報告題目：Logical Representations for Domains
報告人：李慶國
單位：湖南大學(xué)
報告時間：2024年7月14日(周日)上午08:00-08:45
報告地點：翡翠科教樓A座二樓報告廳
報告摘要：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.
報告人簡介：李慶國，湖南大學(xué)數(shù)學(xué)學(xué)院二級教授，博導(dǎo)，校學(xué)術(shù)委員會委員和學(xué)位委員會委員。1999年7月至2000年6月及2008年11月至2009年11月分別在美國科羅拉多大學(xué)數(shù)學(xué)系和康涅底克大學(xué)數(shù)學(xué)系作訪問教授。2000年12月起擔(dān)任湖南大學(xué)應(yīng)用數(shù)學(xué)專業(yè)博士生導(dǎo)師。現(xiàn)為湖南省數(shù)學(xué)學(xué)會副理事長。入選湖南省121人才第一層次，國務(wù)院政府特殊津貼獲得者，湖南大學(xué)岳麓學(xué)者。曾獲2013年湖南省自然科學(xué)一等獎，排名第一。已完成國家基金面上項目五項?，F(xiàn)正承擔(dān)國家基金重點項目一項。主要研究領(lǐng)域為計算機(jī)程序語言的指稱語義--Domain理論，非Hausdorff拓?fù)?。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》等國際期刊上發(fā)表論文100余篇。
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