Sequent calculi for skeptical reasoning in predicate default logic and other nonmonotonic logics
Sequent calculi for skeptical consequence in predicate default logic, predicate stable model logic programming, and infinite autoepistemic theories are presented and proved sound and complete. While skeptical consequence is decidable in the finite propositional case of all three formalisms, the move to predicate or infinite theories increases the complexity of skeptical reasoning to being Π 1 1 -complete. This implies the need for sequent rules with countably many premises, and such rules are employed.
"Sequent Calculi for Skeptical Reasoning in Predicate Default Logic and Other Nonmonotonic Systems", Annals of Mathematics and Artificial Intelligence 44:1 (2005), 1-34
nnals of Mathematics and Artificial Intelligence