Q-Filters of Quantum B-Algebras and Basic Implication Algebras

Download or read book Q-Filters of Quantum B-Algebras and Basic Implication Algebras written by Xiaohong Zhang and published by Infinite Study. This book was released on with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of quantum B-algebra was introduced by Rump and Yang, that is, unified algebraic semantics for various noncommutative fuzzy logics, quantum logics, and implication logics. In this paper, a new notion of q-filter in quantum B-algebra is proposed, and quotient structures are constructed by q-filters (in contrast, although the notion of filter in quantum B-algebra has been defined before this paper, but corresponding quotient structures cannot be constructed according to the usual methods). Moreover, a new, more general, implication algebra is proposed, which is called basic implication algebra and can be regarded as a unified frame of general fuzzy logics, including nonassociative fuzzy logics (in contrast, quantum B-algebra is not applied to nonassociative fuzzy logics). The filter theory of basic implication algebras is also established.