We study the direct product decomposition of quantum many-valued algebras (QMV algebras) which generalizes the decomposition theorem of ortholattices (orthomodular lattices).In detail,for an idempo- tent element of a given QMV algebra,if it commutes with every element of the QMV algebra,it can induce a direct product decomposition of the QMV algebra.At the same time,we introduce the commutant C(S) of a set S in a QMV algebra,and prove that when S consists of idempotent elements,C(S) is a subalgebra of the QMV algebra.This also generalizes the cases of orthomodular lattices.
LU Xian 1 ,SHANG Yun 1,& LU RuQian 1,2 1 Institute of Mathematics,Academy of Mathematics and Systems Science,Beijing 100190,China
The first part of this paper reviews our efforts on knowledge-based software engi- neering, namely PROMIS, started from 1990s. The key point of PROMIS is to gen- erate applications automatically based on domain knowledge as well as software knowledge. That is featured by separating the development of domain knowledge from the development of software. But in PROMIS, we did not find an appropriate representation for the domain knowledge. Fortunately, in our recent work, we found such a carrier for knowledge modules, i.e. knowware. Knowware is a commercial- ized form of domain knowledge. This paper briefly introduces the basic definitions of knowware, knowledge middleware and knowware engineering. Three life circle models of knowware engineering and the design of corresponding knowware im- plementations are given. Finally we discuss application system automatic genera- tion and domain knowledge modeling on the J2EE platform, which combines the techniques of PROMIS, knowware and J2EE, and the development and deployment framework, i.e. PROMIS/KW**.
