Sequents vs Hypersequents for Åqvist Systems

Abstract

AbstractEnhancing cut-free expressiveness through minimal structural additions to sequent calculus is a natural step. We focus on Åqvist’s system $$\textbf{F}$$ F with cautious monotonicity (CM), a deontic logic extension of $$\textbf{S5}$$ S 5 , for which we define a sequent calculus employing (semi) analytic cuts.The transition to hypersequents is key to develop modular and cut-free calculi for $$\mathbf{F + (CM)}$$ F + ( CM ) and $$\textbf{G}$$ G , also supporting countermodel construction.