Soundness for More General Sequents

Establish whether the infinitary and cyclic sequent calculi for first-order logic with non-monotone inductive definitions can be refined to be sound for sequents whose antecedent and succedent are sets of formulas, rather than sequents containing only a single inductive definition.

Background

The paper’s calculi are developed for a restricted sequent format with a single inductive definition. Earlier work introduced a more general notion in which the antecedent and succedent consist of sets of formulas. The authors explicitly leave unresolved whether sound infinitary and cyclic calculi can be obtained for that broader syntax.