It is our great honor and pleasure to announce that Professor Robert Goldblatt, who is famous for his seminal contribution to modal logic and non-classical logic, will deliver three lectures and to receive a special public interview from Sep. 9th to 17th. A longer introduction to Professor Goldblatt is at the end of this announcement. Note that the locations and times vary.
TALK 1
Title Admissible Semantics for Modal Logics
Time Sep. 9th (Tuesday), 15:10 - 17:10
Location Room 211, Natural Sciences Teaching Building (理教)
Abstract In the possible-worlds semantics for modal logic, a proposition is identified with a set of worlds, and the term "admissible semantics" refers to the use of models in which there is a restriction on which sets of worlds can count as propositions. There are axiomatically defined systems of quantified modal logic that cannot be characterised by the kind of models introduced for them by Kripke, even though the propositional fragments of those logics are characterised by their Kripke frames, which are frames in which every set of worlds is admissible as a proposition. We will explain how that this failure of completeness under Kripke semantics to lift from the propositional to the quantificational level can be overcome by developing a suitable notion of admissible model for modal logics with quantification, leading to semantic characterisations of such logics in general. This requires a different interpretation of quantifiers that takes into account the admissibility of propositions.
TALK 2
Title Quantified Temporal Logic for Real Time
Time Sep. 12th (Friday), 15:10 - 17:10
Location Room 109, Lee Shau Kee Humanities Buildings No.3 (李兆基人文学苑3号楼)
Abstract Propositional temporal logic over the real time flow is finitely axiomatisable, but predicate temporal logic over real time is not recursively axiomatisable. What then of the axiom system that combines the standard deductive machinery of first-order logic with that of the propositional temporal logic of real time? We will show how the notion of admissible model leads to a strongly complete semantics over real time for this system.
TALK 3
Title Morphisms and Duality for Polarities
Time Sep. 16th (Tuesday), 15:10 - 17:10
Location Room 211, Natural Sciences Teaching Building (理教)
Abstract We review the theory of bounded morphisms and other validity-preserving constructions on Kripke frames, and their role in defining a duality with the class of modal algebras that provide algebraic semantics for modal logics. We then introduce a notion of morphism between structures based on polarities that provide relational semantics for some non-distributive propositional logics, including orthologic, and show how this gives rise to a duality with certain lattice-based algebras.
Public Interview
Time Sep. 17th (Wednesday), 15:10 - 17:10
Location Room 109, Lee Shau Kee Humanities Buildings No.3 (李兆基人文学苑3号楼)
Abstract In this public interview, Professor Goldblatt will share with us his experience in research, including finding topics, learning about new fields, publishing, etc.
On Professor Robert Goldblatt
Professor Robert Goldblatt is a renowned logician, known for his research in modal logic, algebraic logic, categorical logic, and the foundations of mathematics, whose work and publications have had a profound impact on the development of logic.
He is currently an Emeritus Professor in the School of Mathematics and Statistics at Victoria University of Wellington. He graduated from Victoria University of Wellington in 1974 under the supervision of the renowned logician M.J. Cresswell, and was promoted to professor in 1981 and retired in 2018.
Professor Goldblatt has published more than 90 papers in prominent journals. He has also authored multiple highly acclaimed books: Topoi : The Categorial Analysis of Logic (1979), Axiomatising The Logic of Computer Programming (1982), Logics of Time and Computation (1987), Orthogonality and Spacetime Geometry (1987), Mathematics of Modality (1993), Lectures on the Hyperreals: An Introduction to Nonstandard Analysis (1998), Quantifiers, Propositions and Identity: Admissible Semantics for Quantified Modal and Substructural Logics (2011).
Professor Goldblatt is a Fellow of the Royal Society of New Zealand and served as the President of the New Zealand Mathematical Society. He also served as the Coordinating Editor for The Journal of Symbolic Logic, Managing Editor for Studia Logica, and as an editor for several other prominent journals, including the Notre Dame Journal of Formal Logic, Journal of Applied Logic, New Zealand Journal of Mathematics, and Journal of Automated Reasoning, making significant contributions to academic exchange and development in the field of logic.