A General Result about Sequent Systems and Defining Rules — and its application to modal concepts

In this talk I will explain how it can be that inference rules can be used to define a class of concepts, and why there are at least three grades of logical complexity (propositional connectives, quantifiers, and modals), depending on the kinds of discourse features exploited in those rules. I'll then explain how concepts characterised by “defining rules” (which I’ll characterise) have a number of important features, such as admitting a uniform cut elimination argument.