### Abstract

We introduce model-theoretic semantics [6] for Higher-Order Horn logic programming language. One advantage of logic programs over conventional non-logic programs has been that the least fixpoint is equal to the least model, therefore it is associated to logical consequence and has a meaningful declarative interpretation. In simple theory of types [9] on which Higher-Order Horn logic programming language is based, domain is dependent on interpretation [10]. To define TP operator for a logic program P, we need a fixed domain without regard to interpretation which is usually taken to be a set of atomic propositions. We build a semantics where we can fix a domain while changing interpretations. We also develop a fixpoint semantics based on our model, and show that we can get the least fixpoint which is the least model. Using this fixpoint we prove the completeness of the interpreter of our language in [14].

Original language | English (US) |
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Title of host publication | Logic Programming and Automated Reasoning - International Conference LPAR 1992, Proceedings |

Editors | Andrei Voronkov |

Publisher | Springer Verlag |

Pages | 320-331 |

Number of pages | 12 |

ISBN (Print) | 9783540557272 |

DOIs | |

State | Published - 1992 |

Event | International Conference on Logic Programming and Automated Reasoning, LPAR 1992 - St. Petersburg, Russian Federation Duration: Jul 15 1992 → Jul 20 1992 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 624 LNAI |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | International Conference on Logic Programming and Automated Reasoning, LPAR 1992 |
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Country | Russian Federation |

City | St. Petersburg |

Period | 7/15/92 → 7/20/92 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Logic Programming and Automated Reasoning - International Conference LPAR 1992, Proceedings*(pp. 320-331). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 624 LNAI). Springer Verlag. https://doi.org/10.1007/BFb0013072