Soft Computing

, Volume 21, Issue 10, pp 2521–2529 | Cite as

Quantum B-algebras: their omnipresence in algebraic logic and beyond



Quantum B-algebras are implicational subreducts of quantales. Their ubiquity and unifying rôle in algebraic logic and beyond is discussed in a brief survey, with old and new examples included. A special section is devoted to CKL-algebras (alias HBCK-algebras). Using a natural embedding of any CKL-algebra into a semibrace, Cornish’s identity is derived, which yields a new syntactic proof of Wroński’s conjecture that CKL-algebras form a variety.


Quantum B-algebra CKL-algebra Semibrace Residuated poset Partially ordered group 


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The authors confirm that there is no conflict of interest.


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© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Institute for Algebra and Number TheoryUniversity of StuttgartStuttgartGermany

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