A generalization of the Chen-Wu duality into quantale-valued setting

Document Type: Research Paper


1 Department of Physics, Hebei University of Science and Technology, Shijiazhuang 050018, P.R. China

2 Department of Physics, Hebei University of Science and Technol- ogy, Shijiazhuang 050018, P.R. China

3 Department of Physics, Hebei University of Science and Technology, Shi- jiazhuang 050018, P.R. China

4 Department of Physics, Hebei University of Science and Tech- nology, Shijiazhuang 050018, P.R. China


With the unit interval [0,1] as the truth value table, Chen and Wu
presented the concept of  possibility computation over dcpos.
Indeed, every possibility computation can be considered as a
[0,1]-valued Scott open set on a dcpo. The aim of this paper is to
study Chen-Wu's duality on quantale-valued setting. For clarity,
with a commutative unital quantale $L$ as the truth value table, we
introduce a concept of fuzzy possibility computations over fuzzy
dcpos and then establish an equivalence between their denotational
semantics and their logical semantics.


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