Modal logic, an extension of classical logic, investigates the modes of truth such as necessity and possibility. Its development has been closely intertwined with advances in proof theory, a field ...

We introduce new proof systems for propositional logic, simple deduction Frege systems, general deduction Frege systems, and nested deduction Frege systems, which augment Frege systems with variants ...

We give a general reduction of lengths-of-proofs lower bounds for constant depth Frege systems in DeMorgan language augmented by a connective counting modulo a prime p (the so-called AC0[p] Frege ...