报告题目：Logical Representations for Domains

报告人：李庆国

单位：湖南大学

报告时间：2024年7月14日(周日)上午08:00-08:45

报告地点：翡翠科教楼A座二楼报告厅

报告摘要：This talk investigates the research summarization of logical representations for domains. It is divided into four parts.The first part is an introduction of domain theory, which incorporates the background of domain theory, the fundamental definitions of domain structures, and the role of logic in domain theory.In the second part, the history of the representations of domains in terms of information systems is reviewed. It originated with Scott’s information systems for algebraic bounded complete domains, subsequently developed to Hofmann information systems for continuous bounded complete domains, Spreen and Xu’s information systems for continuous domains, and more information systems for other domains. These results can be seen as syntactic representations for domains.The third part focuses on semantic representations of domains based on complete logical systems, ranging from Abramsky’s domain logics for algebraic bounded complete domains and SFP-domains, over Chen and Jung's domain logic for algebraic L-domains, to our domain logics for Lawson compact algebraic L-domains, continuous L-domains and continuous bounded complete domains.Some topics for further study are given in the fourth part.

报告人简介：李庆国，湖南大学数学学院二级教授，博导，校学术委员会委员和学位委员会委员。1999年7月至2000年6月及2008年11月至2009年11月分别在美国科罗拉多大学数学系和康涅底克大学数学系作访问教授。2000年12月起担任湖南大学应用数学专业博士生导师。现为湖南省数学学会副理事长。入选湖南省121人才第一层次，国务院政府特殊津贴获得者，湖南大学岳麓学者。曾获2013年湖南省自然科学一等奖，排名第一。已完成国家基金面上项目五项。现正承担国家基金重点项目一项。主要研究领域为计算机程序语言的指称语义--Domain理论，非Hausdorff拓扑。已在《Applied Categorical Structures》、《Information and Computation》、《Annals of Pure and Applied Logic》、《Semigroup Forum》、《Theoretical Computer Science》、《Topology and its Applications》、《Journal of Pure and Applied Algebra》、《Algebra Universalis》、《Fuzzy Sets and System》等国际期刊上发表论文100余篇。