Non-commutative Multiple-Valued Logic Algebras [Paperback]

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.
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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.
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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.

This monograph provides a self-contained introduction to non-commutative multiple-valued logic algebras. It includes treatment of pseudo-BCK algebras, pseudo-hoops, residuated lattices, bounded divisible residuated lattices, and pseudo-MV algebras.Pseudo-BCK algebras.- Pseudo-hoops.- Residuated lattices.- Other non-commutative multiple-valued logic algebras.- Classes of non-commutative residuated structures.- States on multiple-valued logic algebras.- Measures on pseudo-BCK algebras.- Generalized states on residuated structures.- Pseudo-hoops with internal states.

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 noncommutativel#[