: Springer International Publishing :Imprint: Springer,
, 2014.
XIV, 276 s. 8 illus. , online resource..
(Springer Monographs in Mathematics,1439-7382)
9783319015880.
Electronic
Summary: 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 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 algebrasain thataalgebraic structures can be developed into fuzzy logics which connect quantum mechanics, mathematical logic, probability theory, algebra and soft computing. a 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.
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.