## A theory of nonmonotonic rule systems II |

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### Contents

Semantical issues and descriptive characterization of various sets | 30 |

Computing extensions weak extensions and minimal deductively | 42 |

Conclusions | 51 |

### Common terms and phrases

algorithm axiom branch canonical index Cantor space Cantor topology Cl(a closed under rules collection Corollary deductively closed sets default extension default logic default rules default theory define degree preserving correspondence derive Mbg effective one-to-one degree elements finitary finite set finitely many minimal follows Herbrand Herbrand base highly recursive nonmonotonic highly recursive society highly recursive tree induction infinitary infinite descent infinite paths Jockusch and Soare knows only finitely least fixpoint lfp(T locally finite logic programs Marek Mbig Mbkg Mbkgj minimal deductively closed minimal derivations minimal proof schemes monotonic rules natural numbers nonmonotonic rule system one-to-one degree preserving partially ordered set produces a canonical proper marriage Proposition 3.10 quasi-finite recursive binary tree recursive nonmonotonic rule recursive set recursive tree T C recursively bounded Ili-classes recursively enumerable Remmel schemes for Mb0g set of infinite stable models symmetrically highly recursive tableau terminal node Theorem 2.7 Turing degree weak extensions