## Abstract

The paper studies the automation of minimal model inference, i.e., determining whether a formula is true in every minimal model of the premises. A novel tableau calculus for propositional minimal model reasoning is presented in two steps. First an analytic clausal tableau calculus employing a restricted cut rule is introduced. Then the calculus is extended to handle minimal model inference by employing a groundedness property of minimal models. A decision procedure based on the basic calculus is devised and then it is extended to minimal model inference. The basic decision procedure and its extension enjoy some interesting properties. When deciding logical consequence, the basic procedure explores the search space of counter-models with a preference to minimal models and each counter-model is not generated more than once. The procedures can be implemented to run in polynomial space, and they provide polynomial time decision procedures for Horn clauses. The extended decision procedure can also be used to finding all minimal models of a set of clauses.

Original language | English |
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Title of host publication | Theorem Proving with Analytic Tableaux and Related Methods - 5th International Workshop, TABLEAUX 1996, Proceedings |

Subtitle of host publication | Terrasini, Palermo, Italy, May 15–17, 1996 |

Editors | P Miglioli, U Moscato, D Mundici, M Ornaghi |

Publisher | SPRINGER |

Pages | 278-294 |

Number of pages | 17 |

ISBN (Electronic) | 978-3-540-68368-1 |

ISBN (Print) | 3-540-61208-4, 978-3-540-61208-7 |

DOIs | |

Publication status | Published - 1996 |

MoE publication type | A4 Article in a conference publication |

Event | International Workshop on Theorem Proving with Analytic Tableaux and Related Methods - Palermo, Italy Duration: 15 May 1996 → 17 May 1996 Conference number: 5 |

### Publication series

Name | Lecture Notes in Artificial Intelligence |
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Publisher | SPRINGER-VERLAG BERLIN |

Volume | 1071 |

ISSN (Print) | 0302-9743 |

### Workshop

Workshop | International Workshop on Theorem Proving with Analytic Tableaux and Related Methods |
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Abbreviated title | TABLEAUX |

Country/Territory | Italy |

City | Palermo |

Period | 15/05/1996 → 17/05/1996 |

## Keywords

- CIRCUMSCRIPTION
- DATABASES