Nonmonotonic rule systems with recursive sets of restraints

We study nonmonotonic rule systems with rules that admit infinitely many restraints. We concentrate on the case when the constraints of rules form a recursive set and there is a uniform enumeration of codes for rules. We show that the theory developed for nonmonotonic rule systems admitting the rules with finite number of restraints can be lifted to such rule systems. We give tight estimates on the complexity of the set of extensions of such rule systems.