Towards Universal Logic: Groups and Patterns in Logics
A wide variety of non-classical logics have been introduced over the past decades, such as intuitionistic logics, linear logics and Lambek calculi, to name just a few. Even if these non-classical logics all share the same terminology and issues, one can argue that they are still disorganized and scattered and somehow miss a common formal ground. This problematic situation has led to the development of a research area in logic called "universal logic''.
In this series of seminars, I will present a general framework aiming at capturing and studying logics in a uniform and systematic way. This generic approach will allow us to (re)define notions which are applicable to all logics. In doing so, we will rediscover and generalize well-known results of model theory for first-order logic. We will also establish connections between logics and groups by means of a specific group action. This will lead us to discuss how group theory could contribute to the study of non-classical logics. No prerequisite will be needed and the talks will be self-contained.