■Date and Time: 2024.01.23.(Tue) 16:00~18:00 (Including a QnA session), 2024.01.25.(Thu) 16:00~18:00 (Including a QnA session)

■Place: ZOOM(Meeting ID: 976 2795 1662 / Passcode: 489146), 

■Presenter: Prof. George Metcalfe (Director, Mathematical Institute, University of Bern)

■Presentation Information:

2024.01.23.(Tue) 16:00~18:00 (Including a QnA session)

Title: Ordered Algebras and Logic

Abstract: Ordered algebras such as Boolean algebras, Heyting algebras, lattice-ordered groups, and MV-algebras have long played a crucial role in logic, although perhaps only in recent years has the significance of the relationship between the two fields been fully recognized and exploited. In the first part of this talk, I will briefly trace the distinct historical roots of ordered algebras and logic, culminating with the theory of algebraizable logics, that demonstrates the complementary nature of the two fields. In the second part, I will explain and illustrate the usefulness of this theory for both logic and algebra in the setting of substructural logics and residuated lattices

Title: Bridges between Algebra and Logic

Abstract: Bridges between algebra and logic allow the methods and results of one field to be imported to the other and have been used with great success to establish logical properties such as decidability, interpolation, and admissibility of rules, as well as algebraic properties such as amalgamation, coherence, and generation by subclasses. In the first part of this talk, I will explain how to build these bridges using a correspondence between equational consequence in a class of algebras and congruences on the free algebras of the class. In the second part, I will describe bridges relating interpolation and amalgamation properties, and their applications in the setting of substructural logics and residuated lattices.

■Website: https://imdarc.snu.ac.kr/

■Inquiries: winsomevely@snu.ac.kr/02-880-6272