© 2014

Non-commutative Multiple-Valued Logic Algebras


Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Lavinia Corina Ciungu
    Pages 1-53
  3. Lavinia Corina Ciungu
    Pages 55-77
  4. Lavinia Corina Ciungu
    Pages 79-106
  5. Lavinia Corina Ciungu
    Pages 107-134
  6. Lavinia Corina Ciungu
    Pages 135-153
  7. Lavinia Corina Ciungu
    Pages 155-190
  8. Lavinia Corina Ciungu
    Pages 191-207
  9. Lavinia Corina Ciungu
    Pages 209-241
  10. Lavinia Corina Ciungu
    Pages 243-262
  11. Back Matter
    Pages 263-276

About this book


This monograph provides a self-contained and easy-to-read introduction to non-commutative multiple-valued logic algebras; a subject which has attracted much interest in the past few years because of its impact on information science, artificial intelligence and other subjects.
A study of the newest results in the field, the monograph includes treatment of pseudo-BCK algebras, pseudo-hoops, residuated lattices, bounded divisible residuated lattices, pseudo-MTL algebras, pseudo-BL algebras and pseudo-MV algebras. It provides a fresh perspective on new trends in logic and algebras in that algebraic structures can be developed into fuzzy logics which connect quantum mechanics, mathematical logic, probability theory, algebra and soft computing.
Written in a clear, concise and direct manner, Non-Commutative Multiple-Valued Logic Algebras will be of interest to masters and PhD students, as well as researchers in mathematical logic and theoretical computer science.


BCI-Algebras BCK-Algebras Congruence Relations Fuzzy Logic Fuzzy Measure Theory Lattices and Duality Lattices and Related Structures MV-Algebras Many-Valued Logic Ordered Abelian Groups Quantum Logic Subalgebras Subdirect Irreducibility Subdirect Products

Authors and affiliations

  1. 1.University of Iowa Department of MathematicsIowa CityUSA

Bibliographic information


From the reviews:

“Over the last 25 years, many-valued logics and their algebras have been increasingly attracting the attention of various researchers worldwide … . The monograph under review provides a virtually self-contained introduction to all these algebras. … This book is a valuable addition to the literature on noncommutative algebraic logic: it will be of interest to researchers in mathematical logic and theoretical computer science.” (Daniele Mundici, zbMATH, Vol. 1279, 2014)