Faculty of Science

January 14, 2020: World Logic Day on the Triolet Campus (in conjunction with the Hiphis seminar)

Published on in News

2ndWorld Logic Day (
) in conjunction with the HiPhiS seminar

Tuesday, January 14,2020, from1:30 p.m.to7:30 p.m.
atthe IAE(University of Montpellier), Robert Reix Lecture Hall
Triolet Campus, Building 29 — free admission

Based on an idea by Jean-Pierre Beziau, the date of World Logic Day (WLD,website) marks, among other things, both the anniversary ofAlfred Tarski’s birth (1901) and that ofKurt Gödel’s death (1978). The second edition of this event is held under the patronage of UNESCO. To mark the occasion, colleagues from the University of Montpellier are organizing a scientific afternoon, combined with the HiPhiS conference in the late afternoon. The presentations are designed to be accessible to as wide an audience as possible, particularly undergraduate students majoring in mathematics and computer science; no one is required to attend all of the presentations.

Program:
(details and summaries athttp://www.lirmm.fr/~retore/WLD/WorldLogicDay.html)

1:30 p.m.–DenisVernant (Professor Emeritus, Université Grenoble-Alpes)
On the Primacy of Incompatibility

2:30 p.m. – 15-minute break

2:45 p.m.–MyriamQuatrini (M.C., Aix-Marseille University / I2M UMR 7373)
A Glance at Proof Theory as a Computational Model

3:45 p.m. – 15-minute break

4:00 p.m.–ZoéMesnil (M.C., Paris-Diderot University / LDAR EA 4434) “
: Some Tools for a Critical Reflection on the Teaching of Logic in Mathematics Classes”

5:00 p.m. – 30-minute break

5:30 p.m.—HiPhiSpar lectureby Denis Vernant (Professor Emeritus, Université Grenoble-Alpes)
On the Nature of Sherlock Holmes’ “Deductions” [see details in the HiPhiS section above]

7:30 p.m. – End

JML Montpellier Contacts:Christian Retoré(LIRMM),Viviane Durand-Guerrier(IMAG),Simon Modeste(IMAG)

Abstracts of JML Presentations

• On the Primacy of Incompatibility
Denis Vernant, Professor Emeritus, University of Grenoble-Alpes

 Our goal is to demonstrate that the incompatibility operator plays a crucial role both in standard logic and in explaining the use of ordinary language. Furthermore, and most importantly, a protology of in/compatibility ensures the structuring of our worlds and, consequently, enables our dialogic mutual understanding.

• A Look at Proof Theory as a Computational Model
, Myriam Quatrini, Associate Professor, Aix-Marseille University / I2M UMR 7373

After a simplified introduction to the theory of proof, which studies formal proofs, we will introduce the elements that allow us to view logic as a computational model. The idea is to view formal proofs as functional programs (the Curry–Howard correspondence), and initially, this applied only to intuitionistic logic. We will see how the emergence of linear logic has allowed us to better understand and extend the correspondence between proofs and programs.

• Some Tools for Critical Reflection on the Teaching of Logic in Mathematics Classes
, Zoé Mesnil, M.C., University of Paris-Diderot / LDAR EA 4434

Objectives related to logical concepts have once again been explicitly included in high school curricula since 2009. This provides an opportunity to reflect on the teaching of logic at this educational level and, more broadly, in mathematics classes from elementary school through college. In the current curricula, there is a strong emphasis on the practical, tool-like nature of logical concepts. In a way, this is consistent with the practice of mathematicians who apply logic in their work, even though not all of them have necessarily studied mathematical logic (at least among those trained in France). However, teachers responsible for introducing their students to this logic of mathematics cannot simply rely on knowing how to apply it in their own practice: for teaching purposes, the question of the content and presentation of this knowledge is crucial—and delicate, since there is no consensus within the mathematical community on a body of work that could serve as a reference. I will therefore propose a study of logical concepts from three perspectives: that of mathematical logic; that of the study of mathematical discourse and the linguistic practices of mathematicians; and that of research in mathematics education. Using a few examples, I will show how these three approaches complement one another not only for a critical analysis of textbooks but also for the design of activities developed, in particular, within IREM groups.