Infinitary logic with infinite sequents: syntactic investigations

Abstract

The present paper deals with a purely syntactic analysis of infinitary logic with infinite sequents. In particular, we discuss sequent calculi for classical and intuitionistic infinitary logic with good structural properties based on sequents possibly containing infinitely many formulas. A cut admissibility proof is proposed which employs a new strategy and a new inductive parameter. We conclude the paper by discussing related issues and possible themes for future research.