Exception and typicality, logically framed

This paper presents a novel proof-theoretic approach to a logic specifically designed to handle exceptions and typicality. Our method extends the classical first-order sequent calculus by incorporating a specialized framework to manage both negative extra-logical information (explicit exceptions) and positive information (background assumptions). We prove that the resulting sequent calculi satisfy the cut-elimination theorem, thereby ensuring strong analytical properties. Furthermore, we show how this framework effectively models traditional reasoning patterns involving conflicting information and typicality. Finally, we establish a natural correspondence between our approach and the Kraus-Lehmann-Magidor postulates, further grounding our work within established theoretical foundations.