Southern Summer Logic Day

2024

With the purpose of celebrating the UNESCO World Logic Day, the Australasian Association for Logic will host a Southern Summer Logic Day. The event will take place on Zoom (contact Guillermo Badia at g.badia@uq.edu.au for the Zoom link). There will be two keynote presentations, one by John Lane Bell and Johan van Benthem. The date and time will be Thursday, 11 January 2024 at 23:00:00 (UTC) (notice that in AU/NZ this will be a Friday 12). In addition to the keynotes, there will be three invited talks: Shay Logan (Kansas State University), Ellen Hammatt (Victoria University of Wellington) and Katalin Bimbo (University of Alberta).

Timetable (in AEDT, Friday 12 January):

John Lane Bell (Keynote): 10AM - 11:10AM

Shay Logan: 11:25AM - 12:30PM

Lunch break

Ellen Hammat: 1:30PM - 2:30PM

Katalin Bimbo: 2:45 PM- 3:45PM

Break

Johan van Benthem (Keynote): 4:30 PM - 5:40 PM

ORGANIZERS

Guillermo Badia (University of Queensland, Australia)

Nick J J Smith (University of Sydney, Australia)

Shawn Standefer (National Taiwan University, Taiwan)

Koji Tanaka (Australian National University, Australia)

Zach Weber (University of Otago, New Zealand)

John Lane Bell (University of Western Ontario)

Mathematics and Aesthetics

In this paper I reflect on the nature of mathematical beauty, and examine the connections between mathematics and the arts. I employ Plutarch’s distinction between the intelligible and the sensible, to compare the beauty of mathematics with the beauties of music, poetry and painting. While the beauty of mathematics is almost exclusively intelligible, and the beauties of these arts primarily sensible, it is pointed out that the latter share with mathematics a certain kind of intelligible beauty. The paper also contains reflections on the formal beauty and timelessness of mathematics, beauty as richness flowing from simplicity, form and content in mathematics, and mathematics and fiction. It concludes with some remarks on the question of why mathematical beauty is so little appreciated by non-mathematicians.

Shay Logan (Kansas State University)

The Joy of Nonuniform Substitutions

Logics are traditionally closed under uniform substitutions. Some historically important substructural logics are (rather remarkably) closed under interesting families of nonunifom substitutions. In this talk, I'll set out the state of the art in nonuniform substitution closure. I'll then show how to use nonuniform substitutions to define interesting logics and to prove otherwise-hard-to-prove variable sharing results.

Ellen Hammatt (Victoria University of Wellington)

Structures computable without delay

In this talk we will discuss the area of logic which concerns computability. In particular we will discuss how computability can be applied to various algebraic structures. In the usual fashion we are interested in which structures have `efficient' presentations, but polynomial time presentations are hard to find and understand. Instead we consider a step towards this goal by noticing that if unbounded search cannot be removed from the computable algorithm then there is no polynomial time algorithm. So we will investigate what happens when we remove unbounded search from our algorithms. I will present various results in this area to illustrate the complications that arise when we can no longer use unbounded search.

Katalin Bimbo (University of Alberta)

Searching for proofs - a bit of history

The concept of proofs in an axiomatic calculus does not suggest a strategy as to how to find a proof for a particular formula. Sequent calculuses provide more control over the shape of proofs. In this talk, I will show that sequent calculuses are exciting and understandable. Then, I will recall two markedly different approaches to finding proofs and I will mention some older and newer theorems.

Johan van Benthem (Stanford & Amsterdam)

Logic and Natural Language, Chronicle of an On-Again Off-Again Relationship

Logic may have arisen from reflection on reasoning patterns in natural language. But in the subsequent history linguistic form and logical form have had a complex relationship. Eventually, logicians created their own formal languages as their trademark tool. I will discuss the connection between natural and formal languages as vehicles for reasoning, and what fascinating issues emerge when we pay attention to this creative friction in new ways.

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