New Trends in Quantum Structures

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This monograph deals with results concerning different types of quantum structures. This is an interdisciplinary realm joining mathematics, logic and fuzzy reasoning with mathematical foundations of quantum mechanics, and covers many applications. The book consists of seven chapters. The first four chapters are devoted to difference posets and effect algebras; MV-algebras and quantum MV-algebras, and their quotients; and to tensor product of difference posets. Chapters five and six discuss BCK-algebras with their applications. Chapter seven addresses Loomis-Sikorski-type theorems for MV-algebras and BCK-algebras. Throughout the text facts and concepts are illustrated by exercises.