Non-commutative Multiple-Valued Logic Algebras

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.

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.

First monograph which treats unitary the non-commutative multiple-valued logic algebras from general to particular; that is, from pseudo-BCK algebras to pseudo-MV algebras Explains the development of the field over the past few decades Presents a fresh view on new trends in logic and algebra Includes supplementary material: sn.pub/extras

Inhalt
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.