang.
- Łukasiewicz–Moisil_algebra wikiPageWikiLink De_Morgan_algebra.
- Łukasiewicz–Moisil_algebra wikiPageWikiLink Direct_product.
- Łukasiewicz–Moisil_algebra wikiPageWikiLink Embedding.
- Łukasiewicz–Moisil_algebra wikiPageWikiLink Endomorphism.
- Łukasiewicz–Moisil_algebra wikiPageWikiLink Fuzzy_logic.
- Łukasiewicz–Moisil_algebra wikiPageWikiLink Grigore_Moisil.
- Łukasiewicz–Moisil_algebra wikiPageWikiLink Heyting_algebra.
- Łukasiewicz–Moisil_algebra wikiPageWikiLink Intuitionistic_logic.
- Łukasiewicz–Moisil_algebra wikiPageWikiLink Lotfi_A._Zadeh.
- Łukasiewicz–Moisil_algebra wikiPageWikiLink MV-algebra.
- Łukasiewicz–Moisil_algebra wikiPageWikiLink Modal_logic.
- Łukasiewicz–Moisil_algebra wikiPageWikiLink Monadic_Boolean_algebra.
- Łukasiewicz–Moisil_algebra wikiPageWikiLink Pointwise.
- Łukasiewicz–Moisil_algebra wikiPageWikiLink Revaz_Grigolia.
- Łukasiewicz–Moisil_algebra wikiPageWikiLink Roberto_Cignoli.
- Łukasiewicz–Moisil_algebra wikiPageWikiLink Signature_(logic).
- Łukasiewicz–Moisil_algebra wikiPageWikiLink Structure_(mathematical_logic).
- Łukasiewicz–Moisil_algebra wikiPageWikiLink Subdirect_product.
- Łukasiewicz–Moisil_algebra wikiPageWikiLink Substructure.
- Łukasiewicz–Moisil_algebra wikiPageWikiLink Łukasiewicz_logic.
- Łukasiewicz–Moisil_algebra wikiPageWikiLinkText "Łukasiewicz–Moisil (LM) algebra".
- Łukasiewicz–Moisil_algebra wikiPageWikiLinkText "Łukasiewicz–Moisil algebra".
- Łukasiewicz–Moisil_algebra wikiPageUsesTemplate Template:Cite_book.
- Łukasiewicz–Moisil_algebra wikiPageUsesTemplate Template:Doi.
- Łukasiewicz–Moisil_algebra wikiPageUsesTemplate Template:Reflist.
- Łukasiewicz–Moisil_algebra subject Category:Algebraic_logic.
- Łukasiewicz–Moisil_algebra subject Category:Ockham_algebras.
- Łukasiewicz–Moisil_algebra comment "Łukasiewicz–Moisil algebras (LMn algebras) were introduced in the 1940s by Grigore Moisil (initially under the name of Łukasiewicz algebras) in the hope of giving algebraic semantics for the n-valued Łukasiewicz logic. However, in 1956 Alan Rose discovered that for n ≥ 5, the Łukasiewicz–Moisil algebra does not model the Łukasiewicz logic. A faithful model for the ℵ0-valued (infinitely-many-valued) Łukasiewicz–Tarski logic was provided by C. C. Chang's MV-algebra, introduced in 1958.".
- Łukasiewicz–Moisil_algebra label "Łukasiewicz–Moisil algebra".
- Łukasiewicz–Moisil_algebra sameAs Q18385859.
- Łukasiewicz–Moisil_algebra sameAs m.011qdpwk.
- Łukasiewicz–Moisil_algebra sameAs Q18385859.
- Łukasiewicz–Moisil_algebra wasDerivedFrom Łukasiewicz–Moisil_algebra?oldid=678514618.
- Łukasiewicz–Moisil_algebra isPrimaryTopicOf Łukasiewicz–Moisil_algebra.