Quantum MV algebras
type: Item
instance of: scholarly article
title: Quantum MV algebras
zbMATH Open document ID: 0854.03057
DOI: 10.1007/BF00372773
author: Roberto Giuntini
published in: Studia Logica
publication date: 1997-01-07T00:00:00Z
review text: The infinite-valued logic \(L_\infty\) (Lukasiewicz logic) was introduced as a generalization of classical logic. \textit{C. C. Chang} [Trans. Am. Math. Soc. 88, 467-490 (1958; Zbl 0084.00704)] introduced MV algebras in order to provide an algebraic proof of its completeness theorem. Just as MV algebras stand for nonidempotent extensions of Boolean algebras, quantum MV algebras, proposed in this paper, stand for nonidempotent extensions of orthomodular lattices. While every MV algebra is representable as a subdirect product of totally ordered MV algebras, the author shows that there exist quantum MV algebras that can not be represented as subdirect products of quasilinear quantum MV algebras. The paper ends with some open problems.
reviewed by: Hirokazu Nishimura
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 06D30
zbMATH DE Number: 910392
zbMATH Keywords: quantum MV algebras
zbMATH Keywords: nonidempotent extensions of orthomodular lattices
zbMATH Keywords: subdirect products
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 910392