Proof theory for classical modal logics: systems of rules
(David Gilbert, UNICAMP, BR)

In this talk I will discuss proof theory for classical modal logics. In particular, the goal will be to establish a modular sequent-based approach to a family of logics weaker than K, and for which neighborhood semantics are often used. Utilizing a polymodal translation of the standard language of modal logic, we establish a base system for the minimal classical modal logic E, from which we generate extensions in a modular manner. These extensions make use of "systems of rules", rather than the usual types of rules one finds in a sequent system. My talk reflects the work of an ongoing collaboration with Paolo Maffezioli (University of Torino, Italy).