BL algebras and quantum structures

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Thomas Vetterlein
Title: BL algebras and quantum structures
Journal: Mathematica Slovaca
Volume 54
Pages: 127-141
Year: 2004


Endowing a lower-bounded partially ordered set with a total addition or with a total difference operation leads to the basic notion of a NAM, that is, a naturally ordered abelian monoid, or a BCK-algebra, respectively.

BL-algebras may be alteratively viewed as certain NAMs or certain BCK-algebras. We characterize the appropriate subclasses by making use of those properties which have been so far considered in an apparently rather different context, namely for certain quantum structures.

The three most important subclasses of BL-algebras, MV-, product, and Gödel algebras, are also taken into account.