Non-commutative multiple-valued logic algebras

✍ Scribed by Lavinia Corina Ciungu (auth.)

• Publisher: Springer International Publishing
• Year: 2014
• Tongue: English
• Leaves: 284
• Series: Springer monographs in mathematics
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages I-XIV
Pseudo-BCK Algebras....Pages 1-53
Pseudo-hoops....Pages 55-77
Residuated Lattices....Pages 79-106
Other Non-commutative Multiple-Valued Logic Algebras....Pages 107-134
Classes of Non-commutative Residuated Structures....Pages 135-153
States on Multiple-Valued Logic Algebras....Pages 155-190
Measures on Pseudo-BCK Algebras....Pages 191-207
Generalized States on Residuated Structures....Pages 209-241
Pseudo-hoops with Internal States....Pages 243-262
Back Matter....Pages 263-276

✦ Subjects

Mathematical Logic and Foundations; Order, Lattices, Ordered Algebraic Structures; Probability Theory and Stochastic Processes; Measure and Integration