Proof Theory for Quantified Monotone Modal Logics

Explore a comprehensive lecture on proof theory for quantified monotone modal logics presented by Eugenio Orlandelli at the Hausdorff Center for Mathematics. Delve into the first proof-theoretic study of quantified non-normal modal logics, examining labelled sequent calculi for first-order extensions with both free and classical quantification. Investigate the role of Barcan Formulas and discover the structural properties of these calculi, including rule invertibility, height-preserving admissibility of weakening and contraction, and syntactic cut elimination. Learn about the soundness and completeness of the introduced calculi with respect to appropriate classes of neighbourhood frames. Gain insights into the completeness proof, which constructs formal proofs for derivable sequents and countermodels for underivable ones, while providing a semantic proof of cut admissibility. Conclude with a discussion on preliminary results extending this approach to the non-monotonic case, all within the context of the Hausdorff Trimester Program: Types, Sets and Constructions.