## A theory of nonmonotonic rule systems I |

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### Contents

Monotonic formal systems | 14 |

Examples and Applications in Logic Logic Programming and Com | 26 |

Representation of Combinatorial and Algebraic Problems as Struc | 34 |

1 other sections not shown

### Common terms and phrases

5-deduction add the following algorithm answer set apply rules Artificial Intelligence atoms axiom belief set Boolean Algebra classical logic classical negation clauses closed sets containing commutative ring computed conclusion Cs(I Cs(R database deductively closed sets default logic define derive disjoint chain cover elements finitely many girls fixpoint form 21 Gelfond and Lifschitz intersection J.B. Remmel knows only finitely logic programming Marek and Truszczynski marriage problem maximal ideal Mbgi minimal deductively closed monotone system monotonic formal system monotonic rules negation as failure Nerode and Remmel nonmonotonic formal system nonmonotonic logic nonmonotonic rule systems nonmonotonic system operator partially ordered set predicate logic prefixpoint premises prime ideal program with classical proper marriage propositional logic Reiter restraints rules of form S C U secured consequences semantics set of rules set of secured stable models subset symmetric marriage Tarski Theorem 5.1 THEORY OF NONMONOTONIC tr(P Truth Maintenance System weak extension