Zhiguang Zhao

Zhiguang Zhao
Taishan University · School of Mathematics and Statistics

Doctor of Philosophy
Exploring relational, topological and algebraic aspects of correspondence theory

About

23
Publications
1,142
Reads
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215
Citations
Additional affiliations
April 2019 - present
Taishan University
Position
  • Researcher
Description
  • teaching in math and research on logic
January 2014 - February 2018
Delft University of Technology
Position
  • PhD Student
September 2011 - August 2013
Institute for Logic, Language & Computation
Position
  • Master's Student
Education
January 2014 - February 2018
September 2011 - August 2013
Institute for Logic, Language & Computation
Field of study
  • Logic and Mathematics
September 2008 - July 2011
Peking University
Field of study
  • Mathematics and Applied Mathematics

Questions

Question (1)
Question
For Boolean algebras with operators, we know that if a variety/universal class of BAOs is closed under taking MacNeille completions, then it is also closed under taking canonical extensions. Universal classes correspond to algebra classes defined by formulas universally quantified, so they are in the Pi_1 hierarchy. If we consider Pi_2 statements (i.e. statements of the form forall......exists......) and their corresponding inductive classes (closed under taking union of chains or directed limits), would the situation be the same or different?

Network

Cited By

Projects

Projects (4)
Project
This part of research concerns correspondence theory which is more convenient to do with relational semantics, as a supplement of the unified correspondence project which is more on the algebraic side.
Project
This is a line of research started in 2009 and aimed at understanding the phenomenon of Sahlqvist correspondence and canonicity from an algebraic viewpoint. Thanks to Stone-type dualities, we have been able to reformulate the Sahlqvist mechanism in terms of the order-theoretic properties of the algebraic interpretation of the logical connectives. In its turn, this order-theoretic reformulation has made it possible to extend the state-of-the-art in Sahlqvist theory from classical normal modal logic to classes of logics algebraically captured by normal and regular (distributive) lattice expansions, mu calculi, hybrid logics, and many valued logics.