This biannual learning unit is being organized in 2026-2027
Teacher(s)
Language
French
> English-friendly
> English-friendly
Content
This activity aims to explore the mathematical formalization of logic in terms of inference rules (sequents), lattices (and, in particular, Heyting and Boolean algebras), models (topological and Kripke) and quantifier systems (for predicative logic). The following contents are covered in the course:
- Propositional logic, Gentze sequents, Lindenbaum-Tarski algebra.
- Lattices, Heyting algebras and Boolean algebras.
- Models of propositional logic and the theorems of validity, consistency and completeness.
- Dedekind and Stone representation theorems,
- Ideals and filters of an ordered set, the extension-exclusion lemma and the axiom of choice.
- Quantifier systems and predicative logic.
- Propositional logic, Gentze sequents, Lindenbaum-Tarski algebra.
- Lattices, Heyting algebras and Boolean algebras.
- Models of propositional logic and the theorems of validity, consistency and completeness.
- Dedekind and Stone representation theorems,
- Ideals and filters of an ordered set, the extension-exclusion lemma and the axiom of choice.
- Quantifier systems and predicative logic.
Teaching methods
Supervised learning activities consist of lecture sessions. Group discussion and the resolution of exercises by students are integrated into the lecture. The course aims to introduce fundamental concepts, to motivate them by showing examples and establishing results, to show the links with other courses in the Bachelor's program in Mathematical Sciences. The resolution of exercises aims to learn the basic techniques of sequent calculus, lattice theory and adjunctions between ordered sets.
Evaluation methods
The assessment aims to test students' knowledge and understanding of fundamental concepts, examples, and results, their ability to construct a coherent argument, and their mastery of the proof techniques introduced during the course. The assessment consists of a final exam.
On the day of the exam, each student presents a topic of their choice to the entire class for 20 minutes and answers questions about their presentation or other aspects of the course material (questions that anyone can ask) for 10 minutes.
Following the presentation, the instructor assigns a grade out of 15 points, while the other students who attended the presentation propose a grade out of 5 points. To determine the final grade, the instructor will also take into account active participation in the course (uo to +2 points) : questions asked, solutions to exercises presented in class. In any case, the instructor remains solely responsible for the final grade assigned to each student who took the exam.
Students remain responsible for the content of their work (both oral and written), regardless of the sources used (particularly AI).
On the day of the exam, each student presents a topic of their choice to the entire class for 20 minutes and answers questions about their presentation or other aspects of the course material (questions that anyone can ask) for 10 minutes.
Following the presentation, the instructor assigns a grade out of 15 points, while the other students who attended the presentation propose a grade out of 5 points. To determine the final grade, the instructor will also take into account active participation in the course (uo to +2 points) : questions asked, solutions to exercises presented in class. In any case, the instructor remains solely responsible for the final grade assigned to each student who took the exam.
Students remain responsible for the content of their work (both oral and written), regardless of the sources used (particularly AI).
Other information
The course is biennial and will be activated in 2026-2027.
Any use of artificial intelligence within the framework of this course must comply with the guidelines established by the Faculty of Science.
Any use of artificial intelligence within the framework of this course must comply with the guidelines established by the Faculty of Science.
Online resources
Moodle site. The site contains the course syllabus, including many exercises that are integrated into each chapter.
Bibliography
F. W. Lawvere, R. Rosebrugh, Sets for Mathematics, Cambridge University Press, 2003
S. Mac Lane, I. Moerdijk, Sheaves in Geometry and Logic, Springer 1992
S. Mac Lane, I. Moerdijk, Sheaves in Geometry and Logic, Springer 1992
Teaching materials
- Syllabus LMAT1235
Faculty or entity
