January 14, 2020: World Logic Day on the Triolet campus (associated with the Hiphis seminar)

- On the primacy of incompatibility
Denis Vernant, Professor Emeritus Unversité Grenoble-Alpes

 Our aim is to establish that the incompatibility operator plays a crucial role both in standard logic and in explaining the use of ordinary discourse. Moreover, and above all, a protology of in/compatibility ensures the structuring of our worlds and, consequently, enables our dialogical inter-understanding.

- A look at demonstration theory as a model for calculation
Myriam Quatrini, M.C. Aix-Marseille Unversité / I2M UMR 7373

After a simplified presentation of the theory of demonstration that studies formal proofs, we'll introduce the elements that allow us to consider logic as a computational model. The idea is to see formal proofs as functional programs (Curry Howard correspondence), and initially this only concerned intuitionistic logic. We'll see how the emergence of linear logic has enabled us to better understand and extend the correspondence between proofs and programs.

- Some tools for critical reflection on the teaching of logic in the mathematics classroom
ZoéMesnil, M.C. Unversité Paris-Diderot / LDAR EA 4434

Since 2009, objectives relating to logic concepts have once again been explicitly included in high school curricula. This is an opportunity to reflect on the teaching of logic at this level of education, and more broadly in the mathematics classroom from elementary school to university. In current programs, the tool dimension of logic notions is strongly emphasized. In a way, this is consistent with the practice of mathematicians who use logic in their work, but without necessarily having studied mathematical logic (at least in the case of those trained in France). But the teacher who is responsible for introducing his or her pupils or students to the logic of mathematics cannot be content with knowing how to apply it in his or her own practice: for teaching, the question of the content and form of this knowledge is crucial. And it's a tricky one, too, since the mathematical community has no consensus corpus that could serve as a reference. I will therefore propose a study of the notions of logic from three points of view: mathematical logic, the study of mathematical discourse and the language practices of mathematicians, and didactic research. I'll use a few examples to show how these three approaches complement each other in the critical analysis of textbooks, as well as in the design of activities developed by IREM groups.