Title of the Report:Logical Representations for Domains

Presenter: Li Qingguo

Affiliation:Hunan University

Date of the Report: July 14, 2024 (Sunday), 8:00-8:45 AM

Location of the Report:Lecture Hall on the Second Floor, Block A, Feicui Science and Education Building

Abstract:This talk investigates the research summarization of logical representations for domains. It is divided into four parts. The first part is an introduction to domain theory, which includes 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’s 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.

    Biography of the Presenter:Li Qingguo, a Level 2 professor at the School of Mathematics, Hunan University, PhD supervisor, member of the university academic committee and degree committee. He was a visiting professor at the Department of Mathematics, University of Colorado, USA, from July 1999 to June 2000, and at the Department of Mathematics, University of Connecticut, USA, from November 2008 to November 2009. Since December 2000, he has been guiding PhD students in Applied Mathematics at Hunan University. Currently, he serves as the vice-chairman of the Hunan Provincial Mathematical Society. He was selected for the first level of Hunan Province's "121 Talent" program, received a special government allowance from the State Council, and is recognized as a Yue Lu Scholar at Hunan University. He won the First Prize in Natural Sciences of Hunan Province in 2013, ranking first. He has completed five general projects funded by the National Natural Science Foundation of China. Currently, he is undertaking a key project funded by the National Natural Science Foundation of China. His main research areas include denotational semantics of computer programming languages -- Domain Theory and Non-Hausdorff Topology. He has published over 100 papers in international journals such as "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", and "Fuzzy Sets and Systems".