报告内容摘要：

Power domain in domain theory plays an important role in modeling the semantics of nondeterministic functional programming languages. Upper power domain is one of the most classic power domains in domain theory. For a continuous domain with the Scott topology, its upper domain is isomorphic to the set of all nonempty compact upper subsets ordered by the set-theoretic reverse inclusion. However, the construction of upper power domain over a general directedly complete poset (dcpo in short) is not clear for a long time. In this talk, we give a concrete construction of the upper power domain over any dcpo. We give an example to show that, even for a quasi-continuous dcpo, its upper power domain is not continuous, and hence is not isomorphic to the set of all nonempty compact upper subsets ordered by the set-theoretic reverse inclusion. Particularly, we introduce a class of special order structures, called strongly quasi-continuous domains, and show that the upper power domain over any strongly quasi-continuous domain is isomorphic to the set of all nonempty compact upper subsets ordered by the set-theoretic reverse inclusion which is a continuous semilattice.

报告人简介：

寇辉，四川大学数学学院副院长、教授、博士生导师，中国系统工程学会模糊数学与模糊系统专业委员会副主任委员。1998年在四川大学数学系获得博士学位，2003年获得四川省科技进步二等奖，2007年入选教育部新世纪优秀人才支持计划。主要从事理论计算机科学与数学的交叉领域——Domain理论及不确定性数学的研究。先后主持多项国家自然科学基金项目，参与科技部“973”项目一项。