Section: New Results

Focused proofs for modal logics

Participants : Tomer Libal, Sonia Marin, Dale Miller, Marco Volpe.

Several deductive formalisms (e.g., sequent, nested sequent, labeled sequent, hypersequent calculi) have been used in the literature for the treatment of modal logics, and some connections between these formalisms are already known. Marin, Miller, and Volpe [30] have propose a general framework, which is based on a focused version of the labeled sequent calculus by Negri [78], augmented with some parametric devices allowing to restrict the set of proofs. By properly defining such restrictions and by choosing an appropriate polarization of formulas, one can obtain different, concrete proof systems for the modal logic K and for its extensions by means of geometric axioms. The expressiveness of the labeled approach and the control mechanisms of focusing allow a clean emulation of a range of existing formalisms and proof systems for modal logic. These results make it possible to write Foundational Proof Certificate definitions of common modal logic proof systems.