In this paper, we first formulate phase semantics for proof-terms of second-order intuitionistic propositional logic by modifying TaitGirard's saturated sets method. Next, we prove the completeness ...

Propositional proof complexity is the study of the sizes of propositional proofs, and more generally, the resources necessary to certify propositional tautologies. Questions about proof sizes have ...

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 ...